SAT Class Exam 2 Solutions

Copyright 2005 © Test Masters Educational Services, Inc. Solutions: SAT Exam #2

1

Section 2 1. (A) Plug in the values for t and n and then solve for k.

k

k

k

nkt

k

=

=

=

××=

=

5

630

9)(30

66

630

32

32

(A) is correct.

Alternate Explanation: Choice (A) is correct. Substituting the given values for n and

t into the equation 23

t nk= results in the equation ( )230 9 ,3

k=

which simplifies to 30 6 ,k= or 5k = . Choice (B) is not correct.

If 30, 9t n= = , and 6k = the equation reads ( )230 9 6 ,3

= ⋅ or

30 36,= which is a false statement. Choice (C) is not correct. If

30, 9,t n= = and 10,k = the equation reads ( )230 9 10 ,3

= ⋅ or

30 60,= which is a false statement. Choice (D) is not correct. If

30, 9,t n= = and 20,k = the equation reads ( )230 9 20 ,3

= ⋅

or 30 120,= which is a false statement. Choice (E) is not correct.

If 30, 9,t n= = and 45,k = the equation reads

( )230 9 45 ,3

= ⋅ or 30 270,= which is a false statement.

2. (C) Solve for x in the first equation given to us.

40404 44444

4040xx

+ ==

Now plug x=4040 into the 2nd equation. 40404 10(4040) 40404 40400 4− = − =

(C) is correct. Alternate Explanation: Choice (C) is correct. Since 40,404 44,444,x+ = it follows that x equals 4,040.Therefore,

( )40,404 10 40,404 10 4,040 40,404 40,400 4.x− = − = − =Choice (A) is not correct. If 40,404 10 4.04,x− = − then

4,040.804x = and 40,404 44,444.804 44,444.x+ = ≠ Choice (B) is not correct. If 40,404 10 0,x− = then 4,040.4x = and 40,404 44,444.4 44,444.x+ = ≠ Choice (D) is not correct. If 40,404 10 4.04,x− = then 4,039.996x = and 40,404 44,443.996 44,444.x+ = ≠ Choice (E) is not correct. If 40,404 10 40.4,x− = then 4,036.36x = and 40,404 44,440.36 44,444.x+ = ≠

3. (E) If the tick marks are equally spaced out, and there are 4 of

them, each must equal one fourth: Thus, w – p = ½ - ¼ = ¼. (E) is correct.

Alternate Explanation: Choice (E) is correct. Since the tick marks divide the segment between 0 and 1 into four equal parts, the distance between any

two adjacent tick marks must be 1

.4

Therefore p corresponds to

1,

4w corresponds to

1,

2and the value of w p− is

1 1 1.

2 4 4− =

Choice (A) is not correct. 34

is the value of .w p+ The question

asks for the value of .w p− Choice (B) is not correct. The tick marks represent quarter units on the number line, so w p− must

be a whole number multiple of 1

.4

Choice (C) is not correct. 12

is

the value of ,w but the question asks for the difference between w and .p Choice (D) is not correct. The tick marks represent quarter units on the number line, so w p− must be a whole

number multiple of 1

.4

4. (B) In Central and Southern Africa, the bars for 1989 are

approximately ½ the 1979 bars. Only in Eastern Africa is the 1989 bar 1/3 of the 1979 bar. Thus, only II is correct, so (B) is the right choice.

Alternate Explanation: Choice (B) is correct. By looking at the graph, you can see that in region II (Eastern Africa) the elephant population in 1989 was

approximately 13

of the elephant population in 1979. In each of

the regions I and III (Central Africa and Southern Africa, respectively), the elephant population in 1989 was greater than 12

of the elephant population in 1979. Therefore, only in region II

was the elephant population in 1989 approximately 13

of that in

1979. Choice (A) is not correct. In Central Africa, the elephant

population in 1989 was greater than 12

of the elephant population

in 1979. Choice (C) is not correct. In Southern Africa, the

elephant population in 1989 was greater than 12

of the elephant

0 ¼ ½ ¾ 1

p w


2

population in 1979. Choice (D) is not correct. In each of the regions Central Africa and Southern Africa, the elephant

population in 1989 was greater than 12

of the elephant population

in 1979. Choice (E) is not correct. In Eastern Africa, the elephant

population in 1989 was approximately 13

of the elephant

population in 1979, but in each of the regions Central Africa and Southern Africa, the elephant population in 1989 was greater than 12

of the elephant population in 1979.

5. (C) This is a multi step problem. First, find the number of

elephants in 1979: 50+500+550+300=1400. Then, find the number in 1989: 50+300+175+175=700. Now, find the percent change between the two (ignore the negative sign for percentage change):

%50)1400

1400700(100 =

−

(C) is correct. Alternate Explanation: Choice (C) is correct. In 1979, the total elephant population was approximately 50,000 500,000 550,000 300,000 1,400,000.+ + + = In 1989, the total elephant population was approximately 50,000 300,000 175,000 185,000 710,000.+ + + = Since the population fell by about half, the population decrease was approximately 50%. Choice (A) is not correct. The total elephant population in 1979 was approximately 1,400,000. If the total elephant population in the four regions had decreased by approximately 10% from 1979 to 1989, then the population in 1989 would have been approximately

( ) ( )0.90 1,400,000 1,260,000.= Choice (B) is not correct. The

total elephant population in 1979 was approximately 1,400,000. If the total elephant population in the four regions had decreased by approximately 30% from 1979 to 1989, then the population in 1989 would have been approximately

( ) ( )0.70 1,400,000 980,000.= Choice (D) is not correct.

The total elephant population in 1979 was approximately 1,400,000. If the total elephant population in the four regions had decreased by approximately 70% from 1979 to 1989, then the population in 1989 would have been approximately

( ) ( )0.30 1,400,000 420,000.= Choice (E) is not correct. The

total elephant population in 1979 was approximately 1,400,000. If the total elephant population in the four regions had decreased by approximately 90% from 1979 to 1989, then the population in 1989 would have been approximately

( ) ( )0.10 1,400,000 140,000.=

6. (C) The best way to go about this problem is to work backwards. Plug each number from A to E into the function

( ) ( 4)( 2)f x x x= + + , and see if any result in a negative number. (A) (-5+4)(-5+2)=(-1)(-3)=3 (B) (-4+4)(-4+2)=(0)(-2)=0 (C) (-3+4)(-3+2)=(1)(-1)=-1 (D) (-2+4)(-2+2)=(2)(0)=0 (E) (-1+4)(-1+2)=(3)(1)=3 The only answer choice that results in a negative is (C). Alternate Explanation: Choice (C) is correct. The value of the function f at 3x − is

( ) ( ) ( )3 3 4 3 2 1.f − = − + − + = − Choice (A) is not correct. The

value of the function f at 5x = − is

( ) ( )( )5 5 4 5 2 3.f − = − + − + = This is not a negative value.

Choice (B) is not correct. The value of the function f at 4x = − is

( ) ( ) ( )4 4 4 4 2 0.f − = − + − + = This is not a negative value.

Choice (D) is not correct. The value of the function f at 2x = − is

( ) ( ) ( )2 2 4 2 2 0.f − = − + − + = This is not a negative value.

Choice (E) is not correct. The value of the function f at 1x = − is

( ) ( )( )1 1 4 1 2 3.f − = − + − + = This is not a negative value.

7. (B) Let’s redraw the diagram given the facts from the question,

labeling the side lengths we know.

Since AB = 4 and ABCD is a square, both AD and CD are of length 4. Now lets label the point at which CD bisects EF as point O. We can see that the segment EO must also be 4. Since CD bisects EF, OF must also be 4. Further note that CD = 4 because ABCD is a square. The area of a triangle is ½ (base)(height), so:

area of CDF = ½( )( ) = ½ (4)(4) = 8CD OFuuur uuur

V So answer choice (B) is correct. Alternate Explanation: Choice (B) is correct. The area of a triangle is given by the formula

1,

2A bh= where b is the length of the base and h is the height. In

this case, the length of the base of DCF∆ is 4,CD AB= = because ABCD is a square of side 4. Since

EF divides ABCD into two rectangles, it follows that

B

A

E

D

C

F 4 4 4

4


3

.EF CD⊥ Since CD bisects ,EF it follows that 8EF = and

the height of DCF∆ is 1

4.2

EF = Therefore, the area of

DCF∆ is ( ) ( )1 164 4 8.

2 2= = Choice (A) is not correct. The

base CD of DCF∆ is one side of square ,ABCD so its length is 4. If the area of DCF∆ were 9, its height would be

14 .

2However, CD bisects EF so the height of DCF∆ must also

be equal to the side length of square ,ABCD which is 4. Choice

(C) is not correct. The base CD of DCF∆ is one side of square ABCD ,so its length is 4. If the area of DCF∆ were 7, its height

would be 1

3 .2

However, CD bisects ,EF so the height of

DCF∆ must also be equal to the side length of square

,ABCD which is 4. Choice (D) is not correct. The base CD of DCF∆ is one side of square ,ABCD so its length is 4. If the area

of DCF∆ were 6, its height would be 3. However, CD bisects

,EF so the height of DCF∆ must also be equal to the side length of square ,ABCD which is 4. Choice (E) is not correct. The base

CD of DCF∆ is one side of square ,ABCD so its length is 4. If

the area of DCF∆ were 5, its height would be 1

2 .2

However,

CD bisects ,EF so the height of DCF∆ must also be equal to the side length of square ,ABCD which is 4.

8. (B) If Mr. Smith is traveling at 60 miles per hour, and has traveled t hours so far, he must have driven 60*t miles. If he has 500 miles total, the number of miles left must be 500 – 60t. Answer choice (B) is correct. Alternate Explanation: Choice (B) is correct. Since Mr. Smith drives at an average speed of 60 miles per hour for the first t hours, he will have traveled 60t miles. Thus, there are 500 60t− miles remaining to be traveled. Choice (A) is not correct. The number of miles driven, 6 0 ,t must be subtracted from the total length of the trip, 500. Choice (C) is not correct. The total length of the trip is 500 miles, not ( )( )500 60 miles. Also, after t hours, Mr. Smith has driven

60t miles, not t miles. Choice (D) is not correct. After t hours,

Mr. Smith has driven 60t miles, not 60t

miles. Therefore,

500 60t− miles, not 60500t

− miles, remain to be traveled.

Choice (E) is not correct. This expression represents the ratio total miles for the trip .

miles driven after hourst The question asks for number of

miles remaining, not the amount to be traveled relative to the

distance traveled so far.

9. (E) The three circled numbers that are moved from the left column add up to 18, 4+6+8=18. To even out the change just made, 3 numbers that add up to 18 need to be moved from the right column. The only answer choice with 3 numbers that add up to 18 is (E), 5+6+7=18. Alternate Explanation: Choice (E) is correct. Each column has 5 numbers, and the average of each column is ,k so the sum of the numbers in the left column is equal to the sum of the numbers in the right column. When the 3 circled numbers, whose sum is 18, are moved from the left to the right column, a list of numbers with sum 18 needs to be moved from the right column to the left. Of the given options, only the list 7,5,6 has a sum of 18. Choice (A) is not correct. If these numbers were switched with the circled numbers, then the average

of the numbers in the left column would be 36

9,4

= but the

average of the numbers in the right column would be 34 17.6 3

=

Choice (B) is not correct. If these numbers were switched with the circled numbers, then the average of the numbers in the left

column would be 32,5

but the average of the numbers in the right

column would be 38.5

Choice (C) is not correct. If these numbers

were switched with the circled numbers, then the average of the

numbers in the left column would be 33,5

but the average of the

numbers in the right column would be 37 .5

Choice (D) is not

correct. If these numbers were switched with the circled numbers, then the average of the numbers in the left column would be 34,5

but the average of the numbers in the right column would be

36.5

10. (D) Note that the arrival of 30 more people was the difference

between 1/3 and 1/2 of the class. Let x equal the number of people in the junior class. Now, make an equation and solve for x: (D) is correct. Alternate Explanation:

Choice (D) is correct. If the difference between 13

of the junior

class and 12

of the junior class is 30 students, then 30 students

make up exactly 1 1 12 3 6

− = of the junior class. Therefore, the total


4

number of students in the junior class is ( )30 6 180.= Choice

(A) is not correct. If there were only 30 students in the entire junior class, the whole class would have arrived between 7:00 and 8:00 which contradicts the statement in the problem

that 13

of the class had arrived by 7:00. Choice (B) is not

correct. If there were only 90 people in the junior class, 30 would have shown up by 7:00, and when 30 more students had arrived by 8:00, the fraction of the class present would have been

60 2 ,90 3

= not 1

.2

Choice (C) is not correct. If there were only

120 people in the junior class, 40 would have shown up by 7:00, and when 30 more students had arrived by 8:00, the

fraction of the class present would have been 70 7 ,

120 12= not

1.

2

Choice (E) is not correct. If there were 240 people in the junior class, 80 would have shown up by 7:00, and when 30 more students had arrived by 8:00, the fraction of the class present

would have been 110 11 ,240 24

= not 1

.2

11. (D) Since the question states the triangle is equilateral, each angle

is equal to 60 degrees.

Since all of angle S is divided into three equal angles, each x represents 20 degrees. If you focus on the left triangle, we have 2 out of 3 of the angles. Since R+x=80 degrees, the last angles of the left triangle must be 100 degrees since the angles of a triangle add up to 180. Y is on a straight line with a 100 degree angle. Since a straight line is 180 degrees, we can set up this equation: Y+100=180. Therefore, Y=80 degrees, and (D) is correct. Alternate Explanation: Choice (D) is correct. Since triangle RST is equilateral, the measure of RST∠ is 60 ,° thus, 3 60,x = and 20.x = Since the measure of SRT∠ is 60 ,° the three angles of the small triangle on

the left measure 20 , 6 0° ° and ( )180 ,y− ° therefore,

( )20 60 180 180.y+ + − = Solving for y gives 80.y = Choice

(A) is not correct. Since triangle RST is equilateral, 20x = and the angles in the small triangle on the left are 20 , 6 0° ° and

( )180 .y− ° If y were 60, then 180 120,y− = and the sum of the angles in the small triangle on the left would be greater than 180 .° Choice (B) is not correct. Since triangle RST is equilateral, 20x = and the angles in the small triangle on the left

are 20 , 6 0° ° and ( )180 .y− ° If y were 70, then

180 110,y− = and the sum of the angles in the small triangle on

the left would be greater than 180 .° Choice (C) is not correct. Since triangle RST is equilateral, 20x = and the angles in the

small triangle on the left are 20 , 6 0° ° and ( )180 .y− ° If y were

75, then 180 105,y− = and the sum of the angles in the small

triangle on the left would be greater than 180 .° Choice (E) is not correct. Since triangle RST is equilateral, 20x = and the angles in the small triangle on the left are 20 , 6 0° ° and ( )180 .y− ° If

y were 85, then 180 95,y− = and the sum of the angles in the

small triangle on the left would be less than 180 .°

12. (D) To find the value of b, plug it into the formula. b = 2a + 3. But, we do not know a yet. Use the row above to find a: a = 2(4) + 3 = 11. Now plug this value for a into the equation for b: b = 2(11) + 3 = 25. (D) is correct. Alternate Explanation: Choice (D) is correct. The values in each row of the table must satisfy the equation 2 3.y x= + Substitution of the values from the second row of the table into the equation yields

( )2 4 3 11.a = + = Substitution of the values from the third row of

the table into the equation yields ( ) ( )2 3 2 11 3 25.b a= + = + =

Choice (A) is not correct. 4 is the x -coordinate of the point with y -coordinate .a Choice (B) is not correct. 11 is the value of

,a but the question asks for the value of .b Choice (C) is not correct. 15 2 4 7,= +g but this does not give the value of .b Choice (E) is not correct. 28 4 7,= ⋅ but this does not give the value of .b

13. (B) We can turn this problem into a simple equation to solve for x, which would then be used to find the radius of circle R. If the radius of R is twice that of P, then R = 2P, or:

62442

22224

)1(24

=+=+===+

+=++=+

xRxxx

xxxx

Answer (B) is correct. Alternate Explanation: Choice (B) is correct. The radius of the circle with center R is equal to 4 .x+ The radius of the circle with center P is equal to 1 .x+ Since the radius of the circle with center R is twice the radius of the circle with center ,P it follows that

( )4 2 1 .x x+ = + This simplifies to the equation

4 2 2 ,x x+ = + and further to 2.x = Therefore, the radius of the circle with center R is 4 4 2 6.x+ = + = Choice (A) is not correct. If the radius of the circle with center R were 5, then x would equal 1, and the ratio of the radii of the circles would be

R T

S

xº xº xº

yº


5

4 1 52.

1 1 2+

= ≠+

Choice (C) is not correct. If the radius of the

circle with center R were 7, then x would equal 3, and the ratio

of the radii of the circles would be 4 3 7 2.1 3 4

+ = ≠+

Choice (D) is

not correct. If the radius of the circle with center R were 8, then x would equal 4, and the ratio of the radii of the circles would be

4 4 8 2.1 4 5

+ = ≠+

Choice (E) is not correct. If the radius of the

circle with center R were 10, then x would equal 6, and the ratio

of the radii of the circles would be 4 6 10 2.1 6 7

+ = ≠+

14. (D) Each hour contains 60 minutes, and each minute contains 60

seconds. So 1 hour has 3600 seconds. The problem states h represents the number of hours, so we need to multiply 3600 h× . This number represents the total number of seconds during the time span. So if we wanted to know how many times the shutter opened, we would divide by 31 seconds. The final equation for

g(h) is 3600

31h

. (D) is correct.

Alternate Explanation: Choice (D) is correct. Since there are 3600 seconds in an hour, the

number of openings per hour is 3600.

31 If this goes on for h hours,

the shutter will open 3600

31h times. Hence, ( ) 3600 .

31g h h=

Choice (A) is not correct. This equation corresponds to the situation in which the shutter opens 31 times each hour. Choice (B) is not correct. This equation corresponds to the situation in

which the shutter opens ( )31 3600 111600= times each hour, or

31 times per second. Choice (C) is not correct. This corresponds to a situation in which the camera shutter opens less than once an hour. Choice (E) is not correct. According to this equation, the more time that passes, the fewer times the shutter opens. Since the shutter opens every 31seconds, this does not make sense.

15. (E) If marble 2 is the only variable, as it can only be either white

or blue. If it is white, then the colors of the marbles drawn are red, white, blue, red, white, and x (the total number of blue marbles drawn) would be 1. If the marble is blue, then the colors are red, blue, blue, red, blue, and x would be 3. Thus, the only possible values of x are 1 and 3, so (E) is right. Alternate Explanation: Choice (E) is correct. Either the five colors, listed in order, were red, white, blue, red, and white (if marbles 2 and 5 were both white) or red, blue, blue, red, and blue (if marbles 2 and 5 were both blue). In the first case, there was only one blue marble, in the second case there were three blue marbles so 1x = or 3.x =

Choice (A) is not correct. 1 is a possible value for ,x but 3 is also a possible value. Choice (B) is not correct. Marbles 1and 4 were red and 3 was blue. If x were two then the given information would be contradicted since marbles 2 and 5 were the same color (either both white or both blue). Choice (C) is not correct. 3 is a possible value for ,x but 1 is also a possible value. Choice (D) is not correct. Marbles 1and 4 were red and 3 was blue, so 1x = is a possible value. However, 2x = is not a possible value because the given information would be contradicted (marbles 2 and 5 were either both white or both blue).

16. (E) If we can find the values for all the angles, the problem is

simple. From the diagram, it is clear that v+w = 180 (alternate angles), and that w=s=t. If v = 2w, then 2w + w = 180, 3w = 180, and w = 60. Thus, v = 2(60) = 120. If we know the values for v and w, we can find the values for q, s, and t: q=120, s = 60, and t = 60. Plug these values in for the expressions given in the answer choices. Only s+t = 60+60 = 120 works. Therefore, (E) is correct. Alternate Explanation: Choice (E) is correct. The angles labeled s° and v° are supplementary, so 180.s v+ = The angles labeled s° and w° are corresponding angles, so s w= and 180.w v+ = Since

2 ,v w= substitution gives 2 3 180,w w w+ = = from which it follows that 60,w = 120,v = and 60.s = The angles labeled q° and s° are supplementary, as are the angles labeled q° and

,t° so 120q = and 60.t = Now that the measures of all the labeled angles have been found, substitution of the correct values in the five options shows that only 120 .s t q+ = = Choice (A) is

not correct. 120,q = but 180.v t+ = Choice (B) is not correct.

120,q + but 60.v t− = Choice (C) is not correct. 120,q = but 60.t = Choice (D) is not correct. 120,q = but 2 240.v =

17. (C) Find an integer that satisfies the first condition. If 9 is divided

by 7, the remainder is 2, so 9 works. What is the remainder if 5(9) = 45 is divided by 7? 45/7 = 6 r 3. The remainder is 3, so (C) is correct. The modulus function (Mod) on your calculator evaluates the remainder in a division problem. For instance, 9 Mod 7 = 2. The algebraic way to solve this problem is as follows. We can represent the integer n as any number 7x+2, where x is any integer. For instance, if x = 3, then n would be 23, which when divided by 7 will yield a remainder of 2. So now that we have a expression for x, let us multiply it by 5 as the problem states. 5(7 2) 35 10x x+ = + Since 35x will divide into 7 with no remainder, we need to consider the remaining. 10/7 will give you a remainder of 3, and that is our answer. Alternate Explanation: Choice (C) is correct. This problem can be solved quickly by choosing a value that satisfies the “if” clause of the first sentence. For example, if 11m = is divided by 6, then the remainder is 5 , and when 4 4 11 44m = ⋅ = is divided by 6, the remainder is 2. Thus, 11m = is a counterexample to options (A), (B), (D), and (E), so option (C) is the only possibility for the correct answer.


6

More generally, that the remainder must be 2 can be proven as follows. Since there is a remainder of 5 when m is divided by 6, it follows that m must equal 6 5,c + where c is some integer. Therefore, the expression 4m is equal to

( )4 6 5 24 20.c c+ = + When 24 20c + is divided by 6, the only

part that contributes to the remainder is 20, because 6 goes evenly into 24 .c Since the remainder when 20 is divided by 6 is 2, it follows that the remainder when 4m is divided by 6 is also 2. Choice (A) is not correct. If m is equal to 11, then the remainder is 5 when m is divided by 6. However, 4 44,m = and the remainder when 44 is divided by 6 is 2, not 0. Choice (B) is not correct. If m is equal to 11, then the remainder is 5 when m is divided by 6. However, 4 44,m = and the remainder when 44 is divided by 6 is 2, not 1. Choice (D) is not correct. If m is equal to 11, then the remainder is 5 when m is divided by 6. However, 4 44,m = and the remainder when 44 is divided by 6 is 2, not 4. Choice (E) is not correct. If m is equal to 11, then the remainder is 5 when m is divided by 6. However, 4 44,m = and the remainder when 44 is divided by 6 is 2, not 5.

18. (B) If something is reduced by 65%, that means only 35%

remains. Any answer with .65 first should be eliminated. The first 3 minutes of the call cost 90 cents while the remaining 27 minutes cost c per call. This can be represented by the equation 90 27c+ . C is in cents, but the final answer asks for dollars. To convert cents to dollars, divide by 100. This leaves us with the equation 0.90 0.27c+ which should be multiplied by 35%. (B) has that equation multiplied by .35 and is the correct answer. Alternate Explanation: Choice (B) is correct. First, consider the cost of the phone call without the 65% reduction. The first 3 minutes cost 90 cents, or 90 0.90

100= dollar. There are 30 3 27− = minutes remaining, and

each minute costs c cents, or 100

cdollars, for a subtotal of

27 0.27100

c c= dollars. Therefore, the full cost of the call is

0.90 0.27c+ dollars. Now, consider the 65% reduction in price. Subtracting 65% from the original price yields

( )( ) ( )1.00 0.65 0.90 0.27 0.35 0.90 0.27 .c c− + = + Choice

(A) is not correct. Here, only the cost of the first 3 minutes of the calls are reduced by 65%. Also, the term 27c should be 0.27 ,c to account for the expression being in terms of dollars. Choice (C) is not correct. Here, the term 9c should be 0.27 ,c to account for the cost of the last 27 minutes of the call in terms of dollars. Choice (D) is not correct. Here, the total cost of the call is 65% of the daytime rate, rather than being reduced by 65%. Also, the term 27c should be 0.27 ,c to account for the expression being in terms of dollars. Choice (E) is not correct. Here, the total cost of the call is 65% of the daytime rate, rather than being reduced by

65% Also, 30 minutes are charged at c cents per minute, which would make the entire call 3 30 33+ = minutes.

19. (C) According to the problem, the conditions are on the first and last digit. There can be one value for the first digit, and 2 for the fourth digit. The other two digits can have any of 10 values (the 10 digits). To find the total possible numbers now, multiply these numbers together: 1 x 10 x 10 x 2 = 200. (C) is correct. Alternate Explanation: Choice (C) is correct. There are 10 ways of choosing the hundreds digit and 10 ways of choosing the tens digit (any of the 10 digits 0, 1, 2, 3, ...,8, or 9 may go into either of these positions) There are 2 ways of filling the ones digit (it can only be either a 2 or a 5 ), and only 1way to fill the thousands digit since it must be 1.Therefore, the number of integers satisfying the stated conditions is 10 10 2 1 200.× × × = Choice (A) is not correct. The list 1002, 1005, 1012, 1015, ..., 1712, 1715 contains 144 numbers of this form but there are more: 1722, 1725, 1732, 1735, ...1992, 1995. Choice (B) is not correct. This is the number of posit ive three-digit numbers that have 2 or 5 as their last digit. Choice (D) is not correct. This is the number of positive three-digit number that have 1, 2 , or 5 as their first digit. Choice (E) is not correct. The complete list of numbers of this form is 1002, 1005, 1012, 1015, ..., 1992, 1995 and contains only 200 numbers.

20. (B) Let’s redraw this diagram with a few additional lines.

The sides of each smaller square are equal 2 since there are 3 of them per side of the large square, which had sides of length 6. Note that the bases of the triangle are equal to 2 half-sides (or one side) of one of the smaller squares, so they must be 2 also. By the Pythagorean rule, the diagonal (which is the radius of the circle)

must be 22 . The area of the circle is 2rπ , so the area is

ππ 8)22( 2 = . (B) is correct. Alternate Explanation: Choice (B) is correct. Since the sides of the large square have a length of 6 units, each of the small squares has sides of length 2 units. The points A and B are separated by a full side of a small square, and two half sides of a small square, or a total of

( ) 21 2 2 2 2 4

2 + = + =

units. Similarly, B and C are separated

by 4 units, and so on. Moreover, the points , , ,A B C and D are the vertices of a square that has sides of length 4 units. The diagonals of square ABCD are diameters of the circle that passes

A •

D •

• C

• B

6

6


7

through the points , , ,A B C and .D Since the sides AB and

BC and the diagonal AC of square ABCD form a right isosceles triangle, the length of the diagonal (and the diameter of the circle)

is 4 2 , and therefore the radius of the circle is 2 2.Therefore,

the area of the circle is ( )22 2 2 8rπ π π= = square units.

Choice (A) is not correct. The area of the circle would be

6π square units if the diameter of the circle, ,AC had length

2 6 units, but the length of AC is 4 2 units. Choice (C) is not correct. The area of the circle would be 9π square units if the

diameter of the circle, ,AC had length 6 units, but the length of

AC is 4 2 units. Choice (D) is not correct. The area of the circle

would be 10π square units if the diameter of the circle, ,AC had

length 2 10 units, but the length of AC is 4 2 units. Choice (E) is not correct. Since the circle is contained inside the large square, the area of the circle must be smaller than the area of the large square, but 18π square units is greater than 36 square units.

Section 3 1. (B) The word “topography” refers to the shape of land. The word

in the blank must also refer to shapes. (B) is correct because “contours” means curves. (A) “models”, (C) “remnants” (remains), (D) “populations” and (E) “pigments” (colors) do not make sense in this context. If you did not know “topography”, you could still eliminate these other choices since they are not good descriptors of “land.” Alternate Explanation: Choice (B) is correct. "Contours" are the outlines or shapes of curving or irregular surfaces. If one were to insert this term into the text, the sentence would read "New data measuring the contours of land beneath the oceans permit accurate generalizations about the topography of the seafloor." The missing term has a meaning similar to "topography," or the surface features of a place or region. The "contours of land" are the outlines or shape of the land's surface. Choice (A) is incorrect. "Models" are miniature representations of something. If one were to insert this term into the text, the sentence would read "New data measuring the models of land beneath the oceans permit accurate generalizations about the topography of the seafloor." The actual land beneath the oceans, not miniature representations of the land, must be measured in order to make accurate generalizations about the seafloor. Choice (C) is incorrect. "Remnants" are remains or things left over. If one were to insert this term into the text, the sentence would read "New data measuring the remnants of land beneath the oceans permit accurate generalizations about the topography of the seafloor." In this context, it does not make sense to speak of remains of land on the ocean floor. Choice (D) is incorrect. A "population" is the total number of people or organisms in a given area. If one were to insert this term into the text, the sentence would read "New data measuring the populations of land beneath the oceans permit accurate generalizations about the topography of the seafloor." The land beneath the oceans may have a "population" of organisms, but knowing the number of these organisms would not assist in making generalizations about

the seafloor's "topography," or surface features. Choice (E) is incorrect. "Pigments" are substances used for coloring. If one were to insert this term into the text, the sentence would read "New data measuring the pigments of land beneath the oceans permit accurate generalizations about the topography of the seafloor." Colors are not among the surface features typically referred to by the term "topography."

