GRTC GRE Quant Material - Corrections in Progree

5/26/2018 GRTC GRE Quant Material - Corrections in Progree

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1

Exercise-01

(1) If each package of fresh gum contains s

sticks, and each of the students in Mr. Peri s

class chews f sticks each day , how many

packages do 6s students finish in 3 days?

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

(2) If 'n' is an even integer and a multiple of

7, which of the following cannot be an Even

Integer?

(A) (B) (C) 7n (D) 7n+2 (E) 7n+3

(3) If positive integers a and b are not

both odd, which of following must be even?

(A) (B) (C)

(D) (E)( )

(4) If where a, b, and c are

three different prime numbers greater than

2, how many positive factors , including 1

and d, does d have?

(A) 3 (B) 5 (C) 6 (D) 8 (E) 10

(5) If a, b, c are positive integers such that 'a'

is even, 'b' is odd and 'c' is prime and

1


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2

(16) The weight of four packages are 1,3,5,

and 7 pounds, respectively. Which of the

following CANNOT be the total weight, in

pounds, of any combination of the

packages?

(A) 9 (B)10 (C) 12 (D) 13 (E) 14

(17) In an increasing sequence of 10

consecutive integers, the sum of the first 5

integers is 560. What is the sum of the last 5

integers in the sequence?

(A) 585 (B) 580 (C) 575 (D) 570 (E) 565

(18) A cashier mentally reversed the digits of

one customer s correct amount of change

and thus gave the customer an incorrect

amount of change. If the cash register

contained 45 cents more than it should have

as a result of this error, which of the

following could have been the correct

amount of change in cents?

(A) 14 (B) 45 (C) 54 (D) 65 (E) 83

(19) Ifis an even integer andis an odd

integer, which of the following must be an

odd integer?

(A) (B) (C)

(D)( ) (E)

(20) If positive integersandare not both

odd, which of the following must be even?

(A) (B) (C)

(D) (E) 2( )-1


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3

Exercise-02

(1) If a,b,c are positive integers such that 'a'

is a multiple of 'b' and 'a' is a factor of 'c'

which of the following is not an integer?

(A)

( )

(B) (C) (D)

( )

(E) none

(2) If k is a multiple of 2,3 and 5. What is the

next large integer which is divisible by these

numbers?

(A) k (B) k+2 (C) k+3 (D) k+6 (E) k+30

(3) If the numbers 70 and 105 are both

multiples of a prime number n, how many

possible values are there for n?

(A) (B) (C) (D) 3 (E) 4

(4) If the integeris a multiple of both 10

and 12, then all of the following must be

factors ofEXCEPT

(A) 15 (B) 12 (C) 10 (D) 8 (E) 6

(5) If and are positive integers such

that is divisible by, andis divisible by

, which of the following is NOT necessarily

an integer?

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

(6) Which of the following cannot be the

greatest common divisor of two positive

integers 'a' and b ?

(A) 1 (B) a (C) b (D) a-b (E) a+b

(7) If integersandare distinct factors of

30, which of the following CANNOT be a

factor of 30?

(I)2

(II)( )

(III)

(A) I only (B) II only (C) III only

(D)I and II only (E) I, II, and III

(8) Two positive integers are

their greatest common facto

number. For instance, 15 a

compatible because their greate

factor is 5, which is prime. Ifand 98 are

compatible, andis an odd number,

what is the greatest common

and 98?

(A) 2 (B) 5 (C) 7 (D) 14 (E) 49

(9) Three different container

420 gallons, 220 gallons an

Which of the following is

measure that can measure all the

quantities exactly?

(A) 10 (B) 20 (C) 30 (D) 40 (E

(10) Chime A and Chime B

simultaneously at Noon. Aft

A rings every 72 minutes and chi

every 54 minutes. What time is it w

next ring simultaneously?

(A) 3:18 pm (B) 3:24 pm (C) 3:36 pm

(D) 3:54 pm (E) 4:16 pm

(11) Jacob has 60 red, 156 blue & 2

marbles. He distributes them a

group of kids such that each kid

number of marbles and no kid

of more than one color. Fin

kids?

