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Online - Practice Test #7

1Which of the following represents the total cost, in dollars, of compact discs at

each and compact disc cases at each? (Disregard sales tax.)

(A)

(B)

(C)

(D)
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(E)

ANSWERS AND EXPLANATIONS

Explanation for Correct Answer A :

Choice (A) is correct. The cost of the compact discs (CDs)

purchased at a price of each is dollars. The cost of the

CD cases purchased at a price of each is dollars. Therefore, the total

cost, in dollars, is

Explanation for Incorrect Answer B :

Choice (B) is not correct. There were CDs purchased (not ), and CD

cases purchased (not ).

Explanation for Incorrect Answer C :

Choice (C) is not correct. This equation corresponds to the situation

where all the items purchased had a price of not the situation where

some had a price of and others had a price of .

Explanation for Incorrect Answer D :Choice (D) is not correct. See the explanation for the correct response

(A).

Explanation for Incorrect Answer E :

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

(A).

2

If the areas of the two rectangles in the figure above are equal, which of the following couldbe the coordinates of point ?

(A) (B) (C) (D) (E)


Explanation for Correct Answer C :Choice (C) is correct. Since is in the second quadrant, it must have a

negative -coordinate and a positive -coordinate. If has coordinates

then the area of the rectangle in the second quadrant is For the two

rectangles to be of equal area, must equal The only answer choice

that fits both of these criteria is

Explanation for Incorrect Answer A :

Choice (A) is not correct. is in the second quadrant, and is a point in

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the third quadrant.


Choice (B) is not correct. If has coordinates then the rectangle in the

second quadrant has only half the area of the rectangle in the first

quadrant, and the problem requires that they have the same area.

Explanation for Incorrect Answer D :Choice (D) is not correct. is in the second quadrant, and is a point in

the fourth quadrant.


Choice (E) is not correct. is in the second quadrant, and is a point in

the first quadrant.

3 A box contains solid-colored marbles that are either orange, blue, or green. If percent of

the marbles are orange and percent of the marbles are blue, what percent are green?

(A) (B) (C) (D) (E)


Explanation for Correct Answer B :

Choice (B) is correct. Since percent of the marbles are orange,

percent are blue, and the remaining marbles are green, it follows that

percent of the marbles are green.


Choice (A) is not correct. This is the percentage of the marbles that

are blue (and also the percentage of the marbles that are orange).


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

(B).

Explanation for Incorrect Answer D :

Choice (D) is not correct. This is the percentage of the marbles that

are notgreen.


Choice (E) is not correct. This is the percentage of the marbles that

are not orange (and also the percentage that are not blue).4

Sets and are shown above. If is a member of set and is a member of set , which of the

following CANNOT be equal to the product

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(A) (B) (C) (D) (E)



Choice (A) is correct. The only ways to write as the product of two

positive integers (ignoring the order of the factors) are or While

and are both members of neither nor is a member of Also, while is

a member of is not a member of Therefore, cannot be written as the

product of two integers such that one is a member of and the other is

a member of


Choice (B) is not correct. The number can be written as where is amember of and is a member of The question asks for a number that

cannot be written as the product of a member of with a member of


Choice (C) is not correct. The number can be written as where is a

member of and is a member of The question asks for a number that



Choice (D) is not correct. The number can be written as where is a




Choice (E) is not correct. The number can be written as where is a



5 If then could be which of the following?

(A) (B) (C) (D) (E)


Explanation for Correct Answer E :

Choice (E) is correct. If then Of the choices, the only value of that

satisfies this condition is


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Choice (A) is not correct. If then However,


Choice (B) is not correct. If then However,


Choice (C) is not correct. If then However,

Explanation for Incorrect Answer D :Choice (D) is not correct. If then However,

6 If which of the following must be true?

(A) (B) (C) (D) (E)



Choice (B) is correct. The right side of the equation can be expanded:

Then can be subtracted from both sides, leaving


Choice (A) is not correct. See the explanation for the correct response

(B).


Choice (C) is not correct. If were substituted for then the equation

would be which simplifies to So could be equal to but the equation

is only true when is


Choice (D) is not correct. If were substituted for then the equation




Choice (E) is not correct. If were substituted for then the equation



Questions 7-9 refer to the following definition.Let be defined by for all numbers and

7

(A) (B) (C)

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(D) (E)


Explanation for Correct Answer C :

Choice (C) is correct.Explanation for Incorrect Answer A :

Choice (A) is not correct. but is not equal to


Choice (B) is not correct. but is not equal to


Choice (D) is not correct. but


Choice (E) is not correct. but is not equal to

8 If then(A) (B) (C) (D) (E)



Choice (A) is correct. Since this expression is equal to it follows that

Therefore, which gives so .


Choice (B) is not correct. If then but the problem states that


Choice (C) is not correct. If then but the problem states that


Choice (D) is not correct. If then but the problem states that


Choice (E) is not correct. If then but the problem states that

9 For what value of is the statement always true?

(A) (B) (C) (D) (E)


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Choice (B) is correct. Since the equation can be rewritten as

Subtracting from both sides yields or Thus, either or Therefore,

the only value of that always makes true is


Choice (A) is not correct. If then This is only equal to or in thiscase when but the question asks for a value of that will make the

equation true for all values of


Choice (C) is not correct. If then This is only equal to or in this

case when but the question asks for a value of that will make the



Choice (D) is not correct. If then This is only equal to or in this



Explanation for Incorrect Answer E :Choice (E) is not correct. If then This is only equal to or in this



10 In the equation above, is a constant. If the roots of the equation are and what is the value

of

(A) (B) (C) (D) (E)



Choice (A) is correct. Recall that a root of an equation is a number

that, when substituted for the variable in the equation, reduces theequation to an identity. If and are the roots of the equation then

and Since the left-hand sides are each equal to zero, it follows that

Since is a constant, this is true for all values of not merely and


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

(A).