2. (E) If something is secret, you usually want to find out what it is.

Thus, it must “increase” your curiosity. The second word must be the opposite of “guards” because of the word ‘against.’ (E) is correct because “invite” and “provoke” both match the prediction. (A) is incorrect because “inhibit” (stop) is the opposite of “increase.” (B) is incorrect because “supplant” means to replace, which would not fit. (C) is incorrect because “limit” is the opposite of what we need. (D) is incorrect because “deride” means to make fun of in a mean way, which does not fit here. Alternate Explanation: Choice (E) is correct. "To invite" means to encourage. "To provoke" means to give rise to. If one were to insert these terms into the text, the sentence would read "Excessive secrecy tends to invite excessive curiosity and thus serves to provoke the very impulses against which it guards." This sentence makes sense because excessive secrecy encourages excessive curiosity. Secrecy thus gives rise to "the very impulses" that the overly secretive seek to avoid--namely, people's desire to find out what is going on. Choice (A) is incorrect. "To inhibit" means to prevent. "To protect" means to guard. If one were to insert these terms into the text, the sentence would read "Excessive secrecy tends to inhibit excessive curiosity and thus serves to protect the very impulses against which it guards." Excessive secrecy does not prevent excessive curiosity. In fact, it does exactly the opposite. Choice (B) is incorrect. "To disguise" means to conceal an identity. "To supplant" means to oust and take the place of. If one were to insert these terms into the text, the sentence would read "Excessive secrecy tends to disguise excessive curiosity and thus serves to supplant the very impulses against which it guards." Excessive secrecy does not conceal the identity of excessive curiosity. Neither does excessive secrecy oust and take the place of curious interest. Choice (C) is incorrect. "To satisfy" means to meet expectations. "To limit" means to restrict. If one were to insert these terms into the text, the sentence would read "Excessive secrecy tends to satisfy excessive curiosity and thus serves to limit the very impulses against which it guards." Excessive secrecy does not meet the expectations of excessive curiosity, nor does it restrict curious interest. Choice (D) is incorrect. "To compel" means to force. "To deride" means to mock. If one were to insert these terms into the text, the sentence would read "Excessive secrecy tends to compel excessive curiosity and thus serves to deride the very impulses against which it guards." Excessive secrecy may encourage excessive curiosity, but it does not force it.

3. (E) If the water cannot sink, it must remain near the surface. The second blank must be similar to “bog” since it comes after an ‘and.’ (E) is correct because “floods” makes sense if the water is remaining near the surface and “swamp” is similar to bog. (A), (B) and (D) are incorrect because “freezes” can happen anywhere, “parches” means to dry, and “aerates” (to add air) has nothing to


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do with water. (C) is incorrect because “desert” is almost the opposite of “bog.” Alternate Explanation: Choice (E) is correct. "Floods" means covers with water. A "swamp" is a water-soaked patch of land. If one were to insert these terms into the text, the sentence would read "In frigid regions a layer of permafrost under the soil surface prevents water from sinking deep into the soil, and so the water floods the land, helping to create bog and swamp conditions." The first missing term describes what water does when it cannot sink into soil, and the second missing term describes a consequence of that situation. A piece of land "floods" when water cannot sink into it, and this creates watery areas, or "swamps." Choice (A) is incorrect. "Freezes" means turns to ice. "Tropical" refers to a hot region or hot conditions. If one were to insert these terms into the text, the sentence would read "In frigid regions a layer of permafrost under the soil surface prevents water from sinking deep into the soil, and so the water freezes the land, helping to create bog and tropical conditions." It is possible that water might turn to ice atop the cold region's permafrost, but this would not cause hot, "tropical" conditions. Choice (B) is incorrect. "Parches" means dries out. A "marsh" is a patch of watery ground. If one were to insert these terms into the text, the sentence would read "In frigid regions a layer of permafrost under the soil surface prevents water from sinking deep into the soil, and so the water parches the land, helping to create bog and marsh conditions." A piece of land gets very wet when water cannot sink into it. This land could not be called "parched." Furthermore, dried out land could not be considered a "marsh," which is a patch of watery ground. Choice (C) is incorrect. "Inundates" means covers with water. A "desert" is an extremely dry region. If one were to insert these terms into the text, the sentence would read "In frigid regions a layer of permafrost under the soil surface prevents water from sinking deep into the soil, and so the water inundates the land, helping to create bog and desert conditions." A piece of land gets very wet when water cannot sink through it. This is the opposite of "desert conditions." Choice (D) is incorrect. "Aerates" means adds air to. A "jungle" is an overgrown forest. If one were to insert these terms into the text, the sentence would read "In frigid regions a layer of permafrost under the soil surface prevents water from sinking deep into the soil, and so the water aerates the land, helping to create bog and jungle conditions." A piece of land gets very wet when water cannot sink through it. Water does not "aerate" land, or expose land to air. Furthermore, an overgrown forest would probably not occur in "frigid," or cold, climates.

4. (C) The first blank must be opposite to the second one since the first word is “Although.” The first word most likely is negative, while the first is positive since the police officer was likely surprised in a good way. (C) is correct because “implausible” means highly unlikely, and “correct” is opposite to this. (A) is incorrect because “dubious” (doubtful) and “erroneous” are not opposites. (B) is incorrect because “inconsistent” is negative. (D) is incorrect because “pertinent” (relevant) is not opposite to “logical.” (E) is incorrect because “coherent” (sensible) is not opposite to “probable.” Alternate Explanation: Choice (C) is correct. "Implausible" means hard to believe. "Correct" means accurate. If one were to insert these words into the text, the sentence would read "Although the bystander's

account of the car accident at first seemed implausible, the police officer was surprised, on further investigation, to find that it was correct." The word "although" signals that the first missing term will contrast with the second missing term. The police officer would be surprised if a story that at first seemed hard to believe later proved to be correct. Choice (A) is incorrect. "Dubious" means doubtful. "Erroneous" means full of error. If one were to insert these words into the text, the sentence would read "Although the bystander's account of the car accident at first seemed dubious, the police officer was surprised, on further investigation, to find that it was erroneous." The officer would hardly have been surprised had a doubtful account turned out to be full of errors. The sentence is illogical because the contrast signaled by the word "although" does not occur. Choice (B) is incorrect. "Incongruous" means illogical. "Inconsistent" means contradictory. If one were to insert these words into the text, the sentence would read "Although the bystander's account of the car accident at first seemed incongruous, the police officer was surprised, on further investigation, to find that it was inconsistent." The police officer would not be surprised if a story that at first seemed illogical later proved to be contradictory. The contrast signaled by the word "although" does not occur, and, as a result, the sentence does not make sense. Choice (D) is incorrect. "Logical" means rational or making sense. "Pertinent" means relevant. If one were to insert these words into the text, the sentence would read "Although the bystander's account of the car accident at first seemed logical, the police officer was surprised, on further investigation, to find that it was pertinent." The sentence does not make sense because there is no connection between a story being rational and a story being relevant. Choice (E) is incorrect. "Probable" means likely. "Coherent" means logical. If one were to insert these words into the text, the sentence would read "Although the bystander's account of the car accident at first seemed probable, the police officer was surprised, on further investigation, to find that it was coherent." The police officer would not be surprised if a story that at first seemed likely later proved to be logical. The sentence is illogical because the contrast signaled by the word "although" does not occur.

5. (A) The phrase “so ____ that it threatened to shatter…” indicates

that the legislation (proposed law) must have been very dangerous or harmful to the bipartisanship (two parties working together). Look for a negative word that relates to harming cooperation. (A) is correct because “divisive” fits both the context and the prediction. (B) and (D) are incorrect because “transparent” and “repetitive” do not fit the context. (C) is incorrect because “concordant” means harmonious, which is the opposite of what we want. (E) is incorrect because “rhetorical” relates to any speech used to persuade. Alternate Explanation: Choice (A) is correct. "Divisive" means creating division. If one were to insert this term into the text, the sentence would read "The legislation facing Congress was so divisive that it threatened to shatter the governing body's fragile bipartisanship." The missing term describes the nature of a piece of legislation that threatened to break up a relationship between two political parties. Therefore, by definition, "divisive legislation" will tend to divide people and disrupt bipartisan political action. Choice (B) is incorrect. "Transparent" means easily understood. If one were to insert this term into the text, the sentence would read "The legislation facing Congress was so transparent that it threatened to shatter the


9

governing body's fragile bipartisanship." Legislation that can be easily understood does not necessarily threaten a relationship between political parties. Choice (C) is incorrect. "Concordant" means harmonious or agreeing. If one were to insert this term into the text, the sentence would read "The legislation facing Congress was so concordant that it threatened to shatter the governing body's fragile bipartisanship." Legislation that is harmonious would not suggest a threat to a relationship between political parties. Choice (D) is incorrect. "Repetitive" means repeating unnecessarily. If one were to insert this term into the text, the sentence would read "The legislation facing Congress was so repetitive that it threatened to shatter the governing body's fragile bipartisanship." "Repetitive" legislation would not necessarily affect the governing body's bipartisanship. Choice (E) is incorrect. "Rhetorical" refers to saying or asking something for persuasive effect. If one were to insert this term into the text, the sentence would read "The legislation facing Congress was so rhetorical that it threatened to shatter the governing body's fragile bipartisanship." Legislation that states something for effect would not necessarily suggest a threat to a relationship between political parties.

6. (C) The word in the first blank means “brief descriptive sketches.” The second blank should be a positive word since the view “clearly details” aspects of Ghana. (C) is correct because “vignettes” means brief descriptive sketches and “vivid” (very realistic, colorful) is positive. (A) is incorrect because “missives” means letters. (B) is incorrect because “themes” are not sketches. (D) is incorrect because “treatises” are long texts, not “brief.” (E) is incorrect because “ambiguous” (unclear, not well-defined) is not positive. Alternate Explanation: Choice (C) is correct. "Vignettes" are short, descriptive literary sketches. "Vivid" means lively or intensely clear. If one were to insert these terms into the text, the sentence would read "In All God's Children Need Traveling Shoes , author Maya Angelou uses vignettes, brief descriptive sketches, to provide a vivid view of Ghana that clearly details the land and its people." This sentence makes sense because "vignettes" are brief descriptive sketches, and "vivid" sketches clearly describe a subject. Choice (A) is incorrect. "Missives" are letters. "Illusory" means deceptive. If one were to insert these terms into the text, the sentence would read "In All God's Children Need Traveling Shoes, author Maya Angelou uses missives, brief descriptive sketches, to provide an illusory view of Ghana that clearly details the land and its people." A letter is not a brief descriptive sketch. Also, a deceptive view of Ghana would not clearly describe the land and its people. Choice (B) is incorrect. "Themes" are main ideas. "Thorough" means complete. If one were to insert these terms into the text, the sentence would read "In All God's Children Need Traveling Shoes , author Maya Angelou uses themes, brief descriptive sketches, to provide a thorough view of Ghana that clearly details the land and its people." Since all books have main ideas, one does not need to specify that author Maya Angelou uses them. Choice (D) is incorrect. "Treatises" are typically lengthy, complex, and often analytical pieces of writing. "Authentic" means real or factually correct. If one were to insert these terms into the text, the sentence would read "In All God's Children Need Traveling Shoes , author Maya Angelou uses treatises, brief descriptive sketches, to provide an authentic view of Ghana that clearly details the land and its people." A "treatise" is not a brief sketch. Choice (E) is incorrect. "Abstracts" are summaries of main points. "Ambiguous" means

uncertain or indistinct. If one were to insert these terms into the text, the sentence would read "In All God's Children Need Traveling Shoes , author Maya Angelou uses abstracts, brief descriptive sketches, to provide an ambiguous view of Ghana that clearly details the land and its people." An "ambiguous" view of Ghana would not offer clear details about the country's land and people.

7. (D) The correct word should imply that the older horse is safer. (D) is correct because “tractable” means manageable, which would mean the horse is safer to ride. (A) and (B) are incorrect because “frolicsome” means easily excited, and “cantankerous” means bad tempered. (C) is incorrect because “gargantuan” means very large. (E) is incorrect because “precipitate” means rash, which would not be safe. Alternate Explanation: Choice (D) is correct. "Tractable" means easily handled or controlled. If one were to insert this term into the text, the sentence would read "Because an older horse is more tractable than a younger one, it is safer for a novice rider." The missing term refers to the quality of a horse that will make it safe for inexperienced riders. Most likely, an older horse is easier to handle or control than a younger horse and is therefore a good choice for a "novice," or inexperienced, rider. Choice (A) is incorrect. "Frolicsome" means playful. If one were to insert this term into the text, the sentence would read "Because an older horse is more frolicsome than a younger one, it is safer for a novice rider." An older horse is usually less, not more, playful than a younger horse. In addition, the energy of a playful horse might be unsafe for a "novice," or inexperienced, rider. Choice (B) is incorrect. "Cantankerous" means difficult to deal with. If one were to insert this term into the text, the sentence would read "Because an older horse is more cantankerous than a younger one, it is safer for a novice rider." A horse that is difficult to deal with might be dangerous for a "novice," or inexperienced, rider. Choice (C) is incorrect. "Gargantuan" means extremely large. If one were to insert this term into the text, the sentence would read "Because an older horse is more gargantuan than a younger one, it is safer for a novice rider." This would not make sense because the size of a horse is not always correlated with its age. Furthermore, an extremely large horse would not necessarily be safer than a smaller horse. Choice (E) is incorrect. "Precipitate" means being hasty and impulsive. If one were to insert this term into the text, the sentence would read "Because an older horse is more precipitate than a younger one, it is safer for a novice rider." A horse that is impulsive would be extremely unsafe for a "novice," or inexperienced, rider.

8. (D) If it includes “rare materials”, the collection must be very good. Look for a positive word. (D) is correct because “trove” means “a collection of valuable items.” (A) is incorrect because “summary” is not very positive and does not reflect that the library has rare items. (B) is incorrect because “fabrication” means false. (C) is incorrect because “consensus” means agreement. (E) is incorrect because “replication” does not make sense: the library should contain original materials. Alternate Explanation: Choice (D) is correct. A "trove" is a valuable collection. If one were to insert this term into the text, the sentence would read "The library's collection is a trove of Asian American historical


10

documents, including rare materials about race relations." The missing term is characterized by the p hrase that follows the comma. A library collection containing rare materials is a valuable collection. Choice (A) is incorrect. A "summary" is a review of the main points of something. If one were to insert this term into the text, the sentence would read "The library's collection is a summary of Asian American historical documents, including rare materials about race relations." A library collection, which consists of many diverse documents, is not a "summary." Choice (B) is incorrect. A "fabrication" is something made up. If one were to insert this term into the text, the sentence would read "The library's collection is a fabrication of Asian American historical documents, including rare materials about race relations." A library collection includes real historical documents and thus is not a "fabrication.” Choice (C) is incorrect. "Consensus" means general agreement. If one were to insert this term into the text, the sentence would read "The library's collection is a consensus of Asian American historical documents, including rare materials about race relations." The term "consensus" does not make sense in this context because a library collection cannot be described as a "general agreement." Choice (E) is incorrect. A "replication" is a copy. If one were to insert this term into the text, the sentence would read "The library's collection is a replication of Asian American historical documents, including rare materials about race relations." These historical documents would be originals, not copies. A "replication" is a copy of an original, not a collection of rare historical documents.

9. (B) The area for this question is lines 1-4. The capital letters serve to evoke fear of an approaching danger. Also, to make “alert” in line 10 is what the capital letters serve to do. (A) is incorrect because never is the emotion of anger indicated. (C) is incorrect because nothing in the area suggests impatience. (D) is incorrect since disbelief is never brought up in the area. (E) is incorrect because embarrassment is not mentioned in the passage. (B) is correct since alarm is almost synonymous to fear. Alternate Explanation: Choice (B) is correct. The capitalized words are intended to suggest the surprising suddenness of the noise and convey the driver's sense of urgency in finding where the noise is coming from. The driver is clearly startled and "alarmed" by the blast of sound. Choice (A) is incorrect. The passage does not mention the driver showing anger. Rather the capitalized letters indicate the driver's alarm, or concern, over the blast of sound. Choice (C) is incorrect. The capitalized words relate to the driver's experience of a loud, unknown sound. The driver is probably impatient to find where the sound is coming from, but "impatience" is not a strong enough feeling to be expressed in capital letters. Choice (D) is incorrect. There is no question about the existence of the blast of sound, so disbelief cannot apply. Choice (E) is incorrect. The driver is not embarrassed by the sound, but startled and worried.

10. (D) The area for this question is lines 10-12. The next paragraph would most likely continue on with the idea of a chemical reaction. (A) is incorrect because the author could care less about freight trains. (B) is incorrect because the chemical reaction is related to alertness not drivers repeatedly honk their horns. (C) is incorrect because the driver’s haste is of no concern to the author. (E) is incorrect because the difference between truck and train horns is never mentioned or discussed. (D) is correct because the chemical

reaction is what we are looking for, and it is related to being scared. Alternate Explanation: Choice (D) is correct. The last sentence of the passage is "it was a chemical reaction, pure and simple, and it crippled time in your mind" (lines 11-12). The logical next step for the passage would be to provide more detail about this chemical reaction. Choice (A) is incorrect. As is suggested by the last two sentences, the subject of the passage is the nature of the driver's reaction. It is not trains or other loud vehicles. Choice (B) is incorrect. The passage does not discuss the repeated honking of horns. Choice (C) is incorrect. Where the driver was going is irrelevant, and the passage does not indicate that the driver was in a hurry. Choice (E) is incorrect. Since the "chemical reaction" does not make distinctions between types of noises, it is unlikely that the passage would go on to discuss those distinctions.

11. (D) The area for this question is the entire passage. The answer should focus on Jemison and her accomplishments. (A) is incorrect because it does not mention Jemison. (B) is incorrect because the focus of the passage is more general than just her interest in science. (C) is incorrect since her rise to fame was never mentioned. (E) is incorrect because Jemison’s introduction to science is never discussed. (D) is correct because it focuses on Jemison and her goals which are pretty much her accomplishments. Alternate Explanation: Choice (D) is correct. The passage's first sentence explains Jemison's primary achievement: she "blasted into history as the first woman of color to go into space" (lines 3-4). The remainder of the passage sums up Jemison's background and her goals for science. Choice (A) is incorrect. This passage describes the achievements and goals of a particular individual who was undaunted by the obstacles before her. The primary purpose of the passage is not to note the "obstacles facing women in science." Choice (B) is incorrect. Although the passage does indicate that Jemison is an advocate for science and technology, this is not the passage's central focus. In addition, the passage does not explain how she "fosters," or encourages, interest in science. Choice (C) is incorrect. The idea of fame is not discussed in this passage. Choice (E) is incorrect. The passage does not mention how Jemison first became involved in science.

12. (E) The area for this question is lines 9-12. The main idea of

those lines is to “change the image of who does science.” (A) is incorrect because politics are never mentioned in the area. (B) is incorrect since the area never mentions disputes or arbitration. (C) is incorrect because women are not the focus of the last three lines, science is the focus. (D) is incorrect because her charisma is not mentioned in the area. (E) is correct since reform is indicative of “change.” Alternate Explanation: Choice (E) is correct. The passage calls Jemison an "advocate for science and technology" and quotes her as saying, "we need to change the image of who does science" (lines 9-10). These lines indicate that Jemison would like to "reform," or change, common perceptions about who can or should participate in science. Choice (A) is incorrect. Jemison is concerned not with politics but with science. Choice (B) is incorrect. Jemison shows no interest in


11

"arbitrating," or refereeing, an argument. Rather, she wants to expand the public's understanding of science and technology, and change common perceptions people have of scientists. Choice (C) is incorrect. Jemison would no doubt make a fine mentor, but the focus of this passage is on her and her ideas about science. Choice (D) is incorrect. Although Jemison clearly has many gifts, she is not portrayed as having unusual personal magnetism or as being an idealist.

13. (D) The area for this question is both passages. The first author praises Twain, while the second criticizes. Choices (A) through (C) are incorrect because they suggest that the first author had a negative view of Twain. (E) is incorrect because the second author thought the work was rude, not ‘understated.’ (D) is correct because the first author did praise Twain’s universality, while the second criticized his inability to choose appropriate topics for humor. Alternate Explanation: Choice (D) is correct. The author of Passage 1 claims that Twain respects citizens from every nation and describes "the universal traits of ... that nation's humanity." The author of Passage 2 accuses Twain of a lack of discrimination, or good judgment and taste, saying that Twain "brings whatever time has honored down to the level of a Yankee drummer." Choice (A) is incorrect. Although the author of Passage 2 does state that Twain thinks the customs of other countries are ridiculous, there is no indication that the author of Passage 1 finds Twain's humor offensive. Choice (B) is incorrect. Although the author of Passage 2 finds Twain's humor highly distasteful, the author of Passage 1, far from viewing Twain's humor as mediocre, calls Twain "the greatest genius" that emerged out of American journalism. Choice (C) is incorrect. The author of Passage 1 calls Twain a "genius" and mentions his "worldwide popularity," so clearly this author would not describe Twain's humor as trivial. The author of Passage 2 calls Twain "a bull in the china shop of ideas," suggesting that Twain is far from harmless. Choice (E) is incorrect. The author of Passage 1 does appear to admire the vigor, or liveliness, of Twain's humor. However, the author of Passage 2 contrasts Twain's humor with the "moderation" of writers like Aristophanes, Shakespeare, and Chaucer, suggesting that Twain's humor is the opposite of understated, or restrained.

14. (A) The area for this question is line 23. Look at the context of the word “range.” The correct word needs to be modifiable by “international” and make the sentence mean that Twain could reach international audiences. (B), (D), and (E) are incorrect because “distance”, “ranking”, and “value” do not make sense in the context of literature and an audience. (C) is incorrect because the author has not made any mention of ‘variation’ in Twain’s style. If anything, Twain is a great writer because he is consistent. (A) is correct because “scope” means having a certain ability, and Twain indeed did have the ability to reach an international group of readers. Alternate Explanation: Choice (A) is correct. The term "range" is used to express the vast amount, or scope, of people throughout the world who appreciate Twain's humor. Choice (B) is incorrect. "Distance" gives the sense of how far two points are from each other. The use of the term "range" here is not to describe the distance between Twain and the

people his humor touches, but to indicate the vast amount of different people who understand his jokes. Choice (C) is incorrect. Although it could make sense to say that Twain's humor "has international variation," the end of the sentence suggests that the humor has a universal quality that does not depend on variations among people. Choice (D) is incorrect. The reason given for the humor's "international range" does not suggest that the humor has been ranked, or judged in relation to others. Choice (E) is incorrect. Although the author does suggest that Twain's humor could have international value, the term "range" refers to vast amount of people who value Twain's humor, not the value itself.

15. (C) The area for this question is lines 23 to 27. In this area, the

author makes note of Twain’s extensive knowledge of human nature, which he incorporated into his writing. (A) is incorrect because the author’s point is not about comedic style, but rather about Twain’s grasp of humanity. (B) is incorrect because the author does not mention Twain’s academic knowledge. (D) is incorrect because the passage never states any foreign languages that Twain spoke. (E) is incorrect because the author’s entire point is that Twain did not resort to ethnic humor, but rather that his humor transcended racial lines. (C) is correct because Twain’s humor was so successful because of his understanding of people. Alternate Explanation: Choice (C) is correct. The passage states that Twain's humor is based on "a deep comprehension of human nature," or a profound understanding of what it means to be human. Choice (A) is incorrect. According to the sentence in lines 20-23, Twain's popularity, or widespread public acclaim, is not the result of a tricky or adept use of literary style. Choice (B) is incorrect. In lines 20 to 21, the author denies that Twain's popularity, or widespread public acclaim, results from "any breadth of knowledge, or . . . depth of intellectuality." Choice (D) is incorrect. In lines 26-27, the author claims that Twain's humor can be translated easily into other languages, not that Twain himself was familiar with those languages. Choice (E) is incorrect. The author argues that Twain's humor is not ethnic or local, but universal.

16. (B) The area for this question is lines 34 to 38. Twain is trying to

suggest that his ‘secret’ is his ability to remark only on universal human truths, not merely details particular to one area. (A) is incorrect because Twain tries to complete remove these local details from his work, not mix them in. (C) is incorrect because Twain is not trying to ‘place the specific’ at all. (D) is incorrect because Twain is not discussing how to restate old truths. (E) is incorrect because Twain wants his humor to be “independent of local conditions,” so why would he try to reap its benefits? (B) is correct because Twain takes out the local references from his writing in order to let people read about what is universal about humanity. Alternate Explanation: Choice (B) is correct. Twain is saying that in order to "create humor independent of local conditions," or to create a more universal humor, he removes the obstacles to universal humor that local ideas present. Choice (A) is incorrect. To "winnow out" means to get rid of something, not to mix it with something else.


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Choice (C) is incorrect. Instead of placing the specific, or local, in context, according to the sentence, Twain seeks to eliminate the local altogether. Choice (D) is incorrect. Twain is speaking of removing obstacles, not expressing truth. Choice (E) is incorrect. By the expression "winnow out," Twain means that he ignores local customs when they hinder understanding universal truths, not that he reaps the benefits of the local customs.

17. (B) The area for this question is the entire first passage. The

passage mainly deals with Twain’s ability to write for an international audience. To undermine this, the choice would have to state that Twain’s avoidance of local customs was not good. (A) is incorrect because the piece is not about ‘morality.’ (C) is incorrect because this is not the focus of the passage. (D) is incorrect because Twain never claimed that this was a strength of his. (E) is incorrect because this agrees with Twain’s point in the first passage. (B) is correct because if cultural differences were so influential, Twain’s writing would not have been as able to reach an international readership. Therefore, this statement would undermine the first author’s point. Alternate Explanation: Choice (B) is correct. If some cultural differences could not be transcended, or risen above, then the author's argument that looking beyond cultural differences is the basis of Twain's humor would be seriously undermined. Choice (A) is incorrect. The discovery of a link between humor and a sense of morality would not necessarily undermine the argument that Twain's humor is based on universal rather than local characteristics. Choice (C) is incorrect. The combination of imagination and humor is precisely the way the author defines American humor. If this were proven true, the argument would be strengthened, not undermined. Choice (D) is incorrect. The passage quotes Twain as saying that his experience and knowledge of particular localities has enabled him to find universal humor, so the idea that a humorist must have such knowledge would not undermine the author's argument. Choice (E) is incorrect. The author quotes Twain as agreeing that "[h]umor, like morality, has its eternal verities," or perpetual truths. If this were proven true, the argument would be strengthened, not undermined.

18. (A) The area for this question is the entire second passage. The author states that the best humorists used their humor sparingly and in a wise manner, not “at every turn [slapping] their readers on the back.” (B) and (C) are incorrect because the first passage, not this one, is about local customs and different nations. This passage does not touch upon this area. (D) is incorrect because the author’s claim is that Twain is not refined enough, not too refined. (E) is incorrect because Twain’s ability as a public speaker is not the focus. (A) is correct because the author feels that his list of humorists were able to use subtle humor, which he thinks Twain’s writing lacks. Alternate Explanation: Choice (A) is correct. Throughout all of Passage 2, the author argues that, unlike "the true humorists," Aristophanes, Shakespeare, and Chaucer, Twain exhibits no sense of restraint or subtlety in his humor. According to the author, because Twain continually jokes at everything, keeping nothing sacred, his humor lacks the subtle unexpected quality of the masters. The literary masters "laughed in moderation and with a wise purpose," while Twain cannot refrain from "grinning at grave and beautiful things."

Choice (B) is incorrect. The author of Passage 2, in fact, criticizes Twain for not ignoring local customs. According to the author, Twain mocks any custom that does not conform to the culture of the United States. Choice (C) is incorrect. The author of Passage 2 accuses Twain of mocking all nations other than the United States. The author does not claim that Twain confuses the standards, rather that he inappropriately thinks that the standards of all nations should conform to those of the United States. Choice (D) is incorrect. Far from suggesting that Twain tries to seem refined, Passage 2 implies that Twain's humor "turns whatever is beautiful or noble into a stupid jest." Choice (E) is incorrect. There is no indication in the passage that the author distinguishes between Twain's performance as a public speaker and his performance as a writer.

19. (E) The area for this question is the entire second passage. The author feels Twain’s writing is crude. (A) and (D) are incorrect because an “aristocrat” and a “visionary” would not correspond to crude writing. (B) is incorrect because the author does not state who Twain would be conforming (trying to imitate) to. (C) is incorrect because Twain is not defending any particular issue. (E) is correct because a chauvinist is a person who lacks refinement, which corresponds with the author’s opinion of Twain. Alternate Explanation: Choice (E) is correct. The statement in Passage 2 that Twain "finds every custom ridiculous that does not conform with the standard of the United States" suggests that Twain is a chauvinist, one who shows an extreme preference for a particular group or place. Choice (A) is incorrect. The negative view of Twain's humor, for example, calling one of Twain's works "a masterpiece of vulgarity," suggests that the author of Passage 2 would not describe Twain as having the refined manners of an aristocrat. Choice (B) is incorrect. There is no evidence in the passage that the author would describe Twain as a reformer, one who wishes to correct whatever is defective, corrupt, or evil. Choice (C) is not correct. The passage suggests that rather that being an apologist, one who defends someone or something, Twain uses humor to attack and undermine "whatever is beautiful or noble." Choice (D) is incorrect. There is nothing in the passage that indicates whether the author would describe Twain as a dreamer or a visionary, one whose ideas are idealistic or impractical.