(A) 12 (B) 21 (C) 35 (D) 36 (E) 40

(12) A computer is programmed to

a list of multiples of Prime Numb

5 as shown below

Program I __ List of Multiples o

Program II____ List of Multiples

Program III ___ List of Multiples

How many integers between 1 an

appear on all three of the lis

programs produced above?

(A) 1 (B) 3 (C) 5 (D) 6 (E) none


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Questions 13 and 14 refer to the following

definition.

For any positive integer n, n>1, the length

of n is the number of positive primes (not

necessarily distinct) whose product is n. For

example, the length of 50 is 3 since

50 = (2)(5)(5).

(13) Which of the following integers has

length 3?

(A) 3 (B) 15 (C) 60 (D) 64 (E) 105

(14) What is the greatest possible length of a

positive integer less than 1000?

(A) 10 (B) 9 (C)8 (D) 7 (E) 6

(15) How many positive integers less than 20

are either a multiple of 2, an odd multiple of

9, or the sum of a positive multiple of 2 and

a positive multiple of 9?

(A) 19 (B) 18 (C) 17 (D) 16 (E) 15

(16) Ifis a positive integer less than 200

and is an integer, thenhas how many

different positive prime factors?

(A) 2 (B) 3 (C)5 (D)6 (E) 8

(17) Simplify 30-54+(7-3)28

(A) 10 (B) 13 (C) 12 (D) 16 (E) none

(18) - =

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

(19) ()() ()( ) =

(A)4

(B) 24 (C) 25 (D) 4

+8

(E)32

(20)

16

9

4

8

3

3

2

2

1

(A)

16

29

(B)

16

19

(C)

16

15

(D)

13

9

(E) 0


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Exercise -03

(1) Peter traveled 13miles by Taxi , 17

miles by Bus and 14 miles by Train. In the

return journey he traveled 11miles by

Train, 19miles by Taxi and the rest of the

distance by Bus. How much distance did he

travel by Bus in the return Journey?

(A) 12(B) 14(C) 13(D) 14 (E) 12

(2) 0.2 + 0.02 + 0.002 is equal to

0.02 0.002 0.0002

(A) 10 (B) 20 (C) 30 (D) 0.04 (E) 40

(3) If k is an integer and 0.0010101 x 10k is

greater than 1000, what is the least possible

value of k

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

(4) If 1/2 of the money in a certain trust fund

was invested in Stocks, 1/4 in Bonds 1/5 in a

Mutual Fund, and the remaining $10,000 in

a government certificate, what was the total

amount of the trust fund?

(A) 100,000 (B) 150,000 (C) 200,000

(D) 50000 (E) 180,000

(5) In a mayoral election, Candidate X

received 1/3 more votes than Candidate Y,

and Candidate Y received 1/4 fewer votes

than Candidate Z. If candidate Z , received

24,000 votes, how many votes did candidate

X received?

(A) 18000 (B) 22000 (C) 24000

(D) 26000 (E) 28000

(6) A collection of books went on sale, and

2/3 of them were sold for $2.5 each. If none

of the 36 remaining books were sold, what

was the total amount received for the books

that were sold?

(A) $180 (B) $135 (C) $90 (D)$ 60 (E)$ 54

(7) In a certain class con

students, some boys and some

1/3 of boys and 1/4 of girls wa

What is the greatest possible

students in this class who walk

(A) 9 (B) 10 (C) 11 (D) 12 (E) 13

(8) During the four years that

owned his car, he found that h

expenses were $18000. Fuel

maintenance costs accounte

total and depreciation accou

the remainder. The cost of ins

times the cost of financing

these two costs accounted fo

total. If the only other expens

and license fees, then the cos

was how much more or less than

taxes and license fees?

(A) $1,500 more (B) $1,200 more

(C)$ 100 less (D) $ 300 less (E) $

(9) In a nationwide poll, N p

interviewed. If 1/4 of them ans

to question 1, and of those,

"yes" to question 2, which of

expressions represents the

people interviewed who DID NOT

"yes" to both questions?