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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).Explanation for Incorrect Answer E :


(A).

11 Which of the following represents the area, of a circle as a function of its diameter,

(A) (B) (C) (D) (E)



Choice (E) is correct. The area of a circle is given by the formula

where is the radius of the circle. The diameter of a circle, is twice the

radius, so Substituting for gives the equation


Choice (A) is not correct. If is the radius of the circle, then This is

the circumference of the circle.


Choice (B) is not correct. If is the radius of the circle, then This is

twice the circumference of the circle.


Choice (C) is not correct. If is the radius of the circle, then This is

four times the area of the circle.


Choice (D) is not correct. If is the radius of the circle, then This is

twice the area of the circle.

12

The table above shows some values for the functions and If and are linear functions,

what is the value of

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(E) Superior


Explanation for Correct Answer D :

Choice (D) is correct. To determine the lake with the third greatest

depth, you must determine the depth of each lake by subtracting thelowest point from the highest point. The depth of Lake Superior is

the depth of Michigan is the depth of Huron is the depth of Erie is

and the depth of Ontario is Ontario is the lake with the third greatest

depth, at feet.



(D).



(D).

Explanation for Incorrect Answer C :Choice (C) is not correct. See the explanation for the correct response

(D).



(D).

14

In the figure above, and If is an integer, what is the greatest possible value of

(A) (B) (C) (D) (E)



Choice (B) is correct. Since the fact that implies or The equationcan be rewritten as Substituting for in the previous inequality

yields which can be simplified to Since is an integer, it follows that

must also be an integer, and the greatest integer that satisfies the

inequality is


Choice (A) is not correct. Although is a possible value for there are

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greater possible values of and the question asks for the greatest

possible value.


Choice (C) is not correct. If then and However, the problem states

that

Explanation for Incorrect Answer D :Choice (D) is not correct. If then and However, the problem states

that


Choice (E) is not correct. If then and However, the problem states

that

15 Molly is inches tall. At 10:00 A.M. one day, her shadow is inches long, and the shadow of

a nearby tree is inches long. In terms of what is the height, in inches, of the tree?

(A) (B) (C) (D) 4s

(E) ANSWERS AND EXPLANATIONS


Choice (D) is correct. The ratio of Mollys height ( inches) to the

length of her shadow ( inches) is proportional to the ratio of the trees

height () to the length of its shadow (). So This simplifies to


Choice (A) is not correct. Height is proportional to the length of the

shadow; it is not the length of the shadow plus a constant.



(D).


Choice (C) is not correct. The height of the tree is times the length of

its shadow, not the length of its shadow.



(D).16 If a number is chosen at random from the set what is the probability

that it is a member of the solution set of both and

(A) (B) (C)

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(D) (E)



Choice (C) is correct. To determine this probability, you must firstlook at the solution sets of the inequalities. The inequality simplifies

to and simplifies to Of the five numbers in the set, only and are

greater than and less than Therefore, the probability of picking

a number from the set that is in the solution set of both these

inequalities is



(C).



(C).Explanation for Incorrect Answer D :


(C).



(C).

17 If the length of is and the length of is which of the following could be the length of

(A) (B) (C) (D) (E)



Choice (A) is correct. If and lie on a line, the greatest possible

length of is If and do not lie on the same line, then a triangle is

formed by these three points, and the length of must be less than the

sum of the lengths of and which is The only choice that is less thanor equal to is


Choice (B) is not correct. The greatest possible length of is equal to


Choice (C) is not correct. The greatest possible length of is equal to


Choice (D) is not correct. The greatest possible length of is equal to

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Choice (E) is not correct. The greatest possible length of is equal to

18 In triangle above, if and what is the area of triangle

(A) (B) (C) (D) (E)



Choice (C) is correct. If the base of triangle is then its height is

Substituting the values given in the problem, the area of triangle is



(C).


Choice (B) is not correct. This is the area of triangle


Choice (D) is not correct. This is the area of triangle

Explanation for Incorrect Answer E :Choice (E) is not correct. See the explanation for the correct response

(C).

19 If and are two different integers and the product is the square of an integer, which of the

following could be equal to

(A) (B) (C) (D) (E)



Choice (D) is correct. The prime factorization of is Thus, since is the

square of an integer, where is an integer. It follows that If then


Choice (A) is not correct. which is not an integer. The question asks

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for a value of that makes the square of an integer.


Choice (B) is not correct. which is not an integer. The question asks



Choice (C) is not correct. which is not an integer. The question asksfor a value of that makes the square of an integer.


Choice (E) is not correct. which is not an integer. The question asks


20

On the number line above, the tick marks are equally spaced. Which of the lettered points

represents

(A) A

(B) B

(C) C

(D) D

(E) E



Choice (E) is correct. Regardless of the position of on the number

line, which is the average of and will always be exactly halfway

between and Since is units to the left of the point labeled it follows

that must be units to the right, or at the point labeled .



(E).



(E).


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



(E).

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