20. (B) The area for this question is lines 71 to 74. The author is stating that Twain would be even more famous if he had not tried to write humorous pieces. (A) is incorrect because the author states that the vulgarity and crudeness are what prevent Twain from enjoying fame. (C) is incorrect because the sentence is not about comedic technique. (D) is incorrect because the author never calls Twain an amateur in this sentence. (E) is incorrect because the author never suggests that Twain will be failure, nor does he mention any “insensitivity to his audience.” (B) is correct because the author is stating that Twain’s attempts at humor hurt his writing. Alternate Explanation: Choice (B) is correct. According to the last sentence in the passage, if Twain had "never cut a joke," that is, if Twain had not tried to be humorous, he would have achieved a "brilliant" fame as a writer. Choice (A) is incorrect. Although the author of Passage 2 criticizes Twain for his vulgarity earlier in the passage, the subject of the last sentence in the passage is the effect the author believes


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that Twain's attempts at humor had on his work. Choice (C) is incorrect. The last sentence in the passage indicates that the author believes that Twain would have had to avoid comedy altogether in order to have "brilliant" fame. Choice (D) is incorrect. There is no indication in the sentence that the author saw Twain as an amateur or a dilettante, one who has a superficial interest in the arts. Choice (E) is incorrect. There is no indication that the author of Passage 2 thinks of Twain as likely to be a failure; nor is there any suggestion that Twain's own audience thinks of him as insensitive.

21. (B) The area for this question is the entire second passage. The author’s point is that humorists should not be too offensive and should respect certain things, instead of making fun of anything they can. The correct choice should add support to this theme. (A) is incorrect because the author is criticizing Twain, who writes offensive satire, but the subject of that satire is not “literary greatness.” (C) is incorrect because this is not the focus of the essay. (D) is incorrect because the author never claims that Twain ridiculed past writers. (E) is incorrect because the author’s point is not that the modern writers are not insightful but rather that they go too far. (B) is correct because the author is trying to show that old writers respected certain areas, whereas modern writers try to inject humor into any topic. Alternate Explanation: Choice (B) is correct. The idea that certain subjects are not easily satirized, or held up to ridicule, supports the argument that certain subjects should not be ridiculed. As the author of Passage 2 argues, "there are certain manifestations of genius which should be sacred even for the jester" but that modern humor, like that of Twain, treats every subject with ridicule. Choice (A) is incorrect. The idea that any sort of greatness can be subjected to offensive satire is inconsistent with the argument that certain subjects should not be ridiculed. Choice (C) is incorrect. Whether intelligent people appreciate certain kinds of humor is irrelevant to the argument that certain subjects should not be ridiculed. Choice (D) is incorrect. The reception humorists are likely to receive is irrelevant to the argument that certain subjects should not be ridiculed. Choice (E) is incorrect. Although the author of Passage 2 does suggest that contemporary humorists are less insightful than past writers, this idea is irrelevant to the argument that certain subjects should not be ridiculed.

22. (A) The area for this question is the first passage. The author states that Twain has made as many damaging admissions about the United States as any other place. (B) and (C) are incorrect because they do not reply adequately to the second author’s claim. (D) is incorrect because the first author’s point is that Twain’s style appeals to all and is not just “uniquely American.” (E) is incorrect because the first author never states this. (A) is correct because this choice reflects what the first author wrote in his passage, that Twain criticizes the United States more than any other place. Alternate Explanation: Choice (A) is correct. The author of Passage 1 claims that, in addition to showing respect for others by having "sympathized with and admired the citizens of every nation," Twain "has made far more damaging admissions concerning America than concerning any other nation." It is clear that Twain's sympathy and respect for other nations, combined with his willingness to criticize

America, is evidence that he reserves, or keeps, his harshest criticism for America. Choice (B) is incorrect. The author of Passage 1 does imply that Twain is a great journalist, but this statement is not a response to the statement about Twain's use of ridicule. Choice (C) is incorrect. There is no indication in Passage 1 that the author believes that Twain's popularity was due to his being American. Choice (D) is incorrect. Unlike the author of Passage 2, the author of Passage 1 suggests that Twain's humor is not uniquely American but is based on "a deep sympathy for human relationships and human failings." Choice (E) is incorrect. The idea that Twain is fascinated by American culture is not suggested in Passage 1.

23. (E) The area for this question is both passages. Remember that the

first author likes Twain, whereas the second does not. We can eliminate (B) because “envy” is not positive. We can also remove (C) because “embarrassment” does not relate to Passage 2. Looking more closely at Passage 1, the author is praising Twain (the humorist), but not really having fun with the term ‘humorist,’ so “amusement” cannot be correct. (D) is incorrect because the second author does not like the term at all, so “smugness” (self-satisfaction) does not fit. (E) is correct because the first term is positive, and “disdain” (does not care for) fits with the second author’s attitude. Alternate Explanation: Choice (E) is correct. In Passage 1, the term "humorist" is applied to Twain by others though Twain himself claims to be unconcerned with humor. In Passage 2, the author portrays Twain the humorist as "a bull in the china shop of ideas," indicating a scornful view of Twain's humor. The respect felt by the author of Passage 1 is reflected in the description of Twain as a "genius." The disdain, or contempt, of the author of Passage 2 can be inferred from the negative remarks made in comparing Twain with the earlier literary masters. Choice (A) is incorrect. There is no evidence in Passage 1 that the author is amused by the term. Although the author of Passage 2 is critical of Twain as a humorist, "anger" would be too strong a word to describe the author's tone. Choice (B) is incorrect. Although the tone of the discussion in Passage 2 could be seen as mocking, there is no indication that the author of Passage 1 is envious of Twain or other humorists. Choice (C) is incorrect. There is no indication that the author of Passage 1 feels pride with regard to the term, or that the author of Passage 2 feels embarrassment. Choice (D) is incorrect. Though the author of Passage 1 seems to express approval of Twain as a humorist, the author of Passage 2 expresses contempt for modern humorists rather than the self-satisfaction that smugness suggests.

24. (C) The area for this question is the second passage. The second author feels that Twain’s humor is crude and too ‘American.’ He would respond by disagreeing. (A) is incorrect because this does not reflect the second author’s point. (B) is incorrect because the second author feels that Twain is not as good as the writers of the past, so “share” would not be a term he would use. (D) is incorrect because “humor for a wise purpose” contradicts the second author’s criticism of Twain. (E) is incorrect because the second author does not challenge “how funny” Twain is. (C) is correct because the second author thinks that Twain’s American perspective takes away from his writing.


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Alternate Explanation: Choice (C) is correct. The author of Passage 2 claims that Twain "finds every custom ridiculous that does not conform to the standard of the United States." This suggests that Twain's ability to understand other people and their customs is limited by his American perspective, or point of view. Choice (A) is incorrect. The author of Passage 2 claims that "The modern humorist [such as Twain] is never unexpected." Choice (B) is incorrect. The author of Passage 2 suggests that Twain does not share any characteristics with great humorists of the past. Choice (D) is incorrect. The author of Passage 2 argues that Twain's humor has no wisdom at all, and that it is largely characterized by irreverence, or disrespect. Choice (E) is incorrect. The author of Passage 2 does not claim that Twain is not funny, but rather that he never stops trying to be funny.

Section 4 1. (B) The original sentence is grammatically incorrect. The

underline portion is not parallel with the remainder of the sentence. (A) is incorrect. ‘There were’ fails to follow the same parallel form as the rest of the sentence. The sentence follows the form “were a drawing room with a piano, bath fixtures of silver…” Thus, to follow the correct parallel form, the underline portion should read “draperies trimmed with Brussels lace”. (B) is correct. ‘Draperies trimmed with Brussels lace’ follows the same form as “bath fixtures of silver”. (C) is incorrect. ‘Trimmed with Brussels lace’ is not in the same form as “bath fixtures of silver”. ‘Trimmed’ is a verb while “bath fixtures” is a noun. (D) is incorrect. Use of the word ‘the’ in front of ‘draperies’ is different from the form “bath fixtures of silver” which uses no ‘the’. Thus this choice is not parallel. (E) is incorrect. The addition of ‘were there’ at the end of the choice incorrectly adds two verbs into the sentence. The sentence would read “Inside… [the] railroad car were… draperies trimmed with Brussels lace were there”. Alternate Explanation: Choice (B) is correct. It avoids the error of the original by making the third item in the series a noun phrase, as the other two items are. Choice (A) involves an error in parallelism. The third item in the series should be a noun phrase like the other two ("a drawing room with a piano," "bath fixtures of silver"), not an independent clause. Choice (C) involves an error in parallelism. The third item in the series should be a noun phrase like the other two ("a drawing room with a piano," "bath fixtures of silver"), not an independent clause. Choice (D) involves an error in parallelism. The third item in the series should be a noun phrase like the other two ("a drawing room with a piano," "bath fixtures of silver"), not an independent clause. Choice (E) involves an error in parallelism. The third item in the series should be a noun phrase like the other two ("a drawing room with a piano," "bath fixtures of silver"), not an independent clause.

2. (D) The original sentence is grammatically incorrect. “Has been” is in the incorrect tense. It should follow the same tense as the rest of the sentence. (A) is incorrect. ‘Has been’ is in the incorrect tense. The word “was” indicates that the sentence is in simple past tense. Thus ‘has been’ should be changed to the simple past ‘was’. (B) is incorrect. ‘Had been’ is in the incorrect tense. It should be changed to simple past in order to follow the word “was”, which was earlier in the sentence. (C) is incorrect. The use of ‘having’ makes this choice sound awkward. (D) is correct. The choice

correctly changes “has been” to its simple past form ‘was’ in order to fit with the earlier “was” in the sentence. (E) is incorrect. The use of ‘having been’ sounds awkward. Alternate Explanation: Choice (D) is correct. It avoids the error of the original by using the past tense consistently. Choice (A) involves an error in verb tense. It shifts from past tense ("was") to present perfect tense ("has been") for no reason. Choice (B) involves an error in verb tense. It shifts from past tense ("was") to present p erfect tense ("had been") for no reason. Choice (C) involves an error in verb form. The participle "Having conceived" should be the infinitive form "to conceive." Choice (E) creates a fragment. There is no subject for the verb "having been."

3. (C) The original sentence is grammatically incorrect. The pronoun

“it” refers to “plans”. Since “it” is singular while “plans” is plural, “it” should be changed to its plural form “them”. (A) is incorrect. ‘It’ is still incorrectly in its singular form. (B) is incorrect. ‘It’ is still incorrectly in its singular form. (C) is correct. ‘It’ has been correctly changed to its plural form ‘them’. (D) is incorrect. ‘Is’ is in the incorrect tense. Since the first part of the sentence is in simple past as indicated by the word “were”, ‘is’ should also be in its simple past form instead of its present form. ‘Is’ should be changed to ‘was’. (E) is incorrect. ‘It’ is still incorrectly in its singular form. Alternate Explanation: Choice (C) is correct. It avoids the error of the original by using a plural pronoun ("them") to refer to the plural noun "plans." Choice (A) involves an error in agreement. The singular pronoun "it" cannot correctly refer to the plural noun "plans." Choice (B) involves improper modification. To modify the verb "made," "hasty" should be "hastily”. Choice (D) involves improper modification. To modify the verb "made," "hasty" should be "hastily." Choice (E) involves an error in agreement. The singular pronoun "it" cannot correctly refer to the plural noun "plans."

4. (B) The original sentence is awkward. “It is because” is awkward

because “it is” is unnecessary and makes the sentence longer without purpose. (A) is incorrect. This choice is awkwardly phrased. ‘It is’ is unnecessary and sounds awkward. (B) is correct. This is the most concise and grammatically correct choice. (C) is incorrect. Use of ‘for the reason’ instead of “because” sounds more awkward. Additionally ‘with resulting wariness’ is an awkward use of an –ing word. (D) is incorrect. ‘Of knowing very little’ is an awkward use of a –ing word. (E) is incorrect. The use of the comma between ‘practices’ and ‘their’ is a comma splice. A comma is not enough to connect two independent thoughts. A conjunction (such as because) or a period and a new sentence is needed. Alternate Explanation: Choice (B) is correct. It avoids the error of the original by using a second verb phrase ("are therefore wary of it as a result") instead of a second independent clause. Choice (A) involves improper coordination. Two complete thoughts ("Many...practices" and "it...result") are joined by only a comma. Choice (C) involves improper phrasing. Whose "wariness" is being referred to is not clear. Choice (D) involves improper coordination. Two complete thoughts ("Many...it" and" therefore...result") are joined only by a


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conjunction ("and"), without a comma to proceed it. Choice (E) involves improper pronoun case. "It" should be "its."

5. (E) The original sentence is grammatically incorrect. The verb “was” refers to “two”. Since “two” is plural, “was” should be in its plural form “were”. (A) is incorrect. ‘Was’ is still incorrectly in its singular form. (B) is incorrect. ‘Was’ is still incorrectly in its singular form. (C) is incorrect. ‘Was’ is still incorrectly in its singular form. (D) is incorrect. The phrase ‘the calling’ sounds awkward. Use of the word ‘the’ is unnecessary and makes the sentence sound awkward. (E) is correct. ‘Was’ has correctly been changed to its ‘were’ form. Additionally this is the most fluent grammatically correct choice. Alternate Explanation: Choice (E) is correct. It avoids the error of the original by using a plural verb ("were") for the subject "two." Choice (A) involves an error in agreement. The subject "two" requires a plural verb ("were"). Choice (B) involves an error in agreement. The subject "two" requires a plural verb ("were"). Choice (C) involves an error in agreement. The subject "two" requires a plural verb ("were"). Choice (D) involves wordiness. The wordy phrase "the calling of them" should simply be "calling them."

6. (B) The original sentence is grammatically incorrect. The semicolon is used incorrectly. A semicolon by itself is a conjunction, there is no need to follow it with the additional conjunction “and”. Thus either the semicolon or “and” needs to be eliminated. (A) is incorrect. The conjunction “and” follows the semicolon. (B) is correct. By replacing the semicolon with a comma, the answer choice uses the correct punctuation. A comma is placed before “and” when the second clause contains its own subject. In this case, the second clause contains the subject “he”, therefore the comma is appropriate. (C) is incorrect. This is a comma splice. The comma is not enough to connect two independent thoughts. An additional conjunction is needed. (D) is incorrect. The usage of ‘To think’ makes the answer choice awkward and slightly alters its meaning. Now the sentence means ‘the grandson has the blue ribbons in order to think that he is better’, rather than ‘the grandson thinks he’s better and also he has blue ribbons to prove it’. (E) is incorrect. The use of ‘Thinking’ makes the answer choice sound awkward. The clause ‘Thinking… fair’ implies that the grandson is thinking while he is doing something else (an active action, like fishing). However, the clause modifies a passive action (having ribbons) rather than an active one. This makes the answer choice sound awkward. Alternate Explanation: Choice (B) is correct. It avoids the error of the original by using a comma to link two independent clauses joined by the conjunction "and." Choice (A) involves improper coordination. It uses a semicolon where a comma is necessary. Choice (C) creates an illogical sentence. It illogically suggests that the grandson's having blue ribbons is a result of his thinking that he is the best cook at the fair. Choice (D) results in an illogical sentence. There is no relationship between the idea in the first part of the sentence ("To think . . . fair") and the idea in the last part of the sentence ("my grandson . . . to prove it."). Choice (E) creates an illogical sentence. It does not make sense to say that the blue ribbons that the grandson had somehow prove that he was "thinking he can cook better . . . fair."

7. (B) The original sentence is grammatically incorrect. The sentence

contains a faulty comparison. Apples need to be compared with apples. The same object needs to be compared with the same object. In this sentence, “Greeks” are compared with “Roman theaters”. People cannot be compared with objects. (A) is incorrect. ‘Greeks’ is incorrectly compared with ‘Roman theaters’. People cannot be compared with objects. (B) is correct. ‘Greek theaters’, a theater, is correctly compared with ‘Roman theaters’, a theater. Since a theater is compared with a theater, the comparison is correct. (C) is incorrect. ‘Greeks’ is incorrectly compared with ‘Roman theaters’. People cannot be compared with objects. (D) is incorrect. The revision changes the meaning of the sentence. Instead of stating that the difference is between Greek theaters and Roman theaters, the answer choice now states that the difference is between Greeks and Romans. People are usually not described as freestanding or part of a hillside. (E) is incorrect. The answer choice contains an ambiguous pronoun reference. The pronoun ‘they’ could refer to either ‘Greek theaters’ or ‘Roman theaters’. Alternate Explanation: Choice (B) is correct. It avoids the error of the original by correctly comparing "Greek theaters" to "Roman theaters." Choice (A) involves an illogical comparison. It compares "the Greeks" with "the Roman theaters." Choice (C) involves an illogical comparison. It compares "the Greeks" with "the Roman theaters." Choice (D) involves improper coordination. Two complete thoughts ("The Greeks...Romans" and "they...hillside") are joined by only a comma. Choice (E) involves an error in pronoun reference. There is no place to which "where" can refer.

8. (D) The original sentence is grammatically incorrect. The tense of

“are obscuring” and “clarifying” is incorrect. Instead, the simple present tense should be used to make the sentence sound more concise. Additionally, the sentence contains a pronoun-subject error. The plural pronoun “they” refers to the singular subject “chronological order”. Thus “they” should be changed to its singular form. (A) is incorrect. Use of ‘are obscuring’ and ‘clarifying’ makes the sentence sound awkward. (B) is incorrect. ‘Clarifying’ conflicts with the tense of ‘obscures’. Both should be in the same tense. Thus ‘clarifying’ should be changed to ‘clarifies’. (C) is incorrect. The use of the pronoun ‘it’ before ‘clarifies’ is unnecessary and makes the sentence sound awkward. (D) is correct. ‘Clarifies’ and ‘obscures’ are both in their simple present tense. (E) is incorrect. This choice is longer and less concise than choice (D). Thus choice (D) rather than choice (E) is the correct answer. Alternate Explanation: Choice (D) is correct. It avoids the error of the original by omitting the plural pronoun ("they"), which did not agree with the singular noun "chronological order." Choice (A) involves an error in agreement. The plural pronoun "they" is used incorrectly to refer to the singular noun "chronological order." Choice (B) involves an error in verb form. The verb "clarifying" should be "clarifies." Choice (C) involves a pronoun error. The pronoun "it" is unnecessary. Choice (E) involves a pronoun error. It is not clear what the pronoun "it" is meant to refer to.


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9. (C) The original sentence is grammatically correct. (A) is incorrect. This is not the shortest, most concise, and grammatically correct choice. (B) is incorrect. This choice is longer and more awkward than choice (C). Thus it is not preferred. (C) is correct. This is the shortest, most concise, grammatically correct choice. Additionally, it is slightly parallel. The use of ‘eaten by people’ follows the same form as “fed to animals”. Typically, “fed” is used for animals and infants, while “eat” is used for people. The rationale is that people have a choice to eat, while feeding implies no choice. (D) is incorrect. This choice is longer and less concise than choice (C). (E) is incorrect. This choice is longer and less concise than choice (C). Alternate Explanation: Choice (C) is correct. It avoids the error of the original by avoiding unclear pronoun usage. Choice (A) involves an error in pronoun reference. "There" does not refer to anything in the sentence. Choice (B) involves wordiness. The wordy phrase "consumption is not done much by people" should be simply "are rarely consumed by people" or "are rarely eaten by people." Choice (D) involves an error in pronoun reference. The pronoun "them" incorrectly refers to the closest previous plural noun, "farm animals." Choice (E) involves an unclear reference. The object of "consumption" is not clear.

10. (A) The original sentence is grammatically correct. (A) is correct.

This is the shortest, most concise, grammatically correct choice. (B) is incorrect. This answer choice removes all verbs from the sentence, making the sentence grammatically incorrect. (C) is incorrect. Starting the answer choice with ‘there’ is awkward. ‘There’ is the incorrect preposition to follow “stressed”. Instead, “stressed” should be followed with “that” in order to clarify what the educator stressed. (D) is incorrect. ‘And everyone will gain’ is incorrect. Since the first part of the answer choice begins with a noun phrase ‘a need for… programs’, the second part of the answer choice should also be a noun phrase. However ‘everyone will gain’ does not follow that form. (E) is incorrect. The use of ‘being’ and ‘gaining’ is awkward. Use of –ing words tends to make a sentence sound awkward. Alternate Explanation: Choice (A) is correct. It correctly uses a relative clause (introduced by "that") to indicate what the educator was stressing. Choice (B) involves improper verb form. The verb "needed" lacks an auxiliary verb ("are"). Choice (C) involves improper coordination. Two complete thoughts ("The educator's...programs" and "everyone...society") are joined by only a conjunction ("for"), without the comma that should precede it. Choice (D) involves improper coordination. Two complete thoughts ("The educator's...programs" and "everyone...society") are joined by only a conjunction ("and"), without the comma that should precede it. Choice (E) creates an illogical sentence. A noun can be "stressed," but an adverb ("why") cannot.

11. (C) The original sentence is grammatically incorrect. The use of the preposition “of” after “because” is idiomatically incorrect, since “of” is used to show possession, but the pronoun “their” already indicates possession (it is in the possessive form). (A) is incorrect. The use of ‘of’ is idiomatically correct. (B) is incorrect. The use of ‘of’ is idiomatically correct. (C) is correct. This choice

eliminates the use of “of” and is the shortest, most concise, grammatically correct choice. (D) is incorrect. Since ‘the songs’ indicates no possession, the preposition ‘of’ should be added to indicate possession. (E) is incorrect. The choice contains an incorrect pronoun reference. The pronoun ‘their’ should refer to the Portuguese. However, the Portuguese are not mentioned in the sentence, and thus they cannot be referenced. Alternate Explanation: Choice (C) is correct. It avoids the error of the original by using the pronoun "its," which correctly refers to the noun "The Portuguese...fado." Choice (A) involves an error in pronoun reference. The pronoun "their" does not refer to anything that comes before it. Choice (B) involves an error in pronoun reference. The pronoun "their" does not refer to anything that comes before it. Choice (D) creates a fragment. The subordinate clause "that...love" is not completed. Choice (E) involves an error in pronoun reference. The pronoun "their" does not refer to anything that comes before it.

12. (B) (A) contains no error. “gather” is correctly in its plural form to reflect its plural subject “toy manufactures”. (B) is the answer. “as predicting” is grammatically incorrect. Idiomatically, the phrase should be “to predict” instead of “as predicting”. (C) contains no error. “which” is correctly used to refer to an object. (D) contains no error. “most popular” is correctly used. Alternate Explanation: Corrected Sentence: Every year, toy manufacturers gather groups of children into playrooms, observing their choices of toys and predicting which new products will become the most popular. The error in this sentence occurs at (B), where there is an incomplete verb form. The word "as" cannot properly join the verbs "observing" and "predicting" to form the compound predicate. Instead, the conjunction "and" should be used. There is no error at (A). The verb "gather" appropriately agrees with its subject, "toy manufacturers." There is no error at (C). The relative pronoun "which" appropriately refers to the noun "new products" in describing the kinds of products that "will become most popular." There is no error at (D). The adverb "most" properly modifies the adjective "popular." There is an error in the sentence.

13. (B) (A) contains no error. “During the last” is grammatically correct. “During” is the correct preposition to use. (B) is the answer. “come” is in the incorrect tense. It should be changed to “have come”, because “during the last fifty years” indicates that “come” should not be in the simple past form. (C) contains no error. “to take” uses the correct preposition “to”. (D) contains no error. “in such” is correctly used. Alternate Explanation: Corrected Sentence: During the last fifty years, we have come to take radio communication for granted, but the mere suggestion that we could communicate in such a fashion must once have seemed outlandish. The error in this sentence occurs at (B), where there is an improper verb tense. The introductory prepositional phrase "During the last fifty years" establishes that the action of the main clause (taking radio communications for granted) takes place over the whole period. Therefore, the present -tense verb, "come" should be in the present perfect tense ("have come"). There is no error at (A). The preposition "During" is an appropriate and necessary part of the prepositional phrase "During the last fifty years." There is


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no error at (C). The infinitive "to take" appropriately introduces its object, "radio communications." There is no error at (D). The preposition "in" appropriately introduces the prepositional phrase "in such a fashion," and the adjective "such" appropriately modifies "a fashion." (E)There is an error in the sentence.

14. (C) (A) contains no error. “uncompromising” is an adjective that

correctly modifies “tone”. (B) contains no error. “concerning” is correctly used. (C) is the answer. The subject of “carry” is “tone”. Since “tone” is singular, “carry” should be changed to its singular form “carries”. (D) contains no error. “to” is the correct preposition to use. Alternate Explanation: Corrected Sentence: The uncompromising tone of a recent city call ordinance concerning the blocking of emergency vehicles in traffic jams carries a stern warning to motorists. The error in this sentence occurs at (C), where there is subject-verb disagreement. The plural verb "carry" cannot refer to the singular subject, "The uncompromising tone." The singular verb "carries" is needed. There is no error at (A). The adjective "uncompromising" appropriately modifies the noun "tone." There is no error at (B). The participle "concerning" appropriately modifies the preceding noun "ordinance." There is no error at (D). The preposition "to" properly links the noun phrase "a stern warning" to the noun "motorists." There is an error in the sentence (E).

15. (B) (A) contains no error. “over” is correctly used as a preposition.

(B) is the answer. “containing” is not used as a verb. Thus it should be changed to its verb form “contain”. (C) contains no error. “incredibly wide” is grammatically correct. “Incredibly” is an adverb that modifies “wide”. (D) contains no error. “nowhere else” is used correctly. It fits idiomatically with the rest of the sentence. Alternate Explanation: Corrected Sentence: Formed by volcanic eruptions over the last five million years, the Hawaiian Islands contain an incredibly wide variety of species--many found nowhere else on Earth. The error in this sentence occurs at (B), where a sentence fragment is created. The use of the participle "containing," instead of the present-tense "contain," leaves the sentence without a main verb. There is no error at (A). The preposition "over" properly introduces the prepositional phrase "over the last five million years," which establishes when the volcanic eruptions took place. There is no error at (C). The adverb "incredibly" appropriately modifies the adjective "wide." There is no error at (D). The phrase "nowhere else" properly indicates that the "wide variety of species" are found mainly in one place. There is an error in the sentence (E).

16. (B) (A) contains no error. “is usually nocturnal” is grammatically

correct. The verb “is” correctly fits its subject “owl”. Both words are in their singular form. (B) is the answer. “plus being” is grammatically incorrect. Although when speaking, the word “plus” may be used instead of “and”, in writing the two words are not interchangeable. “Plus” creates an error because it is not enough to link the two parts of the sentence. Instead a conjunction, such as “and”, should be used. (C) contains no error. “it” is correctly used as a pronoun. The subject of “it” is “owl”. Both words are appropriately singular. (D) contains no error. “is seldom seen” is

grammatically correct. “is” is correctly in its singular form to fit its subject “it”. Alternate Explanation: Corrected Sentence: Because the owl is usually nocturnal and is virtually noiseless in flight, it is seldom seen by the casual observer. The error in this sentence occurs at (B), where there is an awkward construction. The phrase "and is" should be used in place of "plus being" to properly join one characteristic (nocturnal behavior) with the other (noiselessness in flight). There is no error at (A). The singular verb, "is," agrees with its singular subject, "the owl," and the adverb "usually" properly modifies the adjective "nocturnal." There is no error at (C). The pronoun "it" refers correctly to the noun "the owl." There is no error at (D). The singular verb "is" agrees with its singular subject ("the owl"), and the adverb "seldom" appropriately modifies the verb "seen." There is an error in the sentence (E).

17. (C) (A) contains no error. “economical and efficient” is

grammatically correct. Both words are correctly used adjectives that describe the “recycling center”. (B) contains no error. “is accessible” correctly uses “is” in its singular form, because its subject is “recycling center”. (C) is the answer. “comply with” is grammatically incorrect. Whenever something is in a list, it is assumed that the original verb carries over. Thus, the list reads “is accessible… (is) responsive… and (is) comply with”. Since “is comply with” incorrectly places two verbs next to each other, “comply with” should be changed to “in agreement with”. (D) contains no error. “governing” is correctly used. Alternate Explanation: Corrected Sentence: An economical and efficient recycling center is accessible to the public, responsive to community needs, and complies with current federal regulations governing waste disposal. The error in this sentence occurs at (C), where there is subject-verb disagreement. The plural verb "comply" does not agree with its singular subject ("recycling center"). There is no error at (A). The compound adjective, "economical and efficient," appropriately modifies "recycling center." There is no error at (B). The singular verb "is" agrees with its singular subject, "recycling center," and the adjective "accessible" appropriately modifies "recycling center" to indicate one aspect (accessibility) of an "economical and efficient" recycling center. There is no error at (D). The participle "governing" appropriately indicates the kind of regulations being discussed (those governing waste disposal). There is an error in the sentence (E).

18. (E) (A) contains no error. “not only” is correctly used, since “but

also” follows later in the sentence. The idiomatic phrase is “not only -----, but also -----”. (B) contains no error. “has been viewed” is in the correct tense indicating an event has happened in the past and may continue in the present. (C) contains no error. “as making” is idiomatically correct. (D) contains no error. “among Quakers” is idiomatically correct. Alternate Explanation: Choice (E) is correct. There is no error in this sentence. There is no error at (A). The phrase "not only" operates appropriately as the first part of the correlative construction "not only . . . but also."


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There is no error at (B). The tense of the verb correctly indicates that the action described (the way the novel is viewed) is still going on. There is no error at (C). The adverb "as" joins with the participle "marking" to produce an appropriate idiom. There is no error at (D). The preposition "among" joins with the plural noun "Quakers" to correctly describe where Toomer was "a respected advisor."