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

(10) A restaurant buys frui

containing 3cups of fruit each. I

restaurant usescup of the fruit in

serving of its fruit compote, w

number of cans needed to pr

servings of the compote.

(A) 7 (B) 8 (C) 9 (D) 10 (E) 12


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(11) Drum X is 1/2 full of oil and drum Y ,

which has twice the capacity of drum X, is

2/3 full of oil. If all of the oil in drum X is

poured into drum Y, then the drum Y will be

filled to what fraction of its capacity

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

(12) In a certain flower shop, which stocks

four types of flowers, there are 1/3 as many

violets as carnations, and 1/2 as many tulips

as violets. If there are equal number of roses

and tulips, what fraction of the flowers in

the shop are carnations?

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

(13) During a sale, a store sells 20 percent of

its remaining stock each day, without

replenishment. After 4 days, what fraction of

its original stock has it sold?

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

(14) Company Z spentof its revenue last

year on marketing andof the remainder on

maintenance of its facilities. What fraction of

last year s original revenue did company Z

have left after its marketing and

maintenance expenditures?

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

15) Which of the following fractions has the

greatest value?

(A)()()

(B)()()

(C)()()

(D)()()

(E)()()

16) At a certain pizzeria,of the pizzas s

in one week were mushrooms an of the

remaining pizzas sold were pep

of the pizzas sold were peppero

many were mushroom?

(A) (B) (C) (D) (E) 3

(17) of the final grades rece

students in a certain math couare A s,

are B s,are C s, and the remain

grades are D s. What is the nu

students in the course?

(A) 80 (B) 110 (C) 160 (D) 200 (E

(18) Ifof the air in a tank is rem

each stroke of a vacuum pump

fraction of the original am

been removed after 4 strokes?

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

(19) Equal amounts of water we

into two empty jars of differe

which made one jarfull and the other

full. If the water in the jar wit

capacity is then poured into the

greater capacity, what fraction

jar will be filled with water?

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

(20) In company X, no employe

technician and an Account

company X,of the employees a

technicians andof the remain

employees are Accountants. W

of the total number of empl

company X are neither techn

Accountants.

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


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Exercise -04

(1) A vessel contains 48 liters mixture of milk

and water in the ratio 5:3. How much water

should be added to the mixture so that the

ratio of milk and water is 1:1?

(A) 8 (B) 10 (C) 12 (D) 14 (E) 16

(2) At a certain party the ratio of men and

women was 2:1. If 2 men and 3 women left

the party, the ratio becomes 4: 1. How many

people were present in the party?

(A) 10 (B) 12 (C) 15 (D) 18 (E) 25

(3) A fruit Salad mixture consists of Apples,

Mangoes and grapes in the ratio 7:5:3

respectively by weight. If 60 pounds of the

mixtures is prepared, the mixture includes

how many more pounds of Apples than

grapes?

(A) 8 (B) 10 (C) 12 (D) 14 (E) 16

(4) A container holding 16 Gallons of a

Solution that is 1 Part alcohol to 3 parts

water is added to another container holding

9 gallons of a solution that is 1 part Alcohol

to 2 parts water. What is the ratio of alcohol

to water in the resulting solution?

(A) 7:15 (B) 15:7 (C) 7: 18 (D) 18: 7 (E) 12: 17

(5) In a mixture of 45 liters, the ratio of milk

and water is 5:4 how much milk must be

added to make the ratio 2:1?

(A) 5 (B) 10 (C) 15 (D) 20 (E) 25

(6) If a rectangular photograph that is 10

inches wide by 15 inches long is to be

enlarged so that width will be 22 inches and

the ratio of width to length will be

unchanged, then the length in inches of the

enlarged photograph will be

(A) 33 (B) 32 (C) 30 (D) 27 (E) 25

(7) The amounts of time tha

secretaries worked on a speci

in the ratio of 1 to 2 to 5 . If th

combined total of 112 hours

hours did the secretary who wo

longest spend on the project?