19. (B) (A) contains no error. “came in” is correct. “Came” is in the

correct tense, and “in” is the correct preposition. (B) is the answer. “quite rapid” is incorrect, because “rapid” should be an adverb, because it describes the way in which the returns “came in”. Thus “rapid” should be changed to “rapidly”. (C) contains no error. “were known” is correct. “Were” is correctly plural for its subject “results”. (D) contains no error. “even faster” is correct. In a comparison of two objects, -er is used not -est. Alternate Explanation: Corrected Sentence: Election results came in from upstate New York quite rapidly, but the results from New York City were known even faster. The error in this sentence occurs at (B), where an adjective ("rapid") is incorrectly used to modify the verb "came." The adverb "rapidly" is needed. There is no error at (A). The preposition "in" appropriately modifies the verb "came" to indicate where the election results came from. There is no error at (C). The past tense of the verb is consistent with the tense previously established by the past-tense verb "came." There is no error at (D). The adverb "even" appropriately modifies the adjective "faster" to indicate how quickly the results were known. There is an error in the sentence (E).

20. (B) (A) contains no error. “As” is the correct preposition to use.

(B) is the answer. “your” is grammatically incorrect because the sentence starts with “we”. Thus “your” should be in the same plural form, which in this case would be “our”. (C) contains no error. “to safeguard” is idiomatically correct. (D) contains no error. “has increased” is correctly used to indicate an event that has happened in the past. Alternate Explanation: Corrected Sentence: As we rely more and more on the Internet, the need for effective security planning and design to safeguard data has increased. The error in this sentence occurs at (B), where there is an error in pronoun use. There is nothing in the sentence to which the possessive pronoun "your" can logically refer. There is no error at (A). The subordinating conjunction "As" appropriately introduces the dependent clause ("As we rely . . . on the Internet"). There is no error at (C). The infinitive "to safeguard" appropriately indicates the purpose of "effective . . . design" (to safeguard data). There is no error at (D). The tense of the verb "has increased" appropriately indicates that the action described (the increasing need for effective planning) is ongoing. There is an error in the sentence (E).

21. (E) (A) contains no error. “Is” in “is essentially” is correctly singular for its subject “book”. (B) contains no error. “very well documented” correctly indicates how well documented the book is. (C) contains no error. “of what” correctly uses the preposition “of”. (D) contains no error. “each of” is the correct idiomatic phrase.

Alternate Explanation: Choice (E) is correct. There is no error in this sentence. There is no error at (A). The singular verb "is" agrees with its singular subject "the book," and the adverb "essentially" appropriately modifies the verb "is." There is no error at (B). The adverbs "very" and "well" combine to appropriately modify the adjective "documented." There is no error at (C). The preposition "of" combines with the relative pronoun "what" to produce an appropriate idiom indicating what was documented in the book. There is no error at (D). The pronoun "each" combines with the preposition "of" to form an appropriate idiom linking "what happened" to the group to which it happened.

22. (C) (A) contains no error. “agree that” is grammatically correct.

“Agree” is correctly in its plural conjugation for its plural subject “experts”. (B) contains no error. “merely dieting” is grammatically correct. “Merely” is correctly used as an adverb to describe “dieting”. (C) is the answer. “are the key” incorrectly conjugates “are”. The subject for “are” is “permanently modifying eating and exercise habits”. This subject is singular, because “modifying eating and exercise habits” is one action. Thus, “are” should be conjugated in its singular form “is”. (D) contains no error. “to controlling” is grammatically correct. “to” is the correct preposition for “controlling”. Alternate Explanation: Corrected Sentence: Experts agree that permanently modifying eating and exercise habits rather than merely dieting for brief periods is the key to controlling weight. The error in this sentence occurs at (C), where there is an incorrect verb form. The plural verb "are" should be the singular "is" to agree with the singular gerund, "modifying eating and exercise habits." There is no error at (A). The plural verb ("agree") agrees with its subject, "Experts," and the relative pronoun "that" appropriately introduces the phrase that immediately follows. There is no error at (B). The gerund "dieting" is appropriately modified by the adverb "merely." There is no error at (D). The preposition "to" properly links the noun "the key" with the gerund "controlling weight." There is an error in the sentence (E).

23. (D) (A) contains no error. “to control” is idiomatically correct.

The preposition “to” fits with “control”. (B) contains no error. “is” is correctly conjugated. “Is” is singular for its singular subject “ability”. (C) contains no error. “have shown” is grammatically correct. “Have” is correctly plural for its plural subject “researchers”. (D) is the answer. “you want” is grammatically incorrect. Since the sentence previously used “we”, the entire sentence must be in the third person not second person. “You” should be changed to “we”. Alternate Explanation: Corrected Sentence: The ability to control the plots of our dreams is a skill, researchers have shown, that we can learn if we want to change recurrent dreams. The error in this sentence occurs at (D), where there is improper pronoun use. The second-person pronoun "you" should be changed to the first-person plural "we" to be consistent with the earlier use of "we." There is no error at (A). The infinitive "to control" prop erly modifies the preceding noun, "The ability." There is no error at (B). The singular verb "is" agrees with its singular subject, "The ability." There is no error at (C). The verb tense appropriately establishes that the action


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described (what researchers have determined about the ability to control dreams) has already taken place. E : There is an error in the sentence.

24. (B) (A) contains no error. “In” is the correct preposition to use in “In swimming”. (B) is the answer. “as to” is idiomatically incorrect. “As to” is not used to compare two sports. A more appropriate expression would be “as well as”. (C) contains no error. “an abler” correctly uses “an”. Whenever a vowel follows the word “a”, “a” is changed to “an”. (D) contains no error. “than” is correctly used to indicate a comparison. Alternate Explanation: Corrected Sentence: In swimming as in soccer, Evangelina proved time after time to be an abler competitor than Juanita. The error in this sentence occurs at (B), where there is an improper idiom. The preposition "in" should be used with the noun "soccer" to convey the idea that what happens "in swimming" is also what happens "in soccer." There is no error at (A). The preposition "in" combines with the gerund "swimming" to create an appropriate idiom. There is no error at (C). The comparative form of the adjective "able" is correct and properly modifies the noun "competitor." There is no error at (D). The conjunction "than" is used correctly to introduce the object of the comparison ("Juanita"). There is an error in the sentence (E).

25. (E) (A) contains no error. “one of our most” is grammatically correct. “Most” is correct because there are more than two diseases. “More” is used when comparing only two items. (B) contains no error. “it makes” correctly conjugates the pronoun “it”. Since the subject of “it” is the singular “common cold”, “it” is appropriately in its singular form. (C) contains no error. “distinction between” is idiomatically correct. “Between” is used to show a difference between two objects. (D) contains no error. While “you and me” sounds awkward, it is grammatically correct. “You” and “me” are both in their objective case, because they follow the preposition “between”. Additionally, the usage of “and” parallels the construction of the rest of the comparisons: “millionaires AND paupers”, “athletes AND couch potatoes”. (E) is the answer. The entire sentence is grammatically correct. Alternate Explanation: Choice (E) is correct. There is no error in this sentence. There is no error at (A). The pronoun "one" is used correctly to refer to "The common cold," and the preposition "of" appropriately introduces the prepositional phrase that modifies "The common cold." There is no error at (B). The pronoun "it" correctly refers to the noun "The common cold," and the singular verb "makes" agrees with its singular subject, "it." There is no error at (C). The noun "distinction" links appropriately with the preposition "between" to create an appropriate idiom. There is no error at (D). Both pronouns ("you" and "me") are properly in the objective case.

26. (A) (A) is the answer. “Like his other” is incorrect, instead “As in

his other” should be used. The two phrases “Like his other cookbooks” and “in his new book” need to be parallel, otherwise the comparison is not complete. The original phrase needs the word “in” to be parallel with “in his new book”. (B) contains no

error. “of what” correctly uses the preposition “of”. (C) contains no error. “he considers” is grammatically correct. “Considers” is correctly in its singular conjugation for its singular subject “he”. (D) contains no error. “to be” is the correct idiomatic phrase to use. Alternate Explanation: Corrected Sentence: As he does in his other cookbooks, in his new book Chef Louis offers lengthy explanations of what he considers to be basic cooking principles. The error in this sentence occurs at (A), where there is an illogical comparison. It would be appropriate to compare what is in "his other cookbooks" with what is in "his new book," but instead the sentence illogically compares a thing ("his other cookbooks") with a person ("Chef Louis"). There is no error at (B). The preposition "of" combines with the pronoun "what" to create an appropriate idiom. There is no error at (C). The pronoun "he" correctly refers to its antecedent "Chef Louis," and the singular verb "considers" agrees with its singular subject, "he." There is no error at (D). The infinitive "to be" joins with the verb "considers" to appropriately indicate what the "lengthy explanations" are about. There is an error in the sentence (E).

27. (C) (A) contains no error. “became” is correctly conjugated for its singular subject “Paul Ecke”. (B) contains no error. “known as” is idiomatically correct. “As” is the correct preposition to use in “known as”. (C) is the answer. “by pioneering” is grammatically incorrect, because the preposition “by” is not needed. Instead, simply “pioneering” would make the sentence flow better. (D) contains no error. “as a living symbol” is grammatically correct. “As” is idiomatically the correct preposition to use. Alternate Explanation: Corrected Sentence: Paul Ecke, flower grower and hybridizer, became known as "Mr. Poinsettia" after developing new varieties of the flower and pioneering it as a living symbol of Christmas. The error in this sentence occurs at (C), where there are excess words. The preposition "by" is unnecessary. There is no error at (A). The past-tense verb "became" appropriately establishes that Mr. Ecke was known a "Mr. Poinsettia" only after he developed "new varieties of the flower." There is no error at (B). The adjective "known" appropriately modifies the subject of the sentence "Paul Ecke." There is no error at (D). The preposition "as" joins with the noun phrase "a living symbol" to create an appropriate idiom. There is an error in the sentence (E).

28. (B) (A) contains no error. “thought of as” is grammatically

correct. “Thought” is correctly in its plural form for its subject “libraries”. “As” is the correct preposition to use. (B) is the answer. “a quiet, stuffy place” is grammatically incorrect, because it describes the plural subject “libraries”. “A” and “place” are both singular. Thus the choice should be changed to “quiet, stuffy places”. (C) contains no error. “people” is grammatically correct. It is not misspelled, and it is the correct word to use. (D) contains no error. “have been changing” correctly conjugates “have” in its plural form for its plural subject “libraries”. Alternate Explanation: Corrected Sentence: Long thought of as quiet, stuffy places where people just borrowed books, libraries have been changing their images dramatically over the last few years. The error in this


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sentence occurs at (B), where there is noun-noun disagreement. To agree with the plural "libraries," the singular noun "place" should be changed to the plural "places." There is no error at (A). The verb "thought" combines with the preposition "of" to create an appropriate idiom. There is no error at (C). The plural noun "people" is logical here because more than one library is being talked about. There is no error at (D). The present perfect progressive tense of the verb appropriately indicates that the action described may be ongoing. There is an error in the sentence (E).

29. (B) (A) contains no error. “To understand” is idiomatically correct as “to” is the correct preposition ot use with “understand”. (B) is the answer. “we must” is incorrect, because of the form of “we”. Since later on in the sentence the second person formal form “one” is used, the same form must be used in the entire sentence. Thus “we” should be changed to “one”. (C) contains no error. “familiar with” correctly uses the preposition “with” with “familiar”. (D) contains no error. “with them” is grammatically correct. “With” is the correct preposition to use in “agrees with them”. Alternate Explanation: Corrected Sentence: To understand twentieth-century economic practices, one must be sufficiently familiar with Keynesian theories, whether one agrees with them or not. The error in this sentence occurs at (B), where there is incorrect pronoun use. The first-person plural pronoun "we" is not consistent with the later pronoun "one." There is no error at (A). The infinitive "To understand" appropriately indicates that a familiarity with Keynesian theories will facilitate one's understanding of "twentieth-century economic practices." There is no error at (C). The adjective "familiar" joins with the preposition "with" to form an appropriate idiom. There is no error at (D). In the p repositional phrase "with them," the object of the preposition, "them," must be in the objective case, as it is here. There is an error in the sentence (E).

30. (D) The reproduced sentence is a run-on with two independent

thoughts joined by the conjunction “and” without a comma. Thus, the sentence can be corrected by either adding a comma or elimination one of the independent thoughts. (A) is incorrect. The original sentence is grammatically incorrect and cannot be left as it is. (B) is incorrect. Switching the position of the reproduced sentence with the position of sentence 2 will not correct the run-on sentence. (C) is incorrect. Changing “leave” to “have left” will not correct the run-on sentence. (D) is correct. Changing “and they have not heard” to “without having heard” will eliminate the second independent thought by removing the second subject “they” and therefore corrects the run-on sentence. (E) is incorrect. Removing the comma and inserting “known as the” will not correct the run-on sentence. Alternate Explanation: Choice (D) is correct. It properly explains that most children hear the Pocahontas story before they leave elementary school. Choice (A) is unsatisfactory because the original sentence connects the two main ideas--children leaving school and the Pocahontas story --with only the conjunction "and." The sentence thus offers no clue about the relationship between the two ideas. Choice (B) is unsatisfactory because it is logical to give the names of the principal figures in a story or event before telling the story, not

after--especially when the names are familiar. Choice (C) is unsatisfactory because it repeats the error of the original in failing to explain the relationship between the children and the story. Choice (E) is unsatisfactory because the original correctly refers to Pocahontas's tribe.

31. (E) Sentence 4 is referring to the “report” mentioned in sentence

3. Therefore, the underlined wording should be combined in such a way. (A) is incorrect. The sentences are not combined correctly. A comma followed by ‘according’ does not make logical sense and is grammatically incorrect. (B) is incorrect. The sentence is grammatically incorrect. The word ‘which’ cannot be used to refer to the person ‘captive.’ “Who” refers to people while “which” refers to things. (C) is incorrect. Beginning the sentence with ‘consequently’ does not fit with the overall flow of the passage and is the wrong transition word to use. (D) is incorrect. The sentence begins with a random ‘it’ that has no particular reference. (E) is correct. The underlined portion of sentences 3 and 4 are combined logically and grammatically correct. Alternate Explanation: Choice (E) is correct. The resulting sentence maintains the sense of the original while eliminating the redundancy. Choice (A) is unsatisfactory because it contains an unclear referent: "which" seems to refer to the incident itself rather than to the report. Choice (B) is unsatisfactory because the word "which" appears to refer to the incident, when it can logically refer only to the report of the incident. Choice (C) is unsatisfactory because the word "consequently" suggests incorrectly that Smith's report is a consequence of the legend. Choice (D) is unsatisfactory because it uses the unnecessary phrase "it seems" to relate a fact.

32. (A) Sentence 9 establishes a contrast between what Smith

described and what actually happened. Smith described a violent execution that could have been merely something harmless. Therefore, a link that establishes this contrast is needed. (A) is correct. The link “Far from being in mortal danger” establishes the contrast between something harmful and something innocent. (B) is incorrect. The pronoun ‘he’ cannot be used to refer to “research.” ‘He’ also cannot refer to “Smith” because then sentence 10 will contradict sentence 9 since Smith was the one who described an execution, not a mere drama. (C) is incorrect. The answer choice does not make logical sense with sentence 9. Sentence 9 talks about the difference between research into Powhatan culture and Smith’s accounts, not ‘grade school history.’ (D) is incorrect. The pronoun ‘they’ is used vaguely and does not have a specific reference. (E) is incorrect. The phrase ‘But quite to the contrary’ does not coincide with sentence 9. Sentence 10 is further elaborating on sentence 9, not negating it. Alternate Explanation: Choice (A) is correct. It links sentence 10 to the rest of the paragraph by explaining the harmlessness of the "ritual display" mentioned in the previous sentence (and thus clarifies the contrast between Smith's account and the probable facts). Choice (B) is unsatisfactory because sentence 10 outlines a scenario that challenges Smith's "life-or-death" account, implying that Smith is not a credible source. Choice (C) is unsatisfactory because the inserted phrase unhelpfully interrupts the connection between the "ritual display" introduced in sentence 9 and the explanation of it in sentence 10. Choice (D) is unsatisfactory because the use of


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"and" implies that the "ritual" and the "drama" are two different events, whereas the "drama" actually refers to the "ritual display." Choice (E) is unsatisfactory because nothing in sentence 10 is contrary to sentence 9; the latter sentence logically follows the former.

33. (B) Sentence 10 further elaborates on why Smith’s reports may have been inaccurate. (A) is incorrect. Sentence 10 further supports sentence 9; it does not negate it. (B) is correct. Sentence 10 adds more information about the report in sentence 9 that Smith’s description might have been inaccurate. (C) is incorrect. Sentence 10 does not give an example an “execution” being a “mere display of strength.” (D) is incorrect. Sentence 10 does not bring up an argument since it elaborates on the information presented in sentence 9. (E) is incorrect. Sentence 10 does not introduce a new source. Alternate Explanation: Choice (B) is correct. Sentence 10 elaborates on the information about what may have really happened to Smith presented in sentence 9. Choice (A) is unsatisfactory because sentence 10 offers only support for the claim made in sentence 9. Choice (C) is unsatisfactory because the information in sentence 10 is not an "example"; rather, it is a reasoned clarification of what may have happened to Smith. Choice (D) is unsatisfactory because nothing about sentence 10 contradicts sentence 9. Choice (E) is unsatisfactory because sentence 10 does not make use of any new sources.

34. (C) The third paragraph mentions Pocahontas’s political roles by

mentioning her role as “ambassador” and her “diplomacy” in “England.” (A) in incorrect. The third paragraph does not mention any political shortcomings of Pocahontas. (B) is incorrect. The third paragraph does not talk about the ‘historical Pocahontas.’ (C) is correct. The answer choice mentions Pocahontas’s ‘political talents,’ which is the subject of the third paragraph. (D) is incorrect. The third paragraph does not talk about Pocahontas’s private life. (E) is incorrect. The third paragraph does not mention anything about the ‘real’ Pocahontas. Alternate Explanation: Choice (C) is correct. The third paragraph gives two detailed examples of Pocahontas's political successes in later life. Choice (A) is unsatisfactory because the passage does not mention any of Pocahontas's shortcomings. Choice (B) is unsatisfactory because focusing on the believability of historical facts is odd and unnecessary. Choice (D) is unsatisfactory because the information in paragraph 3 deals primarily with Pocahontas's public life, not her private life. Choice (E) is unsatisfactory because the third paragraph gives detailed information about Pocahontas that is not in dispute.

35. (E) The third paragraph and sentence 12 talks about Pocahontas’

political roles and public life in England. (A) is incorrect. The main idea of sentence 12 has nothing to do with Pocahontas’s marriage to Rolfe. (B) is incorrect. Sentence 12 does not mention John Smith. (C) is incorrect. Sentence 12 does not mention anything about confrontations between the Powhatans and the

Jamestown settlers. (D) is incorrect. Sentence 12 talks about Pocahontas’s roles, not Rolfe’s roles. (E) is correct. Sentence 12 mentions one aspect of Pocahontas’s political roles in England therefore adding information about other public events in her life would be logical. Alternate Explanation: Choice (E) is correct. This information is consistent with the information presented in the first two sentences of the paragraph. Choice (A) is unsatisfactory because the first two sentences of the paragraph present events chronologically, and it would be illogical to describe Pocahontas's marriage, which occurred before the events described in sentence 12, at the end of the paragraph. Choice (B) is unsatisfactory because the passage has moved from a discussion of Smith's account to a discussion of Pocahontas's life; to return to Smith at this point would be illogical. Choice (C) is unsatisfactory because this information would need to be presented directly after its introduction in sentence 11. Choice (D) is unsatisfactory because the focus of the paragraph is Pocahontas, not her husband.

Section 6 1. (C) For 50 calls, there will be a base charge of $10. Then, there

will be a $0.08 for each of the first 40 calls. Finally, there will be a $0.04 charge for each of the remaining 50 – 40 = 10 calls. Thus, the total cost would be $10 + $0.08*(40) + $0.04*(10) = $13.60. Answer (C) is correct. Alternate Explanation: Choice (C) is correct. The bill for 50 calls will be

( ) ( )$10.00 $0.08 40 $0.04 10 .+ + This simplifies to

$10.00 $3.20 $0.40 $13.60.+ + = Choice (A) is not correct. This amount, $12.20, would only account for the base cost of

$10.00, plus $12.20 $10.00 $2.20− = in additional charges for individual calls. The first 40 calls, which would cost

( )( )$0.08 40 $3.20,= would cost more than $2.20. Choice (B)

is not correct. This amount, $12.80,would only account for the

base cost of $10.00,plus $12.80 $10.00 $2.80− = in additional charges for individual calls. The first 40 calls, which would cost

( )( )$0.08 40 $3.20,= would cost more than $2.80. Choice (D)

is not correct. This amount, $14.40, would be enough for the base cost of $10.00,plus $14.40 $10.00 $4.40− = in additional charges for calls. This would be enough for an average per-call

charge of $4.40 $0.088,

50= which is larger than the given per-call

charges of either $0.08 or $0.04. Choice (E) is not correct. This amount, $17.60, would be enough for the base cost of $10.00,plus in additional charges for calls. This would be

enough for an average per-call charge of $7.60 $0.152,

50= which

is larger than the given per-call charges of either $0.08 or $0.04.


22

2. (C) The only increases are between January and February, March and April, and May and June. This eliminates (B) and (D). Then, the largest increase is $15000 between March and April, so (C) is correct. Alternate Explanation: Choice (C) is correct. Between January and February, profits increased by about $10,000. Between February and March, profits decreased by about $15,000. Between March and April,

profits increased by about $15,000. Between April and May,

profits decreased by about $5,000. Between May and June, profits increased by $10,000.The largest monthly increase

occurred between March and April, with an increase of $15,000. Choice (A) is not correct. Between January and February the profits did increase by about $10,000, but between March and

April profits increased by about $15,000. Choice (B) is not correct. Between February and March profits decreased. Choice (D) is not correct. Between April and May profits decreased. Choice (E) is not correct. Between May and June, profits increased by about $10,000, but between March and April profits increased by about $15,000.

3. (A) Since a right angle is 90 degrees, 2

3PQR∠ = of 90 = 23 90 60× = . The problem also states 2

5SQR PQR∠ = ∠ .

Therefore, 25 60SQR∠ = × , or 24 degrees. (A) is correct.

Alternate Explanation: Choice (A) is correct. A right angle measures 90 ,° so

2 90 60 .3

PQR∠ = × ° = ° Since SQR∠ is 25

the measure of

,PQR∠ 2 60 2 4 .5

SQR∠ = × ° = ° Choice (B) is not correct. This

would be the measure of SQR∠ if its measure were 25

the

measure of a right angle, instead of 25

the measure of .PQR∠

Choice (C) is not correct. This choice is 45

the measure of

,PQR∠ but the problem states that the measure of SQR∠ is 25

the measure of .PQR∠ Choice (D) is not correct. This is the

measure of ,PQR∠ not the measure of .SQR∠ Choice (E) is not correct. The measure of SQR∠ is less than the measure of

PQR∠ which is less than 90 ,° so the measure of SQR∠ cannot

be more than 9 0 .°

4. (E) Since we know the third column contains 0’s, we can

eliminate (B) and (C) since they contain 1’s in that position. Since

G sums to 0, that entire row must contain 0’s. E must contain all 1’s in the blank spots to sum to 3. In the first column, F and H must contain 0’s in order for the column to sum to 1. See the following table:

Based on this information, the remaining two squares should contain 1’s so that the row sums to two. This yields a row of 0-1-0-1. (E) is correct. Alternate Explanation: Choice (E) is correct. Since the sum of row G is 0, there cannot be any 1's in row ,G and it must be filled with 0' .s On the other hand, the sum for row E is 3, so the three empty boxes in that row can be filled in with 1' .s The same is true for the three empty boxes in the second column, which also has a sum of 3. The first column, in order to have a sum of 1, must have zeros except for the 1already in the first position in row .E At this point, t here are only two empty boxes, the column four boxes on row F and on row .H Row F needs a 1 in the column four box to have a total sum of 2. In summary, row F reads (from left to right) 0, 1, 0, 1. Choice (A) is not correct. Row E must have a 1 in the first column and since the sum in the first column is only 1, row F cannot also have a 1 in the first column. Choice (B) is not correct. This choice contradicts the given information that the third column is all zeroes. Choice (C) is not correct. This choice contradicts the given information that the third column is all zeroes. Choice (D) is not correct. Without a 1 in the second column of row ,F the second column would not have a sum of 3.

5. (E) For this equation to be true, either m – 1 = 0 (so

m = 1) or 1 – k = 0 (so k = 1). Clearly I and II can be true. If both are true at the same time, then III could be true as well. Since all of them could be true, (E) is correct. Alternate Explanation:

Choice (E) is correct. Since ( ) ( )1 1 0,m k− − = either 1 0,m − =

or 1 0,k− = or both. If 1 0,m − = then 1.m = If

1 0,k− = then 1.k = It is possible for either k or m to equal 1, or for both k and m to equal 1. Therefore, I, II, and III can all be true. Choice (A) is not correct. Since

( ) ( )1 1 0,m k− − = either k or ,m or both, must equal 1.

Choice (B) is not correct. It is possible that 1,m = but it is also possible that 1k = and .m k= Choice (C) is not correct. It is

E 1 1 0 1 3

F 0 0 2

G 0 0 0 0 0

H 0 0 1

1 3 0 2


23

possible that 1,k = but it is also possible that 1m = and .m k= Choice (D) is not correct. It is possible that both m and k are

equal to 1, and so m k= can be true.

6. (B) Since the function is shifted one to the right of the origin, we

know the equation must be 2( 1)x − . All shifts right (left) will change what’s subtracted (added) from the x in parenthesis. Using FOIL, the equation expands to 2( ) 2 1g x x x= − + . Alternate Explanation: Choice (B) is correct. The graph shown intersects the x -axis at

only one point, ( )1,0 . This implies that the quadratic function has

the form ( ) ( )21 ,g x a x= − where a is a constant. Every answer

choice in this problem has leading coefficient 1,a = so the only possible choice that could represent the graph shown is the

equation ( ) ( )2 21 2 1.g x x x x= − = − + Choice (A) is not

correct. The graph of this equation intersects the x -axis at two points, ( )1,0 and ( )2,0 , because ( ) ( )2 3 2 1 2 .x x x x− + = − − This equation cannot represent the graph shown. Choice (C) is not correct. The graph of this equation does not intersect the x -axis at

the point ( )1,0 , because ( ) 21 1 1 3 5,g = + + = not 0. This equation cannot represent the graph shown. Choice (D) is not correct. The graph of this equation does not intersect the x -axis at

the point ( )1,0 ,because ( ) 21 1 2 1 1 2,g = + ⋅ − = not 0. This equation cannot represent the graph shown. Choice (E) is not correct. The graph of this equation does not intersect the x -axis at the point ( )1,0 ,because ( ) 21 1 3 1 2 2,g = + ⋅ − = not 0. This

equation cannot represent the graph shown.

7. (A) Since AB = 3, AD = 3 too, since the triangle is equilateral. If

D is the midpoint of AC, then AC = 6. A triangle like ABC with sides in a ratio of 1 to 2 (3 to 6 in this case) and an angle of 60° must be a 30-60-90 triangle (you can check this using the usual methods for solving a geometry problem). If so, then the third side BC of ABC must be 3 3 . (A) is correct. Alternate Explanation: Choice (A) is correct. Since it is given that the measures of two of the three angles of triangle ABD are 60 ,° triangle ABD is

equilateral. Also, since D is the midpoint of ,AC 3,AD DC= = and 6.AC = Since 3,BD DC= = BCD∆ is

isosceles and the measures of CBD∠ and BCD∠ are 3 0 .° Thus, ABC∆ must be a 30 60 90° − °− ° triangle. Based on the

properties of 30 60 90° − °− ° triangles, 3 3.BC = Choice (B) is not correct. Since it is given that the measures of two of the three angles of triangle ABD are 60 ,° triangle ABD is equilateral. Also, 3AD DC= = and 6.AC = Since

3,BD DC= = BCD∆ is isosceles and the measures of CBD∠ and BCD∠ are 3 0 .° Thus, ABC∆ must be a 30 60 90 .° − °− °

The properties of such a special right angle triangle do not include sides with lengths 3, 6, and one that is an integer multiple of

2. Choice (C) is not correct. An answer of about 6.93 is too

large. Since the three line segments ,BC ,BD and CD form a

triangle, the length of BC must be less than the sum of the

lengths of BD and .CD Because both BD and CD have length

3, the length of BC must be less than 6. Choice (D) is not correct. An answer of about 8.49 is too large. Since the three line

segments ,BC ,BD and CD form a triangle, the length of

BC must be less than the sum of the lengths of BD and .CD

Because both BD and CD have length 3, the length of BC must be less than 6. Choice (E) is not correct. An answer of about

8.66 is too large. Since the three line segments ,BC ,BD and

CD form a triangle, the length of BC must be less than the sum

of the lengths of BD and .CD Because both BD and CD have

length 3, the length of BC must be less than 6.

8. (E) Let r = 50 and q + 1 = 100. Then, r is 50% of q+1. This is

equal to 100(50 / 100)%. Reverse plugging in gives a formula of 100(r/q+1)%. (E) is correct. Alternate Explanation:

Choice (E) is correct. To find what fraction r is of ( )1 ,q +

divide r by ( )1 :q + .1

rq +

To put this in percent form, multiply

by 100 to get 100

%.1r

q + Choice (A) is not correct. If the formula

( )1

%100 1r q +

were correct, it would work for any values of q

and .r Certainly, 1 is 50% of 2. However, using 1r = and 1 2q + = in this formula gives

( ) ( ) ( )1 1

% % 0.005%,100 1 100 1 2r q

= =+

not 50% Choice

(B) is not correct. If the formula ( )1

%100

q

r

+ were correct, it would

work for any values of q and .r Certainly, 1 is 50% of 2.

However, using 1r = and 1 2q + = in this formula gives

( )( )

1 2% % 0.02%,100 100 1

q

r

+= = not 50% Choice (C) is not

correct. If the formula ( )100 1

%qr

+ were correct, it would work

for any values of q and .r Certainly, 1 is 50% of 2. However,

using 1r = and 1 2q + = in this formula gives


24

( ) ( )100 1 100 2% % 200%,

1qr

+= = not 50% Choice (D) is

not correct. If the formula 100

1 %r

q

+

were correct, it would

work for any values of q and .r Certainly, 1 is 50% of 2.

However, using 1r = and 1 2q + = in this formula gives

( )100 1100 1 % 1 51%,2

rq

+ = + =

not 50%.

9. (100) Assume x is the number of sticks. Then (¼)x = 25, so x = 25

X 4 = 100. Alternate Explanation:

The correct answer is 100. Since the weight of each stick is 14

pound, 4 sticks together make a pound. To get 25 pounds,

requires ( )25 4 100= sticks. The problem can also be

represented algebraically. Let s be the number of sticks needed,

then 1

25.4

s = Therefore, 25

,14

s = or 100.s =

10. (3) Simplify the equation by multiplying both sides by 4,

subtracting 3, and then dividing by 7.

(5 2) 3 647 3 24

7 213

m

mmm

+ + =

+ ===

Alternate Explanation:

The correct answer is 3. The equation ( )5 2 3

64

m+ += can be

solved for m using the following steps: 7 3

6,4

m +=

7 3 24,m + = 7 21,m = and 3.m =

11. (20 or 50) Since the triangle is isosceles, two angles could equal 80. If this were true, then the third angle would be x = 180 – 2(80) = 180 – 160 = 20. Now, if the two remaining angles were the equal ones, then 2y + 80 = 180, 2y = 100, and y = 50. Alternate Explanation: The correct answers are 20 and 50. The sum of the measures of the angles must be 180° and the question states that 80.x ≠ Since the triangle is isosceles, two of the angles must have the same measure. Either the angles are 8 0 ,° 8 0 ,° and ,x° or the angles are 8 0 ,° ,x° and .x° This means that either 80 80 180x+ + = or 80 180.x x+ + = In the first case,

20x = and in the second case 50.x = Either answer is correct.

12. (8/15 or .533) The phrase directly proportional indicates the equation r k s= × , where k represents the ratio between the two variables. Plugging in the two values for the variables r and s, we can solve for k

4 25 3

65

k

k

= ×

=

Now that we have a value for k, we can solve for any r if given s.

6 45 98

or .53315

r

r

= ×

=


The correct answer is 8

15 or .533 (a truncated form of the

repeating decimal). If r is directly proportional to ,s then

,r ks= for some constant .k Using the value of r when 2 ,3

s =

gives the equation 4 2

.5 3

k = Solving for ,k gives that

6 .5

k =

Then for 4 ,9

s = 6 4 8

,5 9 15

r = = or .533. The answer can

be entered into the grid either as a fraction or as a decimal.

13. (180) The students who use computers at school are represented in

the first figure by the 70% who use them in both school and at home as well as the 20% who use them at school only. This is a total of 90% of the 200 twelfth graders, or 90/100 X 200 = 180. Alternate Explanation: The correct answer is 180. The shaded circle in Figure 2 represents all the students who use computers in school, including those who use computers both at home and at school. From Figure 1 in the question, 20% of the 200 students, or 40 students, use computers at school only, and 70% of the 200 students, or 140 students, use computers both at home and at school. The entire shaded circle, then, represents 40 140 180+ + = students who use computers at school.

14. (144) The ratio of A to B equals 35 / 45, or 7/9. The ratio of D to

C must be the same.

7

36 928

D

D

=

=

The total area is A + B + C + D = 35 + 45 + 36 + 28 = 144. Another way to approach this problem would be evaluate the sides of each box. Since A and B share the same width, they must share a common factor that is the width. The common factor of 35 and 35 is 5, so we can label the width of the two boxes as 5. That would make the length of A = 7, and the length of B = 9. Now B and C share the same length, so the length of C must be 9. Since the area of C is 36, then that would make its width 4. Now we have


25

the length (7+9=16) and width (5+4=9) of the entire box, making the area 16*9=144. Alternate Explanation: The correct answer is 144. Rectangle A has an area of 35, which can be factored as 5 7× or 35 1.× Rectangle A and rectangle B share a side. The length of the shared side is either 5 or 1, since the area of rectangle B is 45, which has 5 and 1 as possible factors. If the length of the shared side were 1, then the dimensions of rectangle B would be 1 by 45, and 45 would be the length of the side shared by rectangle B and rectangle .C Since the area of rectangle C is 36, it cannot have a side of length 45. From this it follows that the length of the side shared by rectangle A and rectangle B must be 5. The length of the side

shared by rectangle B and rectangle C is 45 9.5

= Since the area

of rectangle C is 36, the other dimension of rectangle C is

36 4.9

= Since rectangle A has dimensions 5 by 7, rectangle

B has dimensions 5 by 9, and rectangle C has dimensions 9 by 4, the dimensions of the large rectangle are 5 4+ by 7 9.+ Therefore, the total area of the large rectangle is

( ) ( ) ( )5 4 7 9 9 16 144.+ + = =

15. (20) Since n = 39, step 1 is done. In step 2, 39 = 13 x 3, so it is not

prime. Add 2: 39 + 2 = 41. Step 3: 41/2 = 20.5. Step 4: the greatest integer less than 20.5 is 20. Alternate Explanation: he correct answer is 20. First take the chosen number for step 1, which is 39m and use it in step 2. Here 39n = is not prime, because 3 13 39.× = So add 2 to get 41, Then in step 3, divide this number by 2 to get 41 2 20.5.÷ = The result of step 4 is the greatest integer less than or equal to 20.5, which is 20.

16. (60) For this system to work, the number of students must be divisible by 2, 3, and 4. The first such number is 12. If there were 12 students, there would be 6 staplers, 4 rulers, and 3 glue bottles, for a total of 13. This is a ratio that stays fixed, so assume there are x students in the class. Then x to 65 equals 12 to 13.

12

65 1360

x

x

=

=

Alternate Explanation: The correct answer is 60. Let x represent the total number of students in the art class. Since every 2 students had to share a

stapler, there were exactly 12

x staplers. Since every 3 students

had to share a ruler, there were exactly 13

x rulers. Since every 4

students had to share a glue bottle, there were exactly 14

x glue

bottles. From the given information that the sum of the number of staplers, rulers, and glue bottles used by the class was 65, it

follows that 1 1 1 65,2 3 4

x x x+ + = which simplifies to

6 4 365,

12x

+ += and further to

1365.

12x = Therefore,

( ) ( )6512

5 12 60.13

x = = =

17. (608) The decimal 0.625 can be represented as the fraction 625

1000

which reduced to its simplest form is 58

. Therefore, ab

has to be

equal to some multiple of 58

. The multiple can then be

represented by x in the equation 58

a xb x

=

Since (a+b) has to be under 1000,

5 8 1000

13 100076.92

x x

xx

+ <

<<

However since a and b must both be integers, 76 is the largest integer possible for the multiple. Since 8 , 8 76 608b x b= = × = . The greatest possible integer value of b is 608.


The correct answer is 608. Since 50.6258

ab

= = and since 5

and 8 have no common factors other than 1, it must be the case

that a is a multiple of 5 and b is a multiple of 8. Solving for a

in terms of b yields 5 .8ba = Since 1000,a b+ <

5 1000,8b b+ < or

13 1000,8b < or

8000.13

b < The largest

multiple of 8 less than 800013

is 608. So 608,b = and

5 380,8ba = = and 988,a b+ = which is less than 1000.

18. (33) If the numbers are 3 times an even integer, they must also be

multiples of 6 since all even integers are multiples of 2 (2 x 3 = 6). If they have to be multiples of 5 and 6, they must be multiples of 5x6 = 30. The numbers that fit these rules are 30, 60, 90…990. Since 990/30 = 33, there are 33 numbers that fit the rules stated in the problem. Alternate Explanation:


26

The correct answer is 33. Since all of these integers are equal to 3 times an even integer, they are all multiples of 3 and 2. It is given that these integers are also multiples of 5. Since these integers must be multiples of 5, 3, and 2, they must all be multiples of the least common multiple of these numbers, which is 5 3 2 30.× × = The integers must also be less than 1,000. Integers that fulfill all these conditions are 1 30 30,× = 2 30 60,× = 3 30 90,× = and so on, up to 33 30 990,× = which is the greatest such number since 34 30 1020× = is not less than 1,000. So there are 33 integers that meet these conditions.

Section 7 1. (B) The first blank is easier to define first. Notice that the blank is

an adjective describing the author James Baldwin. The words “the success” at the beginning of the sentence imply that the rest of sentence will explain or be somehow related to the success. Thus we’re looking for a positive word for the first blank. Choices (C) and (D) can be eliminated. (C) “surrendered” means to have given up or relinquish control. (D) “decried” means to be condemned openly. Now define the second blank. The blank describes what type of essayist James Baldwin was. Since we are discussing his success, we’re looking for a positive word in the second blank. Choices (A) and (E) can be eliminated. (A) “irrelevant” means unrelated or inconsequential. (E) “mundane” means normal or boring. (B) is the correct answer. “established” means to be recognized or accepted. Thus it is a positive word. “prominent” means to be important or at the fore front. Thus it is also a positive word. Alternate Explanation: Choice (B) is correct. “Establish” means to cause to be recognized and accepted. “Prominent” means widely and popularly known. If one were to insert these terms into the text, the sentence would read “The success of Notes of a Native Son established author James Baldwin as one of the most prominent essayists of his time.” The success of Notes of a Native Son gave Baldwin recognition and acceptance within literary circles. Choice (A) is incorrect. “Buoyed” means supported or uplifted. “Irrelevant” means unrelated or insignificant. If one were to insert these terms into the text, the sentence would read “The success of Notes of a Native Son buoyed author James Baldwin as one of the most irrelevant essayists of his time.” Success can enhance a writer’s reputation, but it is illogical to claim that it would cause Baldwin to become insignificant. Choice (C) is incorrect. “Surrendered” means abandoned. “Prolific” means to produce abundant works or results. If one were to insert these terms into the text, the sentence would read “The success of Notes of a Native Son surrendered author James Baldwin as one of the most prolific essayists of his time. Many successful authors are prolific, but it does not make sense to say that success abandoned Baldwin as a “prolific” essayist. Choice (D) is incorrect. “Decried” means denounced or belittled. “Cynical” means negative or pessimistic. If one were to insert these terms into the text, the sentence would read “The success of Notes of a Native Son decried author James Baldwin as one of the most cynical essayists of his time.” Some critics may have criticized Baldwin for being cynical, but a book cannot denounce its author. Choice (E) is incorrect. “Categorized” means classified,

and “mundane” means ordinary. If one were to insert these terms into the text, the sentence would read “The success of Notes of a Native Son categorized author James Baldwin as one of the most mundane essayists of his time.” It is unlikely that success would classify or label an author as ordinary.

2. (D) The definition words for this sentence are “central rather than

a ----”. Focus on “rather”. The word “rather” indicates a contrast. Thus the blank must be the opposite of “central”. What is the opposite of central? The opposite is something to the side or ancillary. We’re looking for a word that means “ancillary” in the blank. Choices (A), (B), (C), and (E) can be eliminated. (A) “pivotal” means being of vital or central importance. (B) “ritualistic” means relating to a ritual or a cultural practice. (C) “salient” means prominent or strikingly conspicuous. (E) “solemn” means earnest, serious, or sober. (D) is the correct answer. “supplementary” means something added to complete a thing. Thus, something that is supplementary is on the side or ancillary. Alternate Explanation: Choice (D) is correct. "Supplementary" means something added or in addition to. If one were to insert this term into the text, the sentence would read "In many parts of the world, people use rice as a central rather than a supplementary part of their daily diets." The phrase "rather than" indicates that the blanked word will mean the opposite of the word "central." In this context, "supplementary" does indeed have the opposite meaning of "central." Choice (A) is incorrect. "Pivotal" means being of vital or significant importance. If one were to insert this term into the text, the sentence would read "In many parts of the world, people use rice as a central rather than a pivotal part of their daily diets." "Pivotal" and "central" are synonymous, thus it makes little sense to claim that people use rice as a central rather than a "pivotal" part of their diet. Choice (B) is incorrect. "Ritualistic" means advocating or practicing ritual. If one were to insert this term into the text, the sentence would read "In many parts of the world, people use rice as a central rather than a ritualistic part of their daily diets." A "ritualistic," or ceremonial, use of rice does not necessarily mean that the rice is not a "central" part of the diet. Choice (C) is incorrect. "Salient" means prominent. If one were to insert this term into the text, the sentence would read "In many parts of the world, people use rice as a central rather than a salient part of their daily diets." A "salient" part of a diet would be an important part. It is illogical to contrast the use of rice as a "central" part of the diet with the use of rice as an important part of the diet. Choice (E) is incorrect. "Solemn" means somberly or gravely impressive. If one were to insert this term into the text, the sentence would read "In many parts of the world, people use rice as a central rather than a solemn part of their daily diets." It makes little sense to describe rice as a "solemn," or somber, part of a diet.

3. (B) The definition words are “because he constantly bullied other

children”. What type of reputation would a person gain if he bullied children? The person would have a reputation for being evil or a brute. We’re looking for a word that means “brute” in the blank. Choices (A), (C), (D), and (E) can be eliminated. (A) “bungler” is an especially clumsy person. (C) “stickler” is someone who insists on something or is unyielding, usually in reference to neatness. (D) “daredevil” is a person who enjoys doing dangerous things. (E) “naysayer” is someone with an aggressively negative


27

attitude. (B) is the correct answer. A “ruffian” is a tough or rowdy person; a brute. Alternate Explanation: Choice (B) is correct. "Ruffian" describes a person who is a hoodlum or bully. If one were to insert this term into the text, the sentence would read "Victor gained a reputation for being a ruffian because he constantly bullied other children." Bullying other children is precisely the behavior that would give Victor a reputation as a ruffian. Choice (A) is incorrect. "Bungler" describes a person who is clumsy or inept in behavior. If one were to insert this term into the text, the sentence would read "Victor gained a reputation for being a bungler because he constantly bullied other children." The claim that Victor had a reputation for being a "bungler" does not fit with the claim that "he bullied other children," as a bully is not necessarily clumsy. Choice (C) is incorrect. "Stickler" describes a person who insists on something unyieldingly. If one were to insert this term into the text, the sentence would read "Victor gained a reputation for being a stickler because he constantly bullied other children." Although Victor may be a "stickler," or perfectionist, his reputation is based on his tendency to bully other children. Choice (D) is incorrect. "Daredevil" describes a person who is recklessly bold. If one were to insert this term into the text, the sentence would read "Victor gained a reputation for being a daredevil because he constantly bullied other children." While Victor may be a "daredevil," or risktaker, the sentence offers no evidence of this. Choice (E) is incorrect. "Naysayer" describes a person who opposes in order to take a pessimistic view. If one were to insert this term into the text, the sentence would read "Victor gained a reputation for being a naysayer because he constantly bullied other children." The sentence offers no evidence that Victor is a "naysayer," or contrarian.

4. (C) The definition words for this sentence are “she publicly

defended the rights and wisdom of the people, but she often spoke with a disdainful air of superiority” as indicated by the colon. The colon indicates that the second part of sentence (as split by the colon) is an elaboration or parallel with the first part of the sentence. Thus the two blanks must correspond exactly with the definition words. Hence “defended the rights and wisdom of the people” corresponds with the first blank, and “spoke with a disdainful air of superiority” corresponds with a second blank. Define the first blank. How would you describe someone who defends the rights of the people? The person would be described as democratic or supporting the population. We’re looking for a word that means “democratic” in the first blank. Choices (A), (B) and (E) can be eliminated. (A) “demagogue” is a person who obtains power by appealing to the prejudice of the population. (B) “conservative” is a person who represents the conservative (traditional) side of the population. (E) “partisan” is a militant follower or a firm believer. Now define the second blank. How would you describe some who speaks with an air of superiority? The person would be condescending and arrogant. The attitude is against the people. Thus we’re looking for a word that denotes “condescending” or “arrogant” in the second blank. Choice (D) can be eliminated. A “reactionary” is an extremely conservative person. That does not necessarily mean that the person is arrogant. (C) is the correct answer. A “populist” is a supporter of the rights and powers of the people. An “elitist” is a person who believe that

certain classes should be treated as superior. Thus an elitist would be condescending and arrogant. Alternate Explanation: Choice (C) is correct. A "populist" is an advocate for the interests and rights of the common people. An "elitist" believes that certain persons deserve favored treatment by virtue of their perceived superiority. If one were to insert these terms into t he text, the sentence would read "Paradoxically, the senator was both a populist and an elitist: she publicly defended the rights and wisdom of the people, but she often spoke with a disdainful air of superiority." The term "paradoxically" indicates that the two missing terms will be contradictory. The senator's behavior is inconsistent because she supports common people publicly, while believing in the superiority of certain classes of people. Choice (A) is incorrect. A "demagogue" is a leader who obtains power by means of impassioned appeals to the emotions and prejudices of the populace. A "maverick" is one that resists adherence to a group. If one were to insert these terms into the text, the sentence would read "Paradoxically, the senator was both a demagogue and a maverick: she publicly defended the rights and wisdom of the people, but she often spoke with a disdainful air of superiority." A "demagogue," a person who stirs up emotion, can also be a "maverick" or independent politician. The two are not necessarily opposed to one another, and so the behavior of a person who exhibits both of these characteristics would not logically be described as paradoxical. Choice (B) is incorrect. "Conservative" is one favoring traditional values and views. "Anarchist" is an advocate of political disorder and confusion. If one were to insert these terms into the text, the sentence would read "Paradoxically, the senator was both a conservative and an anarchist: she publicly defended the rights and wisdom of the people, but she often spoke with a disdainful air of superiority." A "conservative" politician does not necessarily defend the rights of the common people. An "anarchist" opposes the idea of government and is unlikely to hold a government office. Choice (D) is incorrect. "Moderate" is one who holds average views or opinions. "Reactionary" means an opponent of progress or liberalism. If one were to insert these terms into the text, the sentence would read "Paradoxically, the senator was both a moderate and a reactionary: she publicly defended the rights and wisdom of the people, but she often spoke with a disdainful air of superiority." "Moderate," or middle-ground, and "reactionary" are not the polar opposites implied by the term "paradoxically." Choice (E) is incorrect. "Partisan" is a supporter or proponent of a party, cause, faction, person, or idea. A "snob" looks down on people he or she regards as socially inferior. If one were to insert these terms into the text, the sentence would read "Paradoxically, the senator was both a partisan and snob: she publicly defended the rights and wisdom of the people, but she often spoke with a disdainful air of superiority." While a "snob" would speak with an air of superiority, it makes little sense to contrast a "snob" with a "partisan," or someone favoring a particular political party. Furthermore, a partisan would not necessarily defend the rights of the common people.

5. (A) The definition words are “the present-day island was actually

a hilltop in a vast forest” as indicated by the comma. What happened to the area if it used to be a hill in a forest, but now is island? The area must have been flooded. We’re looking for a word that means “flooded” in the blank. Choices (B), (C), (D), and


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(E) can be eliminated. (B) “situated” means having a place or location. (C) “rejuvenated” means reborn or restored. (D) “supplanted” means to displace and substitute for another. Usually, supplant refers to moving trees from one area to another. (E) “excavated” means to expose or uncover by digging. (A) is the correct answer. “inundated” means to cover with water (especially flood waters). Alternate Explanation: Choice (A) is correct. "Inundated" means to cover completely as in a flood. If one were to insert this term into the text, the sentence would read "The geologist speculated that eons ago, before the area was inundated, the present-day island was actually a hilltop in a vast forest." The words "before" and "actually" in this sentence suggest that something happened to transform the hilltop into an island. An inundation of water would be the most logical cause of such a transformation. Choice (B) is incorrect. "Situated" means having a location. If one were to insert this term into the text, the sentence would read "The geologist speculated that eons ago, before the area was situated, the present-day island was actually a hilltop in a vast forest." The location, or where the island is "situated," has not changed. Choice (C) is incorrect. "Rejuvenated" means restored to an original or new condition. If one were to insert this term into the text, the sentence would read "The geologist speculated that eons ago, before the area was rejuvenated, the present-day island was actually a hilltop in a vast forest." While parts of the area may have been rejuvenated, or restored, this would not have turned the area from a hilltop into an island. Choice (D) is incorrect. "Supplanted" means displaced and substituted for. If one were to insert this term into the text, the sentence would read "The geologist speculated that eons ago, before the area was supplanted, the present -day island was actually a hilltop in a vast forest." The information in the sentence does not support the idea that the area was supplanted, or displaced. Choice (E) is incorrect. "Excavated" means removed or exposed by digging. If one were to insert this term into the text, the sentence would read "The geologist speculated that eons ago, before the area was excavated, the present-day island was actually a hilltop in a vast forest." Although the area may have been excavated, or exhumed, this does not explain how the hilltop became an island.

6. (B) The area for this question is both passages. (A) is incorrect.

Passage 1 does not state that Earth’s carrying capacity for humans is routinely underestimated. The passage only states that it is difficult to estimate. (C) is incorrect. Neither passage states that the debate has been started recently. (D) is incorrect. Neither passage asserts how valuable the Earth’s carrying capacity for humans is. (E) is incorrect. Passage 1 does not talk about technology at all. (B) is the correct answer. Both passages say that it cannot be easily determined. Passage 1 states this concept in lines 9-12. Passage 2 states this concept in lines 17-21. Alternate Explanation: Choice (B) is correct. Both passages discuss the difficulty of accurately estimating how many people the Earth can support. Passage 1 asserts that estimating the Earth's "carrying capacity" is a "dark art," and Passage 2 explains why such estimates are problematic. Choice (A) is incorrect. Passage 2 asserts that biologists' estimations of the Earth's "carrying capacity" for humans cover a broad range, but neither author claims that these existing "estimates" are too low. Choice (C) is incorrect. Nothing in these passages suggests that the debate regarding human

"carrying capacity" is a new one. Choice (D) is incorrect. Both passages clearly question the value of estimating the Earth's "carrying capacity" for humans. Passage 1 declares that "anyone with any sense stays away" from the concept, and Passage 2 says that "it makes little sense to talk about carrying capacity in relationship to humans." Choice (E) is incorrect. The first passage does not discuss recent "technological innovations" at all, and the second passage supports this conclusion indirectly at best.

7. (A) The area for this question is Passage 1. (B) is incorrect. The

passage does not talk about resistance from the general public. (C) is incorrect. The passage does not discuss beliefs that scientists question. (D) is incorrect. The passage does not state that most biologists are concerned with wildlife mortality issue. The passage only implies that biologists can easily determine this information. (E) is incorrect. The passage does not discuss the skill of biologists at mathematics. Additionally, the passage does not make a claim on ALL biologists. (A) is the correct answer. Using the term “any” implies that virtually all biologists can make the calculation. Thus the calculation can be made with great confidence. Alternate Explanation: Choice (A) is correct. The author of Passage 1 contrasts the ease of calculating how many animals an area can support with the difficulty of making such a calculation for people. The use of the word "any" conveys the author's belief that predicting an animal population's "carrying capacity" is a relatively simple task for biologists. Choice (B) is incorrect. Passage 1 does not include any reference to the "general public." Choice (C) is incorrect. The author questions biologists' ability to accurately estimate the Earth's "carrying capacity" for humans but makes no reference to "beliefs" of any kind. Choice (D) is incorrect. It may be true that the majority of biologists care about "wildlife mortality," but the author of Passage 1 makes no such claim. Choice (E) is incorrect. While one might infer that the biologists mentioned in Passage 1 need to be skilled in mathematics, this is certainly not a point of emphasis in the passage.

8. (E) The area for this question is both passages. The “estimates”

refers to estimation about the amount of humans earth can support. (A) is incorrect. Passage 1 does not state that the estimations are overly generous. (B) is incorrect. Neither passage states that the estimations are undocumented. Documentation is not discussed. (C) is incorrect. Neither passage states that the estimations are misunderstood. The problem is not with people misinterpreting the estimates, but rather the accuracy of the estimate itself. (D) is incorrect. Neither passage discusses the motivation for the estimate. Thus we cannot assume that they are politically motivated. (E) is correct. The estimates are essentially unreliable. This idea is stated in Passage 1 (lines 9 – 12) and stated in Passage 2 (lines 15-21). Alternate Explanation: Choice (E) is correct. Passage 2 highlights the "elasticity" of scientists' "estimates," suggesting that such figures are fundamentally "unreliable." The author of Passage 1 echoes this assertion in describing the estimation of the Earth's "carrying capacity" for humans as an inexact science. Choice (A) is incorrect. Passage 2 asserts that biologists' estimations of the Earth's "carrying capacity" for humans cover a broad range, but neither author claims that these existing estimates are too high.


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Choice (B) is incorrect. Neither author claims that the "estimates" in Passage 2 are generally "undocumented." Choice (C) is incorrect. While the authors question the accuracy of certain carrying capacity "estimates," there is no suggestion that these figures have been "misunderstood." Choice (D) is incorrect. Neither author ascribes a political motivation to the scientists responsible for the "estimates" mentioned in Passage 2.

9. (C) The area for this question is both passages. (A) is incorrect.

Passage 2 does not refute Passage 1. In fact, both passages agree that estimating the amount of humans that earth can support is difficult. (B) is incorrect. Passage 1 never states that it is describing a popular misconception. (D) is incorrect. Passage 1 does not attack Passage 2. In fact, both passages agree with each other. (E) is incorrect. Passage 2 is not an anecdote (a story) that explains the theory of Passage 1. Passage 2 is written in the same conceptual terms that Passage 1 is. (C) is correct. Passage 2 elaborates on Passage 1. The end of Passage 1 merely states that determining the Earth’s carrying capacity for humans is difficult. Passage 2 explains why this is so. Alternate Explanation: Choice (C) is correct. Passage 1 claims that estimating the Earth's "carrying capacity" for humans is "not an exact science." Passage 2 elaborates on this point by explaining how "carrying capacity" is a subjective concept when applied to humans. Choice (A) is incorrect. Passage 2 supports, not refutes, the claim made in Passage 1 that scientists should stay away from "carrying capacity" estimates. Choice (B) is incorrect. While the notion that human sustainability can be easily estimated may be a popular misunderstanding, Passage 2 counters, rather than exemplifies, such a "misconception." Choice (D) is incorrect. Passage 1 criticizes scientists who attempt to calculate the Earth's "carrying capacity" for humans, but the author of Passage 2 agrees with this criticism. Choice (E) is incorrect. Passage 2 contains nothing that resembles an "anecdote," or retelling of an interesting incident.

10. (E) The area for this question is the entire passage. (A) is

incorrect. The passage only mentions that the author attended graduate school to help advocate the Black Struggle. We cannot assume that the author discovered Black women’s history in graduate school. (B) is incorrect. While the passage does mention this, it is only a short blurb (lines 10-12) and thus not the primary purpose of the passage. (C) is incorrect. The passage does not state that the author wanted to develop research skills. (D) is incorrect. The passage does not state whether the author became more renown or not. (E) is correct. The passage describes how at first the author did not view Black women as important. Then the passage shows how the author changed her mind and viewed Black women as worthy for historical analysis. Alternate Explanation: Choice (E) is correct. The passage mainly discusses the process by which the author comes to realize that Black women are a worthy subject of historical study. Choice (A) is incorrect. The author explains that she did not discover her interest in Black women's history until she was already a tenured historian. It was only after her discussions with Herd and Downey that the author became interested in the subject. Choice (B) is incorrect. Although the

author does mention that she "went to graduate school to become a historian in order to contribute to the Black Struggle for social justice," the passage was not written to support this claim. Choice (C) is incorrect. The author may have honed her research skills while preparing for her book, but the primary purpose of the passage is to show the development of her beliefs as a historian. Choice (D) is incorrect. Although the author does mention the impact of Herd and Downey on her project, there is no indication that her collaboration with them enhanced her status as a historian.

11. (D) The area for this question is line 1. The key to answering this question is understanding the word “serendipitous”. “Serendipitous” means making a fortunate discovery by accident. (A) is incorrect. The first sentence does not indicate that the entry was troublesome. (B) is incorrect. The first sentence does not indicate that the entry was challenging. (C) is incorrect. The first sentence does not indicate that the entry was inevitable. (E) is incorrect. The first sentence does not indicate that the entry was either startling or provocative. (D) is the correct answer. The entry was described as serendipitous, which means that the entry was fortunate and accidental. This agrees with the description “unexpected (accidental) but agreeable (fortunate)”. Alternate Explanation: Choice (D) is correct. The author describes her introduction to Black women's history as "serendipitous," indicating that she regarded her "entry" into the field as both unexpected and fortunate. Choice (A) is incorrect. The author would almost certainly agree that her entry into Black women's history was "worthwhile," but the term "serendipitous" does not suggest that it was particularly "troublesome." Choice (B) is incorrect. The first sentence alone does not support the claim that the author's initiation into Black women's history was "challenging." Choice (C) is incorrect. "Serendipitous" means the opposite of "inevitable," or unavoidable. Choice (E) is incorrect. The author may have been startled to find so much value in a topic that she had previously ignored, but "serendipitous" does not mean "provocative," or stimulating.

12. (E) The area for this question is lines 13-14. Read on to the end of

the sentence on line 17. (A) is incorrect. The area does not mention whether Herd went to graduate school or not. (B) is incorrect. The area does not mention avoiding controversial projects. (C) is incorrect. The area does not state that the author had too many projects. (D) is incorrect. The area does not state whether Herd’s idea was relevant to the Black Struggle or not. (E) is the correct answer. The author thought the invitation was intrusive because she didn’t think of Black women as important. Thus, the author thought that Herd was irrelevant (i.e., black women aren’t important) and presumptuous (i.e., the invitation was intrusive). Alternate Explanation: Choice (E) is correct. The author clearly considered Herd's request "presumptuous" and "intrusive," but she also believed it to be irrelevant because she "had never even thought about Black women as historical subjects." Choice (A) is incorrect. The author does not mention Herd's educational credentials. Choice (B) is incorrect. The author gives no indication that she thinks historians should avoid controversy. Choice (C) is incorrect. The author does not specifically mention whether she had any other time-


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consuming commitments. Choice (D) is incorrect. The author does not indicate that Herd explicitly discussed a "struggle for social justice."

13. (C) The area for this question is lines 27-30. (A) is incorrect. The

area does not mention payment. (B) is incorrect. The area does not describe historians about being unassuming. (D) is incorrect. The area does not discuss the length of time historians spend on writing books. (E) is incorrect. The area does not discuss interacting with the public. (C) is the correct answer. The analogy shows how historians generally do not write books on request; it’s not like ordering a hamburger from a fast-food joint. Alternate Explanation: Choice (C) is correct. The author's admonishment indicates that she was not accustomed to undertaking academic projects upon request. Choice (A) is incorrect. The author does not mention the issue of payment at any point in the passage. Choice (B) is incorrect. The author does not imply that historians are modest about their work. On the contrary, these lines reflect her initial arrogance regarding Herd's proposed project. Choice (D) is incorrect. While historians may spend many years working on one project, the hamburger comparison does not address this idea. Choice (E) is incorrect. Although it may be rare for a historian to accept a project idea from a member of the public, there is no evidence to support the claim that historians do not "interact with members of the public" in general.


area does not suggest that the author was embarrassed by her lack of knowledge. (B) is incorrect. The area does not discuss the difficulty in regards to finding primary sources. (D) is incorrect. The area does not state the lives of Black women were interesting or historically complex. (E) is incorrect. The topic is not of general interest. Herd wanted the author to research the history of Black women, which would only appeal to specific interest groups. (C) is correct. The author used her ignorance about the topic as an excuse as to why she could not write the book. In order for this excuse to be valid, it must imply that historians should only write books on topics that they are familiar with. Alternate Explanation: Choice (C) is correct. The author tried to excuse herself from fulfilling Herd's request by professing her ignorance of Black women's history. Inherent in this action is the assumption that historians should work within their areas of expertise. Choice (A) is incorrect. The author does not imply that her lack of scholarly training in this previously neglected subject is a source of embarrassment. Choice (B) is incorrect. While the author had not studied any primary sources before accepting Herd's proposal, she does not imply that she had assumed they would be difficult to find. Choice (D) is incorrect. The author clearly states that she had never before "thought about Black women as historical subjects." Choice (E) is incorrect. Nothing in this sentence or in the passage as a whole suggests that Black women's history was considered to be a mainstream subject

15. (A) The area for this question is the last two sentences (lines 53-

55). (B) is incorrect. The area does not discuss the diversity of Black women’s experiences. (C) is incorrect. The area does not

talk about historians studying Black women. (D) is incorrect. The area does not discuss the political power Black women had. (E) is incorrect. The area does not discuss the author’s willingness to write or not. (A) is correct. The area states that the author knew about Black women, but simply did not understand their significance. Alternate Explanation: Choice (A) is correct. The final two sentences of the passage clarify the author's original misconception of Black women's role in history. She writes that she had been aware of "a universe of Black women" without comprehending its historical significance. Choice (B) is incorrect. The author does not indicate that the book was particularly challenging to write. Choice (C) is incorrect. The passage asserts that Black women's history has been widely neglected by academics, but ultimately argues that it is a worthy book topic. Choice (D) is incorrect. The author does not discuss the history of Black women's political power in these sentences or elsewhere in the passage. Choice (E) is incorrect. The last two sentences are less about diversity than they are about Black women's historical significance.

16. (A) The area for this question is the entire passage. (B) is

incorrect. The passage does not reminiscence. It does not explore a past experience in such a way to emphasize the experience and look back at it. (C) is incorrect. The passage does not suggest a solution to a problem. (D) is incorrect. The passage does not use specific examples. There is only one experience being described. (E) is incorrect. The passage does not present opposing viewpoints. Only the viewpoint of the author is presented. (A) is correct. The passage uses narrative description followed by commentary. First the passage describes the author’s experience at the planetarium. Then the passage comments on the experience in the last paragraph (lines 48-64) by reflecting on the awe the show created. Alternate Explanation: Choice (A) is correct. The bulk of the passage recreates the narrator's visit to a planetarium, but the text switches from "description" to "commentary" in the final paragraph. Choice (B) is incorrect. The passage seems to be a "reminiscence," or a recollection, of past events, but t here is no indication that the narrator jumps from the past to the present in either verb tense or content. Choice (C) is incorrect. The narrator suggests that the pursuit of "awe" is fundamentally problematic but does not offer a "solution" of any kind. Choice (D) is incorrect. The narrator uses a myriad of details, not generalizations, to depict the sensory experience created inside of the planetarium. Choice (E) is incorrect. The only viewpoint presented in the passage is that of the narrator.

17. (B) The area for this question is lines 5-7. (A) is incorrect.

Crackling potato chip bags does not show helplessness. Helplessness would be shown by cringing in fright. (C) is incorrect. Crackling potato chip bags does not show awe. Awe would be shown by wide eyes or open mouths. (D) is incorrect. Anticipation is not shown by crackling potato chip bags, rather it would be shown through silence. (E) is incorrect. Irritation is not shown. The children have nothing to be irritated about. (B) is correct. Restlessness is shown. Crackling potato chip bags shows how the children are bored and want to do something that interests them. They are fidgeting.


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Alternate Explanation: Choice (B) is correct. "Restless" means antsy or excitable. The image of "adults all around . . . shushing the children" suggests that the children are too restless to remain quiet in the darkened room. Choice (A) is incorrect. The adults may feel helpless in their efforts to quiet the noisy children, but nothing in these lines indicates that the children themselves are helpless. Choice (C) is incorrect. The children's agitation contrasts with the feelings of "awe" that the planetarium show is presumably meant to inspire. Choice (D) is incorrect. While some of the children in the planetarium audience may look forward to the show, their general noisiness indicates inattention more than "anticipation." Choice (E) is incorrect. Some of the children may act out of mild boredom, but the narrator does not suggest that they are largely irritated, or annoyed.

18. (E) The area for this question is line 11 to the end of the paragraph

(line 13). “Progress” is used in “describe the progress of the Royal Family to Westminster abbey”. Thus the use of “progress” indicates motion or traveling. (A) is incorrect. “evolution” does not denote traveling. (B) is incorrect. “improvement” does not denote traveling. (C) is incorrect. “prosperity” means wealth or well-being. It does not denote traveling. (D) is incorrect. “promotion” does not denote traveling. (E) is correct. “advance” means to move forward, as in ‘First regiment, advance to your positions!’. Thus “advance” denotes traveling. Alternate Explanation: Choice (E) is correct. The word "progress" in this context means a ceremonial journey. Line 11 refers to members of British royalty making such a trip to a famous London cathedral. Choice (A) is incorrect. The term "progress" is sometimes used to refer to "evolution," or gradual development, but it is illogical to describe the "evolution" of a group of people to a place. Choice (B) is incorrect. "Progress" sometimes indicates a positive change, but it makes little sense to describe the Royal Family's procession to Westminster Abbey as an "improvement." Choice (C) is incorrect. While it may be said that one who prospers is progressing financially or personally, this use of the term "progress" does not fit in the context of line 11. Choice (D) is incorrect. The term "promotion" typically refers to a professional progression, which has nothing to do with the Royal Family's ceremonial journey.

19. (C) The area for this question is the first paragraph. (A) is

incorrect. The first paragraph is not jaded. The author does not make sarcastic remarks. (B) is incorrect. The first paragraph is not nervous. The author does not describe him or herself fidgeting or waiting in fright. (D) is incorrect. The first paragraph does not demonstrate initial concern. The author is not worried about what is occurring in the planetarium. (E) is incorrect. The first paragraph is not a mundane routine. “Mundane” means normal or boring. Going to a planetarium is not boring. The author seems interested. (C) is correct. A mood of dramatic anticipation is established. The author describes the dramatic music (line 5) and the dramatic voice of the announcer (lines 7-9).

Alternate Explanation: Choice (C) is correct. The first paragraph attempts to recreate the tension that exists in a darkened planetarium as audience members settle into their chairs and wait for the show to begin. The author's evocative description of the domed screen coming to life as "commanding music" swells under an "eloquent," disembodied voice contributes to the feeling of "dramatic anticipation." Choice (A) is incorrect. At no point does the narrator appear to be "jaded," or tired, of the planetarium experience. Choice (B) is incorrect. The first paragraph is peppered with adjectives such as "comfortable," "splendid," and "eloquent." These terms create a mood that is neither nervous nor apprehensive. Choice (D) is incorrect. The passage does not suggest that the narrator has any concerns about the upcoming presentation. Choice (E) is incorrect. It is unlikely that an author would describe a mundane, routine event or feeling in such colorful detail.

20. (B) The area for this question is line 34. Read a little bit ahead

(from line 27) to understand the context. (A) is incorrect. The area does not mention the children in the audience. (C) is incorrect. The area does not show that the author has troubles with admitting a problem. (D) is incorrect. The implications of space travel are not discussed in the area. (E) is incorrect. The area does not mention studies. (B) is correct. The author is overwhelmed by the information being presented. This is implied because the author sets his or her mind to merely recording simple facts, instead of trying to process all the information. Alternate Explanation: Choice (B) is correct. "Stunning facts" illustrating the immensity of the universe "rolled past" the narrator's head in the second paragraph, creating a dizzying web of information. The narrator's mind seems to dodge and shrink away from the deluge of figures and concepts. Only when the facts become less abstract and more familiar is the narrator capable of mechanically recording information. Choice (A) is incorrect. The reference to the narrator's "dodging and shrinking mind" appears in line 34. It is unlikely that the children who are briefly mentioned in line 6 are responsible for the narrator's mental state almost 30 lines later. Choice (C) is incorrect. The narrator readily admits that the astronomical facts are "troubling" in their complexity. Choice (D) is incorrect. No significant mention of "space travel" appears at any point in the passage. Choice (E) is incorrect. Although the narrator acknowledges in lines 44–45 that "confident" scientific information is often revised, nothing in the passage suggests that the narrator's "dodging and shrinking mind" is related to any doubts regarding the show's accuracy.


author does not show a preference for irony. The area does not describe something ironic. (B) is incorrect. The area does not show that the author prefers inventiveness. Having mercury rotate once rather than three times does not show a contrast in inventiveness. (D) is incorrect. The area does not show a preference for ornamentation. Having mercury rotate only once is not more decorative than having it rotate three times. (E) is incorrect. The area does not show a preference for ambiguity. Having mercury rotate once is not more or less ambiguous than having it rotate three times. Both situations are equally clear. (C) is correct. The


32

author shows a preference for symmetry. One rotation to one orbit is more symmetrical than three rotations to two orbits. Alternate Explanation: Choice (C) is correct. The narrator is disappointed to learn from the planetarium show that Mercury's orbit is more complicated than once thought. Apparently the moonless planet rotates three times per every two trips around the sun, "an odd arrangement" compared to the outdated theory that Mercury rotates just once per solar orbit. The narrator's preference for the simpler "arrangement" implies a preference for "symmetry," or balance. Choice (A) is incorrect. Lines 40–43 do not demonstrate the narrator's sense of "irony." Choice (B) is incorrect. The narrator's reaction to Mercury's "odd arrangement" may be unusual, but it does not particularly demonstrate "inventiveness," or creativity. Choice (D) is incorrect. The narrator includes numerous details in the passage but presents them simply. It is somewhat inaccurate, then, to claim that the narrator's style as it appears in lines 40–43 is ornamental, or embellished. Choice (E) is incorrect. The narrator's feelings regarding Mercury's complicated orbit suggest a discomfort with "ambiguity," or confusion, not a preference for it.

22. (A) The area for this question is line 53. Start at the beginning of

the sentence at line 51 and read to the end of the sentence on line 55. “Fixed” is used in the context as ‘to fix one’s attention’. Thus it is used to mean to focus or to direct. (B) is incorrect. “Prepare” does not mean to focus or direct. (C) is incorrect. “Repair” does not mean to focus or direct. (D) is incorrect. “Decide” does not mean to focus or direct. (E) is incorrect. “Influence” does not mean to focus or direct. (A) is correct. “Focus” means to focus or direct. Alternate Explanation: Choice (A) is correct. "Fix" in this context means to direct one's attention. Lines 51–55 specifically refer to the adults' effort to catch the children's attention and direct it to the planetarium show. Choice (B) is incorrect. "Fix" sometimes means to "prepare," but this definition is illogical within the context of line 53. Choice (C) is incorrect. A common definition of "fix" is to "repair," but it is illogical to claim that adults tried to "repair" children's attention to something. Choice (D) is incorrect. The term "fix" is occasionally used to reflect a decision, but a child's attention cannot be decided on something else. Choice (E) is incorrect. An event or outcome that has been improperly influenced is sometimes described as "fixed," but this sense of the word does not fit the context of line 53.

23. (E) The area for this question is line 54. Start at the beginning of

the sentence at line 51 and read to the end of the sentence on line 55. Horrible immensities refers to what the planetarium is trying to get the children to focus on (instead of their drinks and chips). Thus horrible immensities must refer to the stars or the vastness of the stars. (A) is incorrect. The area does not discuss exaggerated information. (B) is incorrect. The area does not discuss seeing the future and unforeseen events. (C) is incorrect. The area does not discuss history. (D) is incorrect. The area does not discuss any debates. (E) is correct. The vastness of the stars is something that is incomprehensible to the minds of little children. Alternate Explanation: Choice (E) is correct. The astronomical "realities" portrayed in the planetarium show suggest a universe so immense that its sheer size

is "incomprehensible" and horribly intimidating to the narrator. Choice (A) is incorrect. Facts that indicate the vastness of the universe may seem "exaggerated," but there is nothing to suggest that the information presented at the planetarium is overstated. Choice (B) is incorrect. The presentation does not focus on "unforeseen," or unexpected, events. Choice (C) is incorrect. The presentation does not address a single monstrosity, historical or otherwise. Choice (D) is incorrect. Nowhere in the passage does the narrator directly refer to "controversial debates."

24. (D) The area for this question is lines 59-60. Read lines 57-64 to

get a better idea of the context. (A) is incorrect. The echo-chamber effects do not illustrate an appreciation of the universe. Instead, the author implies that such effects are superficial, in the sense that real awe is simply a shiver when looking out a window. (B) is incorrect. The area does not address whether adults want to attend the planetarium or not. (C) is incorrect. The area does not discuss the views of contemporary (today’s) scientists. (E) is incorrect. The use of the effects does not show that the show’s promoters understand how children will react to the said effects. The way children react is not mention in the area. (D) is correct. The show’s promoters do not really appreciate the universe, because they use special effects, which in a sense belittle the awe the vastness of the universe is suppose to create. It is similar to using a firecracker to show the awesome power of a howitzer cannon. Alternate Explanation: Choice (D) is correct. The narrator criticizes the show's promoters by suggesting that they used special effects such as "echo-chamber effects" to create a mere simulation of "the awe that they.. . ought to feel" at the immensity of the universe. Choice (A) is incorrect. The narrator does not imply that the majority of adults appreciate the universe's "horrible immensities," but instead suggests that the adults responsible for infusing the show with special effects are "immune themselves" to the awesome realities of the universe. Choice (B) is incorrect. The narrator does not speculate about the popularity of planetarium shows among adults. Choice (C) is incorrect. Contemporary scientists likely contributed to the planetarium presentation, but the narrator does not discuss how these scientists feel about their work. Choice (E) is incorrect. The show's creators may have included special effects to appeal to children, but the narrator does not mention such a theory. The only implication is that such effects illustrate the promoters' immunity to the awesome nature of the universe.

Section 8 1. (D) Our goal is to find the cost in dollars of n notebooks and b

backpacks. We are told the notebooks cost $2 each and backpacks cost $32 each. Since we have n notebooks and the cost is 2 dollars per notebook, we have

( ) 22

dollarsn notebooks n dollars

notebook =

The same can be done for backpacks

( ) 3232

dollarsb backpacks b dollars

backpacks

=

Since we want the total cost of notebooks and backpacks we can simply add the cost of both:


33

2 32cost n b= + The answer is (D). Alternate Explanation: Choice (D) is correct. If notebooks cost $2 each, then the cost of n notebooks is 2n dollars. If backpacks cost $32 each, then the cost of b backpacks is 32b dollars. So, the cost, in dollars, of n notebooks and b notebooks is 2 32 .n b+ Choice (A) is not correct. See the explanation for the correct response (D). Choice (B) is not correct. See the explanation for the correct response (D). Choice (C) is not correct. Since

( )34 34 34 ,n b n b+ = + this would be the cost, in dollars, of n

notebooks and b backpacks if each notebook cost $34 and each backpack cost $34 . Choice (E) is not correct. Since

( )2 32 2 64 ,n b n b+ = + this would be the cost, in dollars, of n

notebooks and b backpacks if each notebook cost $2 and each backpack cost $64 .

2. (D) Our goal is to find the value of x. We are given that the average of 6, 19, and x is 19. The average of a set of number is equal to the sum of n numbers divided by n. So the sum of 6, 19, and x divided by 3, since there are 3 numbers, is equal to 19.

6 1919

325 57

32

x

xx

+ +=

+ ==

The answer is (D). Alternate Explanation: Choice (D) is correct. If the average of 6, 19, and 19,x then

6 19 193

x+ + = . So 6 19 57,x+ + = and 57 25 32.x = − =

Choice (A) is not correct. Since the average of 6, 19, and x is 19 and 6 19,< x must be greater than 19 . See the explanation for the correct response (D). Choice (B) is not correct. See the explanation for the correct response (D). Choice (C) is not correct. See the explanation for the correct response (D). Choice (E) is not correct. The sum of 6, 19, and x is equal to 57 , but x is not equal to 57 . See the explanation for the correct response (D).

3. (A) Our goal is to find how many sandwiches Ali made. We know that Ali, Ben and Carla made a total of 20 sandwiches

( 20A B C+ + = ). Also we know that Ben made 3 times as

many as Ali ( 3B A= ), and Carla made twice as many as Ben

( 2C B= ). We can substitute A with B/3 and C with 2B in the first equation.

( )

20

2 203

3 6 6010 60

66

23 3

A B C

BB B

B B BBB

BA

+ + =

+ + =

+ + ===

= = =

The answer is (A). Alternate Explanation: Choice (A) is correct. If Ali made x sandwiches, and Ben made three times as many as Ali, then Ben made 3x sandwiches. Carla made twice as many sandwiches as Ben, so Carla made 2 3 6x x⋅ = sandwiches. The total number of sandwiches they made was 3 6 .x x x+ + This is also equal to 20 , so

3 6 20x x x+ + = . Solving for x gives 2x = , so Ali made 2 sandwiches. Choice (B) is not correct. See the explanation for the correct response (A). Choice (C) is not correct. See the explanation for the correct response (A). Choice (D) is not correct. See the explanation for the correct response (A). Ben made 3 times as many sandwiches as Ali, and Ali made 2 sandwiches, so 6 is the number of sandwiches Ben made. However, the question asked how many sandwiches Ali made. Choice (E) is not correct. See the explanation for the correct response (A).

4. (C) Our goal is to find 3 percent of n. We are given that 0.03 percent of n is 3. When dealing with percent, remember that to convert percent to decimal, divide the number by 100. For example 10 percent is the same as 10/100, or 0.1. Now 0.03 percent is the same as .03/100, or .0003. So .03 percent of n is 3, so we have

.03* 3

100.0003 3

310,000

.0003

n

n

n

=

=

= =

Since we want 3 percent of n, we have

3*10,000 300

100=

The answer is (C). Alternate Explanation: Choice (C) is correct. If 0.03 percent of n is 3 , then 0.03 3100

n = . So 0.0003 3n = , and 3 10,000

0.0003n = = . Thus,

3 percent of n is 3 10,000 300

100⋅ = . Choice (A) is not

correct. From the explanation for the correct response (C), you


34

have n is 10,000 . So 900 9 percent of n . However, the question asked for 3 percent of n . Choice (B) is not correct. From the explanation for the correct response (C), you have n is 10,000 . So 600 is 6 percent of n . However, the question asked for 3 percent of n . Choice (D) is not correct. From the explanation for the correct response (C), you have n is 10,000 . So 0.006 is 0.00006 percent of n . However, the question asked for 3 percent of n . Choice (E) is not correct. From the explanation for the correct response (C), you have n is 10,000 . So 0.003 is 0.00003 percent of n . However, the question asked for 3 percent of n .

5. (B)

Our goal is to find the equation of the line l. The general equation

for a line is y = m*x+b, where (x,y) is a point on the line, m is the slope of the line, and b is the y-intercept of the line. The slope of the line is the rise over run. The y-intercept is the y value when the line intersects the y-axis. We can find the slope using any two points on the line. Use points (2,0) and (0,3). Now the rise (change in y) from the former to the later point is 3, and the run (change in x) from the former to the latter is -2. Since slope is rise

over run, the slope m=

32

−. The equation becomes

32

y x b= − +. We can plug in one point, (0,3), to obtain a

value for b as follows

3(3) (0)

23

b

b

= − +

=

So the equation for the line becomes

33

2y x= − +

The answer is (B). Alternate Explanation: Choice (B) is correct. An equation of line l is y mx b= + ,

where m is the slope of l and b is the y -intercept of l . From

the figure, you can see that the points ( )0,3 and (2,0) are on l ,

so the slope is 3 0 3.0 2 2

− = −−

Since l intersects the y -axis at the

point ( )0,3 , the y -intercept of l is 3 . So 32

m = − and 3b = ,

and l has the equation 3

3.2

y x= − + Choice (A) is not correct.

You can see from the figure that the point (2,0) is on line l . But

30 2 2 3 2 1

2 ≠ − + = − + = −

. So 3

22

y x= − + cannot be an

equation of l . Choice (C) is not correct. You can see from the figure that the point (2,0) is on line l . But

2 4 50 2 3 3 .

3 3 3 ≠ − + = − + =

Choice (D) is not correct. You

can see from the figure that the point (2,0) is on line l . But

2 4 100 2 2 2 .

3 3 3 ≠ + = + =

Choice (E) is not correct. You can

see from the figure that the point (2,0) is on line l . But

2 4 130 2 3 3 .

3 3 3 ≠ + = + =

6. (B)

Our goal is to find which lettered point is between ¼ and 3/8. There are 3 tick marks between 0 and 1, thus the space between each tick represents one-fourth of the distance from 0 and 1. Thus the distance from 0 to the first tick mark is .25, and so on. Thus the three tick marks, starting from the one closest to 0, are .25, .50, and .75 respectively. Now 1/4 as a decimal is .25. Looking at the diagram, we see that the point 1/4 should be at the .25 tick mark. Now 3/8 as a decimal is .375. Looking at the diagram, we see that the point 3/8 should be between the .25 tick mark and the .5 tick mark.

Point B is closer to the .25 tic mark and point C is closer to the .50 tick mark. Since we want a letter that is between the 1/4 mark (the .25 mark) and the 3/8 mark (in the middle of the .25 mark and the .50 mark), the only letter in that region is letter B. The answer is (B). Alternate Explanation:

B A C

1

D E

0 14

38

2

4

3

4

B A C

1

D E

0

l

y

x

1

1 O


35

Choice (B) is correct. If the portion of the number line between 0 and 1 is divided into eighths, the result is

The only lettered point between 14

and 38

is B .

Choice (A) is not correct. If the portion of the number line between 0 and 1 is divided into eighths, as in the figure above, you can

see that point A is less than 14

. Choice (C) is not correct. If the

portion of the number line between 0 and 1 is divided into eighths, as in the figure above, you can see that point C is greater

than 38

. Choice (D) is not correct. If the portion of the number

line between 0 and 1 is divided into eighths, as in the figure

above, you can see that point D is greater than 38

. Choice (E) is

not correct. If the portion of the number line between 0 and 1 is divided into eighths, as in the figure above, you can see that point

E is greater than 38

.

7. (D) Our goal is to find the value of h in terms of x. We are given

that 1 1x h− = . When a number is raised to a negative power, it is

the same as the reciprocal of the number raised to the positive power. For example

1 41 4

1 1x or x

x x− −= =

For this problem we now have

1

1* 1

1

hx

hxh x

=

=

= The answer is (D). Alternate Explanation:

Choice (D) is correct. If 1 1,x h− = then 1xx h x− = , so h x= . Choice (A) is not correct. See the explanation for the correct response (D). Choice (B) is not correct. See the explanation for the correct response (D). Choice (C) is not correct. See the explanation for the correct response (D). Choice (E) is not correct. See the explanation for the correct response (D).

8. (D)

Our goal is to find the value of y. When two lines intersect at a point, opposite angles are the same, and accordingly, y = 2x. Also, two adjacent angles which are along the same line have a sum equal to 180°, and accordingly y + 4x = 180. Substituting 2x for y in the second equation yields,

2 4 1806 180

30

x xxx

+ ===

Since we know that y = 2x, we have y = 2(30)=60. The answer is (D). Alternate Explanation: Choice (D) is correct. Since 4 2 180,x x+ = , it follows that 6 180x = and 30.x = Vertical angles are equal, so 2 .y x=

Thus, 60.y = Choice (A) is not correct. See the explanation for the correct response (D). Choice (B) is not correct. See the explanation for the correct response (D). Choice (C) is not correct. See the explanation for the correct response (D). Choice (E) is not correct. See the explanation for the correct response (D).

9. (C) Our goal is to find a possible value for 2x x− . We are

given the equation 2 30x x+ = . We can rearrange this

equation and do foil to solve for possible values of x

( ) ( )

2 30 0

5 6 0

5 6

x x

x x

x x

+ − =

− + =

= = −

Now we can plug in x=5, and x=6, and see which one is in the answer choice.

2 2

2 2

(5) 5 25 5 20

( 6) ( 6) 36 6 42

x x

x x

− = − = − =

− = − − − = + = Twenty and 42 are both possible but only 20 is an answer choice. The answer is (C). Alternate Explanation:

Choice (C) is correct. If 2 30,x x+ = then 2 30 0.x x+ − = So

( )( )6 5 0x x+ − = , and either 6x = − or 5x = . If 5x = , then 2 25 5 20x x− = − = .

Choice (A) is not correct. If 2 30 0,x x+ − = then 2 30 0.x x+ − = So ( )( )6 5 0x x+ − = , and either 6x = − or

5x = . If 5x = , then 2 25 5 20x x− = − = . If 6x = − , then

0 18

14

38

12

58

34

78

1

A B C D E • • • • •

y° 4x

2x


36

( )2 36 6 36 6 42x x− = − − = + = . So 2x x− cannot equal

30− .

Choice (B) is not correct. If 2 30 0,x x+ − = then 2 30 0.x x+ − = So ( )( )6 5 0x x+ − = , and either 6x = − or


( )2 36 6 36 6 42x x− = − − = + = . So 2x x− cannot equal 10 .

Choice (D) is not correct. If 2 30 0,x x+ − = then 2 30 0.x x+ − = So ( )( )6 5 0x x+ − = , and either 6x = − or


( )2 36 6 36 6 42x x− = − − = + = . So 2x x− cannot equal

30 .

Choice (E) is not correct. If 2 30 0,x x+ − = then 2 30 0.x x+ − = So ( )( )6 5 0x x+ − = , and either 6x = − or


( )2 36 6 36 6 42x x− = − − = + = . So 2x x− cannot

equal 870 .

10. (B) Our goal is to find which graph could correctly represent the trip. Mark begins a 4-mile trip by riding slowly uphill for 1 mile. Then he rests for 10 minutes and then rides quickly downhill for the rest of the trip. So we know that he traveled a total distance of 4 miles, and had a 10 minute period of rest. All the graphs in the answer choices have distance traveled in the y-axis and time in the x-axis. We do not know the total trip time but we do know the total distance traveled, he began at 0 miles and ended at 4 miles. Now answer choice (C) starts him at 1 mile at time = 0, instead of 0 miles at time = 0 and thus (C) can be eliminated. Also choices (D) and (E) have him ending at 0 miles instead of 4 miles, and can accordingly be eliminated. Now we are also told that Mark rode slowly first, took a 10 minute break, and then rode fast at the end. In a graph, the slope is rise, the change in y, divided by the run, the change in x. In the graph, the change in y is the change in distance and the chance in x is the change in time. Well slope would then become change in distance divided by the change in time, which is speed. Speed is the distance over time. So the slope of the graph represents the speed at that time. The greater the slope, the greater the speed, and vise versa. Now since Mark was riding slowly at the beginning and rapidly at the end, the slope should be lower at the beginning and higher at the end. A low slope is flatter, since there is little change in y for a large change in x. A high slope is steeper, since there is a big change in y for a little change in x. Therefore we want a flatter graph in the beginning and a steeper graph in the end. In answer choice (A), the graph is steep in the beginning and flatter at the end, implying that Mark rode fast first, and slow at the end, but this is not the case and (A) can be eliminated. In choice (B), we have a flatter beginning (implying slow start), followed by a 10 minute period of no speed (slope = 0), and a steep ending (implying fast end), which is all true of the given criteria. The answer is (B). Alternate Explanation: Choice (B) is correct. This graph could show Mark’s distance traveled as a function of time. The first portion of the graph indicates that Mark rode at a constant rate of 1 mile in 10

minutes ( 6 miles per hour) and covered a distance of 1 mile. The next portion of the graph is horizontal, which indicates that he rested for 10 minutes and did not cover any distance during that period. The graph indicates that during the final 10 minutes Mark rode at a constant rate of 3 miles in 10 minutes, or 18 miles per hour, which is faster than he rode in the first 10 minutes. Choice (A) is not correct. This graph could not represent Mark’s trip. One reason is that it indicates that Mark rode at a rate of 18 miles per hour for the first 10 minutes and at a rate of 6 miles per hour during the last 10 minutes of his trip. If 18 miles per hour is described as riding “slowly,” then 6 miles per hour cannot be described as riding “quickly.” Choice (C) is not correct. This graph could not represent Mark’s trip. One reason is that it shows the total distance of the trip to be 3 miles, but the trip was 4 miles long. Choice (D) is not correct. This graph could not represent M ark’s trip. One reason is that it does not have a horizontal section to indicate the 10 -minute period during which Mark covered no distance. Choice (E) is not correct. This could not represent Mark’s trip. One reason is that it indicates a negative distance traveled during the last 10 minutes of the trip. This is not possible.

11. (E) Our goal is to find the least number of boxes that must be

selected to be sure that 3 or more contain scarves of the same color. We are told that there are 6 red, 6 brown, 6 yellow, and 6 gray scarves packaged individually in 24 identical unmarked boxes. The answer will be a number of boxes that will have at least 3 scarves of the same color 100% of the time. Examine (A). Suppose we randomly choose 3 boxes, we might get (r,r,r), (r,b,y), or (b,b,g) and so on. This may work sometimes but not all the time, thus (A) can be eliminated. Look at (B). Suppose we randomly choose 6 boxes, we might get (r,r,b,g,y,r) is which case we would have 3 red, but we may also get (r,b,y,g,r,b) in which case we do not have 3 of the same color. This also does not work all of the time. To be sure that we have three of the same color, chose the most distributive and random possibility. First p ick one of each color (r,b,y,g), and then pick each one again (r,b,y,g,r,b,y,g). Now we have 8 boxes in our set and we still cannot be sure that there will always be three of the same color. In the ninth box, we will get a color that will make 3 of the same color because we already have 2 of each color in the box. So it does not matter what the ninth box color is, because we will have at least 2 of every color, and the ninth box will make 3 of one color. The answer is (E). Alternate Explanation: Choice (E) is correct. If 8 boxes are selected, there could be red scarves in 2 of them, brown scarves in 2 of them, yellow scarves in 2 of them, and gray scarves in 2 of them; in this case, there would not be 3 or more scarves of the same color among these 8 boxes. However, if one more box is selected, the color of the scarf in that box must be the same as the color of the scarves in 2 of the original 8 boxes, and there will then be 3 of the same color. So, 9 is the least number of boxes that must be selected in order to be sure that among the boxes selected 3 or more contain scarves of the same color. Choice (A) is not correct. If 3 boxes are selected, there could be a scarf of a different color in each box. Choice (B) is not correct. If 6 boxes are selected, there could be red scarves in 2 of them, brown scarves in 2 of them, and yellow scarves in 2


37

of them. Choice (C) is not correct. If 7 boxes are selected, there could be red scarves in 2 of them, brown scarves in 2 of them, yellow scarves in 2 of them, and a gray scarf in 1 of them. Choice (D) is not correct. If 8 boxes are selected, there could be red scarves in 2 of them, brown scarves in 2 of them, yellow scarves in 2 of them, and gray scarves in 2 of them.

12. (B)

Our goal is to find the value of x. We are told that the figure ABCDEF is a regular hexagon and the center is at point O. The sum of the internal angles of any figure with n sides is

( ) °− 180*2n . Since the figure ABCDEF has six sides, the sum of the internal angles is

( ) °==° 720180*4180*2-6 . Since the figure is a regular hexagon, all the sides have equal length and all the angles have equal measure. Thus the measure of each of the six angles is equal to 720º/6=120º. So we know that the

°=∠=∠ 120BmAm . Also since point O is the origin of the figure ABCDEF, any line from a point on the figure (only points A, B, C, D, E, and F) to the origin will bisect (divide into two equal measures) the angle at that point. For instance, The line BO

bisects the angle at point B. Since the °=∠ 120Bm , the

measure of xº will be °=

°=

∠=∠ 60

2120

2Bm

xm. Then

answer is (B). Alternate Explanation: Choice (B) is correct. Since O is the center of the hexagon, it follows that OB OD= . Drawing some additional lines and labeling some angles yields additional information from the

figure: From the symmetry of the regular hexagon, it follows that m AOB m BOC m COD m DOE m EOF m FOA∠ = ∠ = ∠ = ∠ = ∠ = ∠. Since the sum of these angles is 360° , each of these angles has

a measure of 60° . So 60y = . It is also true that OB OC= , so

x z= . Since 180x y z+ + = , and 60y = , it follows that

120.x z= = Therefore, 2 120x = , and 60x = . Choice (A) is not correct. See the explanation for the correct response (B). Choice (C) is not correct. See the explanation for the correct response (B). Choice (D) is not correct. See the explanation for the correct response (B). Choice (E) is not correct. See the explanation for the correct response (B).

13. (C) Our goal is to find an equivalent value to )( rpf + . We

are given that xxf 5)( = for all numbers x. From this function, we can see that when a value, x, goes into the function, the outcome is 5 times the value, x. We can extend this to our desired value. When the value p + r enters the function, the outcome should be 5 times the value of p + r. Thus we have

rprprpf 55)(5)( +=+=+ . The answer is (C). Alternate Explanation: Choice (C) is correct. Since ( ) 5f x x= for all numbers x , you

have ( ) ( )5 5 5f p r p r p r+ = + = + . Choice (A) is not correct.

Since ( ) 5f x x= for all numbers x , you have

( ) ( )5 5 5f p r p r p r+ = + = + . This expression is not

equivalent to 5

p r+. For example, if 1p r= = , then

5 5 10p r+ = , but 2

5 5p r+ = . Choice (B) is not correct. Since

( ) 5f x x= for all numbers x , you have


equivalent to 5p r+ . For example, if 1p r= = , then 5 5 10p r+ = , but 5 6p r+ = . Choice (D) is not correct. Since

( ) 5f x x= for all numbers x , you have


equivalent to ( )10 p r+ . For example, if 1p r= = , then

5 5 10p r+ = , but ( )10 20p r+ = . Choice (E) is not correct.

Since ( ) 5f x x= for all numbers x , you have


equivalent to 25pr . For example, if 1p r= = , then 5 5 10p r+ = , but 25 25pr = .

14. (C)

C D

B E

A F

O

z° x° y°

A F

C

B x?

D

E O


38

Our goal is to find the perimeter of one of the regions. We are told that the area of the circle is 25p and is divided into 8 congruent regions. Remember that the perimeter of a figure is the sum of the sides of the figure. For each of the 8 regions, the perimeter consists of the sum of three parts, (a, b, and c).

Now the length of a and b is simply the radius of the circle. The length of c is part of the circumference of the circle. Now since there are 8 regions in the circle, the circumference is accordingly divided into 8 parts. The length of c is simply one-eight of the circumference of the circle. The formula for the area of a circle is

2rπ . Since the area of the above circle is 25p, we can find the value of r and accordingly a and b.

2

2

25

255

r

rr

π π=

==

Since r = 5 and a = b = r, we have a = b = 5. Now we have to find

c. The formula for the circumference of a circle is rπ2 . So the

circumference of the circle is πππ 10)5(22 ==r . Since the c is equal to one-eight of the circumference, we have

45

810 ππ

==c. So the total perimeter is

45

104

555

ππ+=++=++= cbaperimeter

The answer is (C). Alternate Explanation: Choice (C) is correct. The perimeter of each of the 8 congruent

regions is 128

r C+ , where r is the radius of the circle and C is

the circumference of the circle. The area of the circle is 225 rπ π= , so 5r = . The circumference of the circle is 2 rπ ,

so 10C π= . The perimeter of one of the regions, then, is 1 10 52 10 108 8 4

r C π π+ = + = + . Choice (A) is not correct. See

the explanation for the correct response (C). Choice (B) is not

correct. See the explanation for the correct response (C). Choice (D) is not correct. See the explanation for the correct response (C). Choice (E) is not correct. See the explanation for the correct response (C).

15. (A) Our goal is to find a value of k that will cause the system of equations to have no solution. We are given 2 equations with 2 unknowns (not including k).

174852

=+=−

kyxyx

To solve a system of equations, we solve one equation for one variable, and substitute this value into a second equation and solve. Suppose that k=1, we would have

( )27

414

1441734

33311171610

172

854

1742

85852852

====+

===++

=+

+

=+

+=→+=→=−

xxx

yyyy

yy

yx

yxyxyx

So when k=1, we have a value for x and y and accordingly a solution for the system of equations. But we want a value for k that does not have a solution for the system of equations. No solution occurs when there are more unknowns than equations (one cannot solve a system of 2 equations with 3 unknowns), and when equations are the same, causing there to be more unknowns than equations (two equations with two unknowns is solvable, but if two equations are the same, this leaves only one real equation for two unknowns and is therefore not solvable). In our system, there are 2 unknowns, and in order to solve for the unknowns, we must have two equations. If the two equations are the same, then there is only one real equation for two unknowns, which is not solvable. Thus we want to make equation 1 similar to equation 2, thereby eliminating one equation.

( )

5 82 5 8

24 17

5 84 17

210 16 17

10 1

10 1

yx y x

x ky

yky

y kyy ky

k y

+− = → =

+ =

+ + =

+ + =+ =

+ =

If k = -10, then the y value would disappear and we would have 0=1, which does not make sense. This is the value for k that makes the system of equation unsolvable. Suppose that k =-10.

O

a b

c


39

17104

16104852

=−

=−→=−

yxbut

yxyx

There is no solution when k = -10, we have contradictory information. We have that 4x-10y=16 and also 4x-10y=17, which is not possible, and results in no solution. The answer is (A). Alternate Explanation: Choice (A) is correct. If 10k = − , then the system of equations is 2 5 8x y− = and 4 10 17x y− = . The first equation is

equivalent to 4 10 16x y− = . There are no values x and y for

which 4 10x y− can equal both 16 and 17 . So the system of

equations has no solution if 10k = − . Choice (B) is not correct. If 5k = − , then the system of equations is 2 5 8x y− = and

4 5 17x y− = . The solution to this system is 92

x = and 15

y = .

Choice (C) is not correct. If 0k = , then the system of equations is

2 5 8x y− = and 4 17x = . The solution to this system is 174

x =

and 110

y = . Choice (D) is not correct. If 5k = , then the system

of equations is 2 5 8x y− = and 4 5 17x y− = . The solution to

this system is 256

x = and 115

y = . Choice (E) is not correct. If

10k = , then the system of equations is 2 5 8x y− = and

4 10 17x y+ = . The solution to this system is 338

x = and

120

y = .

16. (E)

Evaluate each I, II, and III. For each I, II, and III eliminated, cross-out corresponding answer choices that become incorrect. Note that the question asks which of the following must be true, not which of the following could be true. The number of throws in the table is the number of throws the person made until he/she missed the target. There were 25 people that played the game. From the table, we can see that 4 people hit the target on their first 3 throws and missed on their 4th throw. First evaluate I. I says that more than half the people hit the target on their first throw. From the

table, we see that 7 people hit the target on zero throws and missed on their first throw. Then 6 people hit the target on their first throw and missed on the second throw. Everyone except the 7 people, hit their first throw, and missed either the second (6 people), the third (6 people), the fourth (4 people), the fifth (2 people). Thus 7 people missed the first throw and 18 people (6+6+4+2=18) made the first throw. So 18 out of 25 people made their first throw, which is more than half of the people. I is true. Now we can eliminate each answer choice that does not include I. Choices (B) and (D) can be eliminated. Next evaluate II. II says that for all the throws attempted, more hit the target than missed the target. Add up the total number missed. Seven people missed one throw, their first throw. Six people missed one throw, their second throw. The next six people missed one throw, their third throw. In the end, every person missed once and only once and since there are 25 people, there are 25 throws that missed the target. Now add up the total number of throws that hit the target. The first 7 people did not hit the target. The next 6 people hit the target once (6*1=6). The next six hit the target twice (6*2=12). The next 4 hit the target three times (4*3=12). The last 2 hit the target four times (2*4=8). So the total number of throws hitting the target is 6+12+12+8=38. Since 38 is greater than 25, more throws hit the target than missed the target, thus II is true. Now we can eliminate each answer choice that does not include II. Choices (A) and (C) can be eliminated. This leaves only choice (E) which is the correct answer. In addition, evaluate III. III says that no one hit the target more than 5 times. This is also true because 2 people made their first 4 throws and missed their 5th throw. Since everyone is accounted for in the table (7+6+6+4+2=25), no body else made 5 throws and missed the sixth throw, to make a total of 6 throws. III is true. So I, II, and III are true. The answer is (E). Alternate Explanation: Choice (E) is correct. To determine the answer to the question, you must decide which of the three statements are true. Statement I : From the table, you can see that only 7 of the 25 people missed the target on their first throw. So 18 , which is more than half of 25 , hit the target on their first throw. I is true. Statement II : The total number of throws attempted was 1 7 2 6 3 6 4 4 5 2 7 12 18 16 10 63.× + × + × + × + × = + + + + = The total number of throws that missed the target was 7 6 6 4 2 25.+ + + + = So 63 25 38− = throws hit the target, which is more than the number of throws that missed the target. II is true. Statement III : Of the 25 people, 23 missed before their fifth throw and 2 missed their fifth throw. So no one hit the target 5 times. III is true. Choice (A) is not correct. From the explanation for the correct answer, I , II , and III are all true. So I is not the only true statement. Choice (B) is not correct. From the explanation for the correct answer, I , II , and III are all true. So II is not the only true statement. Choice (C) is not correct. From the explanation for the correct answer, I , II , and III are all true. So I and III are not the only true statements. Choice (D) is not correct. From the explanation for the correct answer, I , II , and III are all true. So II and III are not the only true statements.

Number of People

1 7 2

4

6 6 3

5 4 2

Number of Throws


40

Section 9 1. (A) Both words should be positive and similar to “appreciative.”

(A) is correct because both ‘admired’ and ‘embraced’ fit the prediction. (B) and (C) are wrong because ‘condemned’ (attacked) and ‘derided’ (made fun of) are negative. (D) is wrong because ‘relinquished’ means given up. (E) is wrong because ‘instigated’ means provoked. Alternate Explanation: Choice (A) is correct. "Admired" means thought highly of. "Embraced" means held closely. If one were to insert these terms into the text, the sentence would read "Originally admired mainly by young, urban audiences, rap music was ultimately embraced by its appreciative listeners of all ages across the country." The phrase "appreciative listeners of all ages" indicates that rap music's fan base expanded from what it was "originally." The correct response is the only one in which both missing terms have a positive meaning, indicating that the appreciation began with one group and expanded to include a much larger group. Both "admired" and "embraced" are positive terms. Choice (B) is incorrect. "Performed" means acted out or achieved. "Condemned" means disapproved of. If one were to insert these terms into the text, the sentence would read "Originally performed mainly by young, urban audiences, rap music was ultimately condemned by its appreciative listeners of all ages across the country." The phrase "appreciative listeners of all ages" indicates that rap music's fan base expanded from what it was "originally." The correct response is the only one in which both missing terms have a positive meaning, indicating that the appreciation began with one group and expanded to include a much larger group. Audiences do not typically perform music, and listeners would not be described as appreciative of something they are condemning. Choice (C) is incorrect. "Derided" means ridiculed. "Ignored" means disregarded. If one were to insert these terms into the text, the sentence would read "Originally derided mainly by young, urban audiences, rap music was ultimately ignored by its appreciative listeners of all ages across the country." The phrase "appreciative listeners of all ages" indicates that rap music's fan base expanded from what it was "originally." The correct response is the only one in which both missing terms have a positive meaning, indicating that the appreciation began with one group and expanded to include a much larger group. Both "derided" and "ignored" have a negative, not a positive, connotation. Music would not be both appreciated and ignored by the same group of listeners. Choice (D) is incorrect. "Appropriated" means something is taken and used. "Relinquished" means abandoned. If one were to insert these terms into the text, the sentence would read "Originally appropriated mainly by young, urban audiences, rap music was ultimately relinquished by its appreciative listeners of all ages across the country." The phrase "appreciative listeners of all ages" indicates that rap music's fan base expanded from what it was "originally." The correct response is the only one in which both missing terms have a positive meaning, indicating that the appreciation began with one group and exp anded to include a much larger group. Listeners would not relinquish the music they appreciate. Choice (E) is incorrect. "Applauded" means approved of. "Instigated" means provoked. If one were to insert these terms into the text, the sentence would read "Originally applauded mainly by young, urban audiences, rap music was ultimately instigated by its appreciative listeners of all ages across the country." The phrase "appreciative listeners of all ages" indicates

that rap music's fan base expanded from what it was "originally." The correct response is the only one in which both missing terms have a positive meaning, indicating that the appreciation began with one group and expanded to include a much larger group. Listeners would not have instigated rap music.

2. (E) The two words should be similar, either both negative or both

positive. Since this is a “Professor”, it is most likely to be positive. (E) is correct because ‘modesty’ and ‘dilettante’ (amateur) fit the prediction. (A) is wrong because ‘embarrassment’ is not similar to ‘paragon’ (model). (B) is wrong because 'magnanimity' (greatness) does not relate to ‘avenger.’ (C) is wrong because ‘insolence’ means rudeness. (D) is wrong because ‘egotism’ means self-centeredness. Alternate Explanation: Choice (E) is correct. "Modesty" means humility. "A dilettante" is someone who merely dabbles in a subject. If one were to insert these terms into the text, the sentence would read "It was out of modesty that Professor Green, the author of several highly respected books in his field, described himself to his colleagues as a dilettante." The correct response for the second missing term will be the result of Professor Green's feelings as described in the first missing term. Because Professor Green is highly respected in his field, his description of himself as a dilettante is simply modest; he describes himself at less than his true value. Choice (A) is incorrect. "Embarrassment" means self-consciousness. "A paragon" is a model of excellence. If one were to insert these terms into the text, the sentence would read "It was out of embarrassment that Professor Green, the author of several highly respected books in his field, described himself to his colleagues as a paragon." The correct response for the second missing term will be the result of Professor Green's feelings as described in the first missing term. Professor Green would not describe himself as a paragon, proclaiming his excellence, as a result of his embarrassment. Choice (B) is incorrect. "Magnanimity" means forgiving. "An avenger" is one who seeks revenge. If one were to insert these terms into the text, the sentence would read "It was out of magnanimity that Professor Green, the author of several highly respected books in his field, described himself to his colleagues as an avenger." The correct response for the second missing term will be the result of Professor Green's feelings as described in the first missing term. Professor Green cannot be both an avenger and magnanimous. Choice (C) is incorrect. "Insolence" means disrespect. "A pedant" is someone overly concerned with the formal rules of his field of knowledge. If one were to insert these terms into the text, the sentence would read "It was out of insolence that Professor Green, the author of several highly respected books in his field, described himself to his colleagues as a pedant." The correct response for the second missing term will be the result of Professor Green's feelings as described in the first missing term. Professor Green would be unlikely to describe himself as a pedant, or someone overly concerned with the formal rules of his field of knowledge. If he described himself as a pedant, however, it would not be as a result of insolence. Choice (D) is incorrect. "Egotism" means conceit. "An apprentice" is a beginning learner. If one were to insert these terms into the text, the sentence would read "It was out of egotism that Professor Green, the author of several highly respected books in his field, described himself to his colleagues as an apprentice." The correct response for the second missing term will be the result of Professor Green's feelings as described in the first missing term. If Professor Green wrote


41

several highly respected books and was egotistical, he would hardly describe himself as an apprentice, or beginning learner.

3. (E) The word should be opposite to “championed” (supported). (E) is correct because ‘denounced’ means to criticize severely. (A) is wrong because ‘invoked’ means to put into effect. (B) is wrong because ‘investigated’ is not the opposite of support. (C) is wrong because ‘conceived’ means to come up with. (D) is wrong because ‘coveted’ means to value greatly. Alternate Explanation: Choice (E) is correct. "Denounced" means spoke ill of. If one were to insert this term into the text, the sentence would read "Historian Carlo Botta often contradicted himself, as when he first championed and then denounced the ideals of the French Revolution." The word "contradicted" indicates that the correct response will mean the opposite of championing, or supporting, ideals. Denouncing ideals is the opposite of championing them. Thus, to do both would be to contradict oneself. Choice (A) is incorrect. "Invoked" means to call upon. If one were to insert this term into the text, the sentence would read "Historian Carlo Botta often contradicted himself, as when he first championed and then invoked the ideals of the French Revolution." The word "contradicted" indicates that the correct response will mean the opposite of championing, or supporting, ideals. For Botta to invoke the Revolution's ideals after having championed them would not be a contradiction. Choice (B) is incorrect. "Investigated" means researched. If one were to insert this term into the text, the sentence would read "Historian Carlo Botta often contradicted himself, as when he first championed and then investigated the ideals of the French Revolution." The word "contradicted" indicates that the correct response will mean the opposite of championing, or supporting, ideals. While it might have been better for Botta to investigate the ideals before he championed them, his investigation doesn't mean he is contradicting himself. Choice (C) is incorrect. "Conceived" means thought up. If one were to insert this term into the text, the sentence would read "Historian Carlo Botta often contradicted himself, as when he first championed and then conceived the ideals of the French Revolution." The word "contradicted" indicates that the correct response will mean the opposite of championing, or supporting, ideals. Botta could not have conceived the ideals of the French Revolution after having championed them. He would have conceived them and later championed them. Choice (D) is incorrect. "Coveted" means strongly desired. If one were to insert this term into the text, the sentence would read "Historian Carlo Botta often contradicted himself, as when he first championed and then coveted the ideals of the French Revolution." The word "contradicted" indicates that the correct response will mean the opposite of championing, or supporting, ideals. Coveting ideals may be odd; however, coveting and championing ideals is not a contradiction.

4. (A) The correct word should relate to “extreme precision.” (A) is correct because ‘meticulousness’ means a great attention to detail. (B) is wrong because ‘effrontery’ means boastful confidence. (C) is wrong because ‘inhibition’ means a limiting factor. (D) is wrong because ‘litigiousness’ means one who sues a lot. (E) is wrong because ‘impetuousness’ means acting without caution. Alternate Explanation:

Choice (A) is correct. "Meticulousness" means excessive care or attention to detail. If one were to insert this term into the text, the sentence would read "Luisa worked with extreme precision, a meticulousness that served her well in her law career." A person who works with extreme precision would be properly described as demonstrating "meticulousness." Choice (B) is incorrect. "Effrontery" means offensive boldness. If one were to insert this term into the text, the sentence would read "Luisa worked with extreme precision, an effrontery that served her well in her law career." Working with precision is very different from the type of shameless or offensive behavior that is termed "effrontery." Choice (C) is incorrect. "Inhibition" means something that holds a person back. If one were to insert this term into the text, the sentence would read "Luisa worked with extreme precision, an inhibition that served her well in her law career." As the sentence makes clear, working precisely allowed Luisa to succeed; it did not hold her back. Choice (D) is incorrect. "Litigiousness" means a tendency to engage in lawsuits. If one were to insert this term into the text, the sentence would read "Luisa worked with extreme precision, a litigiousness that served her well in her law career." Although "litigious" is a word that would describe a lawyer, it does not mean extreme precision. Choice (E) is incorrect. "Impetuousness" means impulsiveness. If one were to insert this term into the text, the sentence would read "Luisa worked with extreme precision, an impetuousness that served her well in her law career." Work that is done on impulse is probably not performed with extreme precision.

5. (D) Since the population went from 25 to 2000, the correct word should be similar to ‘increased.’ (D) is correct because ‘burgeoned’ means to increase sharply. (A) is wrong because ‘dispersed’ means spread out. (B) is wrong because ‘mediated’ means to be judged. (C) is wrong because ‘attenuated’ means to be satisfied. (E) is wrong because ‘reconciled’ means to be calmed. Alternate Explanation: Choice (D) is correct. "To burgeon" means to grow and flourish. If one were to insert this term into the text, the sentence would read "In 1916 Yellowstone National Park had only 25 bison, but the population has since burgeoned to more than 2,000." Since the park began with 25 bison and now has more than 2,000, the correct answer is the word that most closely means "increased." "Burgeoned" and "increased" are similar in meaning. Choice (A) is incorrect. "To disperse" means to spread out. If one were to insert this term into the text, the sentence would read "In 1916 Yellowstone National Park had only 25 bison, but the population has since dispersed to more than 2,000." Since the park began with 25 bison and now has more than 2,000, the correct answer is the word that most closely means "increased." However, "dispersed" and "increased" are not similar in meaning. Choice (B) is incorrect. "To mediate" means to settle a dispute between conflicting parties. If one were to insert this term into the text, the sentence would read "In 1916 Yellowstone National Park had only 25 bison, but the population has since mediated to more than 2,000." Since the park began with 25 bison and now has more than 2,000, the correct answer is the word that most closely means "increased." However, "mediated" and "increased" are not similar in meaning. Mediation does not describe the bison's increase in population. Choice (C) is incorrect. "To attenuate" means to lessen in amount or force. If one were to insert this term into the text, the sentence would read "In 1916 Yellowstone National Park had only


42

25 bison, but the population has since attenuated to more than 2,000." Since the park began with 25 bison and now has more than 2,000, the correct answer is the word that most closely means "increased." However, "attenuated" and "increased" are not similar in meaning. What happened to the bison population is the opposite of attenuate. Choice (E) is incorrect. "To reconcile" means to adapt or make peace. If one were to insert this term into the text, the sentence would read "In 1916 Yellowstone National Park had only 25 bison, but the population has since reconciled to more than 2,000." Since the park began with 25 bison and now has more than 2,000, the correct answer is the word that most closely means "increased." However, "reconciled" and "increased" are not similar in meaning.

6. (B) The word should be similar to ‘celebrated,’ since the doctor did not enjoy “celebrity.” (B) is correct because ‘lionized’ means treated as an important person. (A) is wrong because ‘mollified’ means embarrassed. (C) is wrong because ‘accosted’ means approached. (D) is wrong because ‘galvanized’ means stimulated or strengthened. (E) is wrong because ‘vilified’ means to make someone out to be evil, the opposite of what is needed here. Alternate Explanation: Choice (B) is correct. "Lionized" means celebrated. If one were to insert this term into the text, the sentence would read "Though surgeon and researcher Charles Drew never enjoyed celebrity, he truly deserves to be lionized for his life’s achievements." This sentence makes sense because it states that Drew deserves to be celebrated for his many achievements. Choice (A) is incorrect. "Mollified" means soothed. If one were to insert this term into the text, the sentence would read "Though surgeon and researcher Charles Drew never enjoyed celebrity, he truly deserves to be mollified for his life’s achievements." There is no indication in this sentence that Drew is angry or upset, thus it is unlikely that he would deserve or need to be soothed. Choice (C) is incorrect. "Accosted" means approached aggressively. If one were to insert this term into the text, the sentence would read "Though surgeon and researcher Charles Drew never enjoyed celebrity, he truly deserves to be accosted for his life’s achievements." This sentence is illogical because it does not explain why Drew, a man of many accomplishments, would deserve to be approached aggressively. Choice (D) is incorrect. "Galvanized" means spurred into action. If one were to insert this term into the text, the sentence would read "Though surgeon and researcher Charles Drew never enjoyed celebrity, he truly deserves to be galvanized for his life’s achievements." It is unclear why a man of many achievements would deserve or need to be spurred into action. Choice (E) is incorrect. "Vilified" means to be criticized harshly. If one were to insert this term into the text, the sentence would read "Though surgeon and researcher Charles Drew never enjoyed celebrity, he truly deserves to be vilified for his life’s achievements." If Drew did anything to deserve harsh criticism, this sentence does not mention it.

7. (B) The area for this question is lines 6 to 14. The context is that

all the members of the author’s family liked to tell stories. (A) is wrong because they are not vying (competing) for the mother’s attention. (C) is wrong because there is no mention of ‘household duties’ here. (D) is wrong because the author implies that they liked to tell stories about anything, which means they were not selective. (E) is wrong because the author is not discussing ‘educational accomplishments.’ The stories could be about

anything. (B) is correct because the statement means that the author’s family liked to tell stories. Alternate Explanation: Choice (B) is correct. "Eager" means enthusiastic or impatient. The author describes her family as "an entire clan of storytellers competing for a turn on the family stage" (lines 11-12). This sentence indicates that the entire family was "eager" for a chance to tell their stories on the "family stage." Choice (A) is incorrect. The sentence clearly states that the mother was just one of "an entire clan of storytellers" (line 11). There is no indication that anyone was trying to get her attention. Choice (C) is incorrect. There is no mention of household duties or the family's feelings about them in the passage. Choice (D) is incorrect. The passage does not indicate that family members were selective about sharing information, only that they competed eagerly to be heard. Choice (E) is incorrect. The passage refers to the family members' desire to have their stories heard, regardless of subject. Further, the only educational accomplishments mentioned are those of the daughter.

8. (D) The area for this question is lines 15 to 27. (A) is wrong because the teacher criticizes the author for not bringing a back, not for her ‘grandiose ambitions.’ There is no evidence that the author even had any ambitions. (B) is wrong because this does not match the context of the area. The area relates a story between the teacher and the author. Other students are barely mentioned. (C) is wrong because ‘sense of decorum’ does not match the context. (E) is wrong because the teacher is not described as ‘bitter’ and does not speak out against injustice. (D) is correct because the teacher is arbitrary about her rules: some children are allowed to bring a box the next day, but the author is not. Alternate Explanation: Choice (B) is correct. "Dispensation" means favor or courtesy. The sentences immediately preceding line 26 indicate that the author wished to receive the same "dispensation," the same courtesy, given the "White" children, namely, being allowed to bring a box the next day. Choice (A) is incorrect. The author has already completed the experiment and does not need "an additional day to complete the experiment." Choice (C) is incorrect. The passage indicates that the dispensation the author is requesting is to bring a box the following day, not permission to ask her father for help. Choice (D) is incorrect. The author does not ask to leave school early to look for a box, but to bring a box the next day. Choice (E) is incorrect. The passage indicates that the author wants a "dispensation" to bring a box the following day, not to discuss the experiment with others.

9. (B) The area for this question is lines 25 to 27. In the previous sentence, the author states that the other children were allowed to bring boxes the next day. (A) is wrong because the author is not asking for additional time. (C) is wrong because her father is not mentioned here. (D) is wrong because the author does not ask to leave school. (E) is wrong because this does not relate to the area. (B) is correct because the author wants to bring a box for her experiment the next day like the other students were allowed to do. Alternate Explanation: Choice (B) is correct. "Dispensation" means favor or courtesy. The sentences immediately preceding line 26 indicate that the author wished to receive the same "dispensation," the same courtesy, given the "White" children, namely, being allowed to bring a box


43

the next day. Choice (A) is incorrect. The author has already completed the experiment and does not need "an additional day to complete the experiment." Choice (C) is incorrect. The passage indicates that the dispensation the author is requesting is to bring a box the following day, not permission to ask her father for help. Choice (D) is incorrect. The author does not ask to leave school early to look for a box, but to bring a box the next day. Choice (E) is incorrect. The passage indicates that the author wants a "dispensation" to bring a box the following day, not to discuss the experiment with others.

10. (D) The area for this question is lines 28 to 34. The author’s experiment involved weighing things in water. (A) is wrong because the brick and the piece of wood are most likely the objects being weighed. (B) is wrong because the author does not mention any reason for steadying the scale. (C) is wrong because if the bucket was the container, the author would not have required a box. (E) is wrong because the author does not mention having to ‘transport liquid’ for her experiment. (D) is correct because the author would need something to hold the water when she weighed her objects, and a bucket would do that well. Alternate Explanation: Choice (D) is correct. The author describes the experiment as a "simple buoyancy experiment" which involves weighing "each object in the air and then in water, to prove they weighed less in water" (lines 30-32). Since the experiment calls for weighing objects in water, the bucket is most likely to be used to hold the water that is needed. Choice (A) is incorrect. The experiment involves weighing particular objects in air and in water (lines 30-32). The author does not mention the use of objects to counterbalance the weight of other objects. Choice (B) is incorrect. The author does not mention the need to steady the scale. Further, the piece of wood or the brick from the list would be more appropriate objects to use to steady a scale. Choice (C) is incorrect. The author's statement that "I came out of school carrying the pieces of an experiment" (lines 28-29) suggests that the author does not have a suitable container to carry the materials for the project. Because one of the main points of the story is that the author does not have a suitable container for her materials, it is clear that the bucket is not being used for this purpose. Choice (E) is incorrect. The experiment calls for weighing objects in water; this does not require liquid to be transported from place to place.

11. (E) The area for this question is lines 34 to 45. The mother is defending her daughter in this area. (A) is wrong because the mother responds in a clear way, not with ‘bewilderment’ (confusion). (B) is wrong because the mother is actively working for her daughter, which means she is not ‘weary’ (tired). (C) is wrong because the mother is not giving anything, so how could she have an attitude of ‘generosity’? (D) is wrong because the mother does not show ‘dismay’ (disappointment). If anything, she is very proud of her daughter’s work. (E) is correct because the mother behaves like someone who has been insulted and wants to respond, with indignation (one who feels that they were undeservedly harmed). Alternate Explanation: Choice (E) is correct. "Righteous indignation" suggests just or correct anger. The passage states, "Well, my mother marched me and my armload of buoyant materials right back into the school"

(lines 34-35). This shows the mother's actions as determined and forceful; they are part of an angry response to what she sees as an injustice committed against her daughter. Choice (A) is incorrect. The mother's decisive action in seeking out the teacher indicates not bewilderment but anger and determination. Choice (B) is incorrect. The mother is not disappointed but angry and determined to rectify the situation. Further, there is no sign that the mother is weary of standing up for her daughter. Choice (C) is incorrect. The mother is certainly protective of her daughter's interests, but her attitude is not one of generosity. Rather, she shows her determination to right a wrong. Choice (D) is incorrect. The mother is dismayed but hardly overwhelmed, as her actions in immediately returning to the school to confront the teacher clearly indicate.

12. (A) The area for this question is lines 36 to 40. The mother is not seriously asking the teacher these questions. She is using them to make the point that her daughter’s error was a small one. (B) is wrong because the mother is questioning the teacher, not her daughter. (C) is wrong because the mother is not concerned about the forgetfulness here, but rather her daughter’s project’s qualification for the fair. (D) is wrong because of the same reason as (B). (E) is wrong because the mother is questioning the teacher not herself. (A) is correct because the mother uses the question to show that the teacher’s position is not a strong one, and that she should allow the author to compete. Alternate Explanation: Choice (A) is correct. The mother's questions, "The box was the only problem? Just the box? Nothing wrong with the experiment? An excited eight year old had forgotten a lousy, stinking box" and "for that she was out of the running?" (lines 36-40), are part of her doubting query. The mother clearly believes that the teacher has placed undue importance on the box. Her questions are intended to highlight the "absurdity of the teacher's position." Choice (B) is incorrect. The questions are being put to the teacher and not to the child. This is clearly shown by the continuing dialogue which occurs between mother and teacher in lines 40-45. Choice (C) is incorrect. The mother's disdain for the idea that a box alone should keep her daughter's experiment out of the competition indicates that she is not concerned—or at least not interested in expressing concern to the teacher—about her daughter's forgetfulness. Choice (D) is incorrect. The questions are being asked of the teacher. The mother is more interested in securing the author's place in the competition than in reassuring the author about the project's reception. Choice (E) is incorrect. The mother does not need help understanding her child's defensiveness about the box, since her questions indicate that she finds the issue ridiculous.

13. (B) The area for this question is line 23 and line 38. In line 23, the box is described as something essential, whereas in line 38, the box is has hardly any importance. (A) is wrong because the author still needs to have a box. The mother is not questioning that. (C) is wrong because the box was not a diversion for anything. It was supposed to be a required container. (D) is wrong because the box is not a tool. (E) is wrong because the box is never characterized as a puzzle. (B) is correct because the box was at first a necessity, but later, “lousy, stinking”; in other words it had become something of little value. Alternate Explanation:


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Choice (B) is correct. In line 23, the box as the teacher sees it is a necessary element for the presentation of the experiment at the science fair. In line 38, it is, as the mother sees it, a "lousy, stinking box that you can get from the supermarket," and its degree of importance has shifted from necessary to minor. Choice (A) is incorrect. The box is still a requirement, as indicated by the fact that the mother and daughter find a box for the experiment materials before the experiment proceeds to the fair. Choice (C) is incorrect. Neither the teacher nor the author considered the box a "diversion," or something that is amusing, and it does not later require a "desperate search." As the mother points out, a box can be found almost anywhere (line 39). Choice (D) is incorrect. The box is never a tool, but a required carrier for the experiment. At no point is the box considered a source of entertainment for anyone involved. Choice (E) is incorrect. The box is never presented as either a puzzle or as something that provides clarity and strength. It is a requirement that later becomes, as the mother indicates, a petty impediment to her daughter's potential success.

14. (C) The area for this question is line 55. The daughter feels that the story embarrassed her because her mom had been too “forward and pushy.” (A) is wrong because the mother was talking, so there was no void here. (B) is wrong because this is about the story her mother just told, not the quality of the boarding school. (D) is wrong because the mother has only words here (by telling the story); she is not performing any action. (E) is wrong because ‘interviewers’ praise’ is not mentioned here. Alternate Explanation: Choice (C) is correct. In this context, the word "plug" means promote or boost. The author uses the word "plug," a word associated with selling a product, to express her sense that her mother is over promoting her. Choice (A) is incorrect. The author is not embarrassed because of a pause in conversation; she is embarrassed because her mother is openly promoting her. Choice (B) is incorrect. In this passage, the author does not indicate what her feelings are about the boarding school. Choice (D) is incorrect. The author feels that her mother's words and actions are in harmony; both are intended to promote and protect her daughter. Choice (E) is incorrect. The author uses the word "plug" to describe her feelings about what she sees as her mother's shameless promotion. She worries that this promotion will have the unintended effect of causing the interviewers not to praise her, sincerely or otherwise, but to see her family as "forward and pushy" (line 56).

15. (E) The area for this question is line 59. The context is her mother’s defense of her lack of a box. To answer this question, simply find the word that is not similar to the rest. (A) and (D) are similar since someone who is determined would be unswerving, so these are wrong. (B) and (C) are wrong because someone who is overpowering could be described as dazzling. (E) is correct because ‘sudden’ refers to quickness of action, whereas none of the other words do. Also, substituting ‘sudden’ into the passage makes little sense. Alternate Explanation: Choice (E) is correct because "blinding" is not used to mean "sudden" in this context. We can infer that the mother's instinct is always to defend her daughter and that her sense of purpose can therefore not be described as "sudden." Choice (A) is incorrect because the mother's "blinding" sense of purpose can be described as "unswerving," or steady. Choice (B) is incorrect because the mother's "blinding" sense of purpose was sufficiently effective to

overrule, and thus stun or dazzle, the teacher. Choice (C) is incorrect because "overpowering" is a word that can be used to describe the mother's "blinding" sense of purpose. Indeed, her argument overpowers the teacher's objections. Choice (D) is incorrect because the mother's "blinding" sense of purpose can certainly be described as "determined."

16. (E) The area for this question is line 62. The author is implying

that where she came from, her mother was always there to protect her. (A) is wrong because the author is not discussing her life overall here. (B) is wrong because there is no mention of the ‘results.’ (C) is wrong because this was discussed in an earlier area. (D) is wrong because this was also discussed much earlier. (E) is correct because in this area, the statement refers to the mother’s ability to help her daughter at home, which she could not do at a boarding school. Alternate Explanation: Choice (E) is correct. The phrase "somebody was home" is part of a sentence in which the author describes her mother defending her. For the author, her mother's vigorous defense is a way of conveying that the author is important to and supported by her family. This clearly captures the mother's "sense of responsibility toward her daughter." Choice (A) is incorrect. Undoubtedly the mother wants to create a comfortable life for her family, but the phrase in line 62 refers specifically to the mother's support and defense of her daughter. Choice (B) is incorrect. Although we can assume that the mother was eager to learn the results of the interview, the passage describes only part of the interview. The passage does not discuss the results of the interview or the feelings of the participants as to those results. Further, the phrase in line 62 refers to an earlier event, not to the interview. Choice (C) is incorrect. The mother's story indicates that she feels not despair but determination to confront injustice toward her daughter. Choice (D) is incorrect. Although the passage indicates elsewhere that the mother enjoys attention, the phrase "somebody was home" refers specifically to her defense of her daughter.

17. (A) The area for this question is lines 63 to 66. (B) is wrong because the officials had little reaction; they did not act with ‘pomposity’ (arrogance). (C) is wrong because the parents’ reactions are just reactions; they do not make up a unifying force. (D) is wrong because the parents and the author’s father seem happy, not uneasy. (E) is wrong because these details do not relate to any earlier statement. (A) is correct because these are just the various reactions of the audience after the mother completed her story. Alternate Explanation: Choice (A) is correct. These lines indicate the various reactions, ranging from approval to amusement, of the story's listeners: "[t]he other mothers nodded approvingly. My father gave me a wide, clever-girl smile. The officials from the school looked at me deadpan" (lines 63-65). Choice (B) is incorrect. The details in lines 63-66 are straightforward rather than satirical. The author interprets the school officials' "deadpan" reaction as amused, not pompous or arrogant. Choice (C) is incorrect. Although the other mothers nod in approval, possibly signaling a sense of unity with the author's mother, lines 63-66 also stress how the author herself and the school officials reacted to the mother's story. Choice (D) is incorrect. Although the author expresses embarrassment, the point of lines 63-66 is not to show her unease, but to show the reactions


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of everyone in the room to her mother's story. Choice (E) is incorrect. Lines 63-66 do not clarify a previous statement; instead, they indicate the listeners' reactions to the mother's story.

18. (B) The area for this question is the final paragraph. The author notes that the purpose of the story was to inform the school’s officials about her “maternal concerns.” (A) is wrong because the author never discusses ‘forgiveness.’ (C) is wrong because the story is about her daughter, not the mother’s own hard work. (D) is wrong because there is no mention of ‘theory.’ (E) is wrong because the message is for the school’s officials, not the daughter. (B) is correct because the author states that the story was “part rebuke and part condolence” for the stories the officials told the parents. Alternate Explanation: Choice (B) is correct. In the final paragraph, the author calls her mother's story "a message about her maternal concerns, and a way to prove that racism was not some vanquished enemy" (lines 69-71). She adds, "[w]hen I was in third grade, Mama could do her maternal duty" (lines 73-74), and asks, "[w]ho at this new school would stand up for her child in her stead?" (75-76). The author sums up the purpose of her mother's story as a challenge to the school officials to protect her daughter as fiercely as she has done and will, if necessary, continue to do. Choice (A) is incorrect. The author indicates that her mother's story was "an answer (part rebuke and part condolence) to the school stories that the admissions people told, where no parents figured at all" (lines 67-69). Forgiveness and understanding do not figure prominently in the mother's story. Choice (C) is incorrect. The author sees the story in terms of her mother's determination to defend her daughter rather than as her mother's way of conveying her personal ideas on hard work. Choice (D) is incorrect. Although the author describes a theory about a particular social attitude—one that might imagine that "racism was not some vanquished enemy, but a real, live person, up in your face, ready, for no apparent reason, to mess with your kid" (lines 71-73)—this theory is one part of her mother's story. The author sees the story as her mother's way of expressing her reaction to this theory rather than as a defense of the theory. Choice (E) is incorrect. As the author sees it, the message of the mother's story is intended for the school officials and not for her daughter.

19. (A) The area for this question is the entire passage. (B) is wrong because the passage is mostly about the story the mother tells. (C) is wrong because the author does not show any hostility, only embarrassment at certain parts. (D) is wrong because there is only one example given here. (E) is wrong because the author does not discuss any such thing. (A) is correct because the entire passage focuses on how the mother relates the story to the officials and why she does so. Alternate Explanation: Choice (A) is correct. The main point of the passage is to show what kind of person the author's mother is. Choice (B) is incorrect. The boarding school admissions process is barely mentioned in the passage. Choice (C) is incorrect. Although the author feels embarrassed by her mother's story, the passage does not suggest that she feels hostility, repressed or otherwise, toward her mother. Rather, she feels admiration and thanks for her mother and her actions. Choice (D) is incorrect. The mother's story indicates that

she is well aware of racism; however, this is not the central purpose of the passage. The central purpose of the passage is to describe the mother's response to life and to her family. Choice (E) is incorrect. The author does not indicate or suggest that she has become skeptical of human nature.

Section 10 1. (D): (A), (C), and (E) are all wrong because of the verb “is.”

Since the discovery is recent, meaning it happened in the past, present tense is not appropriate. (B) is wrong since “they” is an ambiguous pronoun and does not refer to anything from the sentence. (D) is correct the verb is now in the correct tense. Alternate Explanation: Choice (D) is correct. It avoids the error of the original by eliminating the unnecessary phrase "the finding." Choice (A) displays wordiness. The phrase "the finding" is not needed, since it merely repeats the idea of the earlier noun "discovery." Choice (B) uses a vague pronoun. The sentence contains no noun to which the pronoun "they" can refer. Choice (C) involves an inappropriate idiom. In context, the adverb "recently" is less effective than the adjective "recent" ("A recent finding is that"). Choice (E) contains an unnecessary word. With a minor change in word order ("A recent discovery is that"), the vague pronoun "it" can be deleted.

2. (A): (A) is correct because the sentence works well as is. (B) is

wrong because it is wordy. (C) and (E) are wrong because “they” is ambiguous. (D) is wrong because it is awkward. Alternate Explanation: Choice (A) is correct. It uses appropriate words to express a complete idea. Choice (B) uses an inappropriate idiom. The phrase "that of being" is not suitable to introduce a phrase describing the prevalent notion. Choice (C) includes a vague pronoun. Since the sentence contains no noun to which the pronoun "they" can refer, its meaning is not clear. Choice (D) creates a sentence fragment. Without a noun, a phrase, or a clause to serve as the subject of the verb "was," this group of words does not state a complete thought. Choice (E) displays wordiness. The adjective "prevalent" is not needed, since it conveys the same idea as the verb "prevailed."

3. (C): (A) and (B) are wrong because they makes it seem like the novel is the native New Yorker instead of Gloria Naylor. (C) is correct because it makes it extremely clear that Gloria Naylor is the native New Yorker. (D) is wrong because of awkwardness and the word “having.” Remember to avoid –ing words. (E) is wrong because it is a run-on sentence. A comma is needed. Alternate Explanation: Choice (C) is correct. It avoids the dangling modifier of the original by using a correctly placed prepositional phrase ("by native New Yorker Gloria Naylor") to embed details describing the "first novel." Choice (A) contains a dangling noun phrase. Although the two noun phrases ("A native New Yorker" and "Gloria Naylor’s first novel") may appear at first to be parallel appositives, the first phrase refers to a person and the second to that person's work. Thus, the first phrase has no grammatical connection to the rest of the sentence. Choice (B) displays improper word order. Since the noun phrase "A native New Yorker" obviously refers to a person (not to that person's "first


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novel"), the phrase should be placed immediately before or after the name "Gloria Naylor." Choice (D) uses improper tense sequence. The present perfect tense of the verbal "having won" illogically suggests that Naylor received the award before she wrote the novel. Choice (E) exhibits ineffective coordination. The coordinating conjunction "and" merely links two complete thoughts without appropriate subordination or embedding to indicate their relationship and relative importance.

4. (D): (A) and (B) are wrong because they are passive. (C) is wrong because the verb cannot shift to past perfect from past. (D) is correct because the verb remains as past. (E) is wrong because it lacks a verb. Alternate Explanation: Choice (D) is correct. It avoids the error of the original by using two parallel active verbs, "developed" and "introduced," with "Charlie Chaplin" as their subject. Choice (A) fails to maintain parallelism. The first independent clause uses active voice ("Charlie Chaplin developed"), but the second shifts awkwardly to passive voice ("were introduced"). Choice (B) uses excess words. The phrase "by him" is not needed. Choice (C) exhibits improper modification. The phrase "having introduced sentiment, satire, and social criticism" cannot coherently modify any part of the sentence, and it incorrectly suggests that this introduction came before the development of Chaplin's ideas about comedy. Choice (E) violates parallelism. Since the noun "introduction" is not parallel with the earlier clause, "Charlie Chaplin developed definite ideas," the second half of the sentence has no verb and is left awkwardly incomplete.

5. (A), (C), (D), and (E) are all wrong because of an illogical

comparison error. “Someone living in a … culture” cannot be compared to “a country such as Myanmar.” The second part should have ‘someone living in’ before naming the country. (B) is the only answer which “someone living” is in both parts of the comparison. Alternate Explanation: Choice (B) is correct. It avoids the error of the original by adding the phrase "someone living in" so that the effects of the actions of two individuals in two different countries are compared. Choice (A) presents an illogical comparison. The effect of a single person ("someone") on the environment is compared to the effect of an entire country ("Myanmar"). Choice (C) has an inappropriate pronoun. The pronoun "you" is used loosely to mean any person. Choice (D) suggests an illogical comparison. The rate at which an individual taxes the environment in a technological culture is compared to the rate in the whole country of Myanmar. Choice (E) makes an illogical comparison. Without the phrase "that of" immediately before "a citizen of Myanmar," the statement compares a rate (of taxing the environment) with a person.

6. (C) (A) is wrong because of the pronoun “it.” The subject of the

verb is already clear. The “it” is not needed. (B) is wrong because of the word “causes.” The subject is “trash and other debris,” so the verb should be ‘cause.’ (C) is correct because “cause” is conjugated correctly and agrees with the subject. (D) is wrong because “preventing a serious accident” is an incorrectly placed modifier. It should be moved towards the beginning of the sentence. (E) is wrong because of an incorrectly placed modifier as well. The phrase “avoiding a serious accident” should be moved towards the beginning of the sentence.

Alternate Explanation: Choice (C) is correct. It avoids the error of the original by using the appropriate conjunction "and" to link a clear cause (debris being sucked into a jet engine) with its expected effect (a serious accident). Choice (A) contains the erroneous singular pronoun "it," which appears to refer to the plural antecedents "trash and other debris." Choice (B) displays incorrect coordination. A comma is used improperly to join two complete thoughts ("Airport runways . . . into a jet-engine intake" and "this causes a serious accident”). Choice (D) exhibits improper modification. The dangling phrase, "preventing a serious accident," apparently indicates a reason for sweeping runways, but it is not in a position to modify correctly any part of the sentence. Choice (E) violates parallelism. The verbal "avoiding" is neither grammatically nor logically parallel with the earlier verb phrase "could be sucked," since this earlier phrase describes a likely cause of an accident, not a method of preventing one.

7. (A) is wrong because it is incorrect to say “In believing that.” The

word “In” has no use in the sentence. (B) is correct because “Believing that” correctly modifies “Professor Morison.” (C) is wrong because it is longer and more awkward than (B). (D) is wrong because there are now two complete sentences joined by only a comma. (E) is wrong because of the word “By.” It is unnecessary. Alternate Explanation: Choice (B) is correct. It avoids the error of the original by eliminating the unnecessary preposition "in." Choice (A) exhibits wordiness. The preposition "in" is not needed. Choice (C) displays wordiness. Four words ("In his belief that") can be reduced to two ("Believing that"). Choice (D) involves improper coordination. Two complete thoughts ("He believed . . . of Columbus" and "Professor Morrison retraced . . . first voyage") are joined with only a comma. Choice (E) uses an inappropriate idiom. The preposition "by" incorrectly suggests a means by which Morrison retraced the route, rather than the mental state in which he did so.

8. (A) (A) is correct because it currently has no errors. (B) is wrong

because “recognize and set” does not make sense. ‘recognize by setting’ makes more sense. (C) is wrong because of the verb “are setting.” Only the verb ‘set’ is needed. (D) is wrong because of the random ambiguous “it.” Remember “it” must refer to one specific thing. (E) is wrong because a ‘by’ is needed between “fact setting.” Alternate Explanation:

9. (C) (A) is wrong because “as” is cannot join two complete sentences. A conjunction is needed. (B) is also wrong for being a run-on sentence. (C) is correct because the two opposing sentences are now joined by a contrasting conjunction. (D) is wrong because it is still a run-on sentence. (E) is wrong for being too long and wordy. Alternate Explanation: Choice (C) is correct. It avoids the error of the original by adding an appropriate conjunction, "but," to join the two independent clauses that express contrasting ideas. Choice (A) displays improper coordination. It uses only a comma to join two complete thoughts ("My grandfather . . . calculator" and "as he shops . . . within a dollar"). Choice (B) uses improper coordination. Two complete thoughts ("My grandfather . . . calculator" and "while shopping . . . within a dollar") are joined by only a comma. Choice


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(D) exhibits improper coordination. Since the transition word "therefore" does not serve as a coordinating conjunction, this choice incorrectly links two complete thoughts ("My grandfather . . . calculator" and "therefore, when shopping . . . within a dollar") with only a comma. Choice (E) results in improper coordination. Two independent clauses ("My grandfather . . . calculator" and "however, he shops . . . within a dollar") are connected by only a comma.

10. (B) (A) is wrong because the second part does not form a

complete thought or sentence. (B) is correct because it makes the second part a complete sentence. (C) is wrong because it is not complete. Also avoid the word “having.” (D) is wrong since it is still a sentence fragment. (E) is wrong because it is redundant to say ‘Gwendolyn Brooks she.’ Alternate Explanation: Choice (B) is correct. It avoids the error of the original by providing a verb, "had," so that the sentence states a complete idea. Choice (A) produces a sentence fragment. With no verb (only the verbal phrases "to win" and "encouraging"), the main clause fails to state a complete idea. Choice (C) creates a sentence fragment. Although this choice has a verb, "was," the verb is part of a dependent clause introduced by "which." The main clause has no verb to complete the thought. Choice (D) is a sentence fragment. The only verb, "had," is part of a dependent clause ("who had a special interest in encouraging young poets"), so the main clause cannot state a complete thought. Choice (E) includes an excess word. The pronoun "she" simply repeats the name immediately before it, "Gwendolyn Brooks," and is, therefore, unnecessary.

11. (C) (A) and (B) are both wrong because the opening phrase needs

to be modifying Paul Austere not his novels. Paul Austere needs to be the subject of the sentence. (C) is correct because Paul Austere is now the subject of the sentence and the verb is correctly conjugated. (D) is wrong because it removes his novels all together from the sentence. (E) is wrong because the verb “had wrote” is incorrectly conjugated. The sentence is not in past tense. Alternate Explanation: Choice (C) is correct. It avoids the error of the original by placing the proper noun "Paul Auster" immediately after the introductory phrase that modifies it. Choice (A) displays improper modification. The introductory phrase, "Although fascinated by chance and coincidence," cannot logically modify the noun that follows, "novels," since it clearly describes the author rather than his books. Choice (B) exhibits improper modification. The introductory phrase, "Although fascinated by chance and coincidence," logically modifies the author Paul Auster, not the novels that he wrote. Choice (D) involves inappropriate modification. The prepositional phrase, "with careful attention to style and balance," functions as an adverb telling how the novels were written, not as an adjective describing the preceding noun, "writer." Choice (E) uses an incorrect verb form. After the helping verb "had," the correct form of this irregular verb is the past participle, "written," not the past, "wrote."

12. (B) (A) is wrong because of the conjunction “but.” The proper

comparision structure would be ‘not so much of as that.” (B) is correct because it uses the proper comparison structure. (C), (D),

and (E) are all wrong because of length and wordiness. There is no need to repeat the subject by adding in the pronoun “they.” Alternate Explanation: Choice (B) is correct. It avoids the error of the original by using the appropriate conjunction "as" to complete the idea of the introductory phrase "so much" and thus properly link two parallel verbs ("replace" and "complement"). Choice (A) uses an inappropriate idiom. After the phrase "so much," the conjunction "but" is improper because it suggests not a limited degree of difference but a more complete contrast. Choice (C) contains an idiom that is not suitable. The conjunction "but" is not appropriate for use with the phrase "so much" because "but" implies a more absolute contrast. Choice (D) employs an improper idiom. The conjunction "and" suggests no contrast but simply indicates that additional information will follow. Choice (E) displays wordiness. The phrase "they were to" is unnecessary.

13. (C) (A) and (D) are wrong because of a lack of parallelism. The

list of items contains “teaching” and “becoming involved.” The last item “founded” needs to be in the same tense. (B) is wrong for repeating “after” again. This is unnecessary and redundant. (C) is correct because it changes the last item to “founding,” which is parallel. (E) is wrong because the verb “having” should be avoided. Alternate Explanation: Choice (C) is correct. It avoids the error of the original by using a gerund, "founding," that is parallel with the earlier gerunds, "teaching" and "becoming." Choice (A) fails to maintain parallelism. The clause "after she founded" is not parallel with two earlier items in the series—the gerunds "teaching" and "becoming." Choice (B) uses excess words. The words "after," "the," and "of" are not needed. Choice (D) violates parallelism. The clause "she had founded" is not parallel with the gerunds "teaching" and "becoming"—the two earlier items in the series. Choice (E) has an error in tense sequence. The present perfect tense of the verbal "having founded" is not consistent with the present tense of the earlier verbals "teaching" and "becoming."

14. (C) (A) is wrong because it is passive voice. (B) is wrong because

of the random ambiguous “it.” (C) is correct because it is now in active tense. (D) is wrong because it is a run-on sentence. (E) is wrong because the second part is not a complete sentence that can stand alone. Alternate Explanation: Choice (C) is correct. It avoids the error of the original by using two parallel clauses ("economic inequalities made" and "this anger fueled"), both in active voice. Choice (A) fails to maintain parallelism. The first independent clause uses active voice ("economic inequalities made many people angry"), but the second shifts to ineffective passive voice ("and a violent revolution was fueled"). Choice (B) contains a vague pronoun. The singular pronoun "it" cannot logically refer to the noun "France" (the only singular noun that precedes it), and it does not agree with the plural nouns "inequalities" and "people." Choice (D) uses improper coordination. It uses only a comma to join two complete thoughts ("In eighteenth-century France . . . many people angry" and "that anger fueled a violent revolution"). Choice (E) exhibits inappropriate coordination. It incorrectly uses a semicolon to link


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parts of unequal grammatical rank (a complete thought before the semicolon and only a phrase after it).

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SAT Class Exam 2 Solutions