(A) 80 (B) 70 (C) 56 (D)16 (E) 14

(8) In a certain class, the ratio

of mathematics majors to the

students who are not mathemati

2 to 5. If 2 more mathematics maj

to enter the class, the ratio wo

2. How many students are in the c

(A) 10 (B) 12 (C) 21 (D) 28 (E) 35

(9) If , which of the followin

true

(A) (B) (C)

(D) (E)

(10) In a certain company, the

number of managers to the n

production line workers is

additional production line

be hired, the ratio of the n

managers to the number of pro

workers would be 5 to 74.Ho

mangers does the company have?

(A)5 (B)10 (C)15 (D) 20 (E) 25

(11) The ratio of two quantiti

each of the quantities is increa

is the ratio of these two quanti

(A) 3 :4 (B) 8 : 9 (C) 18 : 19 (D) 23 : 24

(E) It cannot be determined

information given


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8

(12) The ratio by volume of soap to alcohol

to water in a certain solution is 2:50:100.

The solution will be altered so that the ratio

of soap to alcohol is doubled while the ratio

of soap to water is halved. If the altered

solution will contain 100 cubic centimeters

of alcohol, how many cubic centimeters of

water will it contain?

(A) 50 (B) 200 (C) 400 (D) 625 (E) 800

(13)

Shipment Number of

defective

chips in the

shipment

Total number

of

chips in the

shipment

S1 2 5000

S2 5 12000

S3 6 18000

S4 4 16000

A computer chip manufacturer expects the

ratio of the number of defective chips to the

total number of chips in all future shipmentsto equal the corresponding ratio for

shipments S1, S2, S3 and S4 combined, as

shown in the table above. What is the

expected number of defective chips in a

shipment of 60000 chips?

(A) 14 (B) 20 (C) 22 (D) 24 (E) 25

(14) On a 3 day fishing trip, 4 adults

consumed food costing $60. For the same

food costs per person per day, what would

be the cost of food (in $) consumed by 7

adults during a 5 day fishing trip?

(A) 300 (B) 175 (C) 105 (D) 100 (E) 84

(15) If a fleet ofbuses usesgallons

gasoline every two days, how m

of gasoline will be used by 4 bus

days?

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

(16) A machine can produce 50

chips in 2 hours. At this rate

computer chips can the machine p

7 hours.

(A) 175 (B) 200 (C) 225 (D) 250 (

(17) To make a purple dye, red dye an

dye are mixed in a ratio of 3:4. T

certain orange dye, red dye and

are mixed in a ratio of 3:2. If eq

of the purple and orange dye ar

what fraction of the new mixtur

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

(18) If 4 cows produce 4 cans o

days, how many days does it take e

to produce 8 cans of milk?

(A) 1 (B) 2 (C) 4 (D) 8 (E) 16

(19) In a class of 160 senior

boys to girls is 3 to 5. In the ju

ratio of boys to girls is 3 to 2

classes are combined, the rati

girls is 1 to 1. How many studen

junior class?

(A) 160 (B) 180 (C) 200 (D) 360 (E

(20) If 1 pound of grain can fe

or 2 pigs, then 10 pounds of gr

20 chickens and how many pigs?

(A) 8 (B) 10 (C) 12 (D) 24 (E) 40


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Exercise -05

(1) Peter received grades of 92, 88 and 75 on

three tests. What grade must he receive on

the next test so that his average for thesefour tests is 84?

(A) 78 (B) 80 (C) 81 (D) 86 (E) 88

(2) Mary s average grade for four math tests

is 86 . What grade must she receive on her

next test to increase her average by 2

points?

(A) 92 (B) 94 (C) 96 (D) 98 (E) 100

(3) If the average of a, b and 45, is 15, then

the average of a and b is

(A) 1.5 (B) 10 (C) 5 (D) 1 (E) 0

(4) The average test score earned by a group

of students is 82. If 60 percent of the

students have an average score of 75 then

what is the average score of the remaining

students?

(A) 82.5 (B) 85 (C) 87.5 (D) 90 (E) 92.5

(5) The average weight of 15 students in a

class is increased by 300grams, when one of

the boys whose weight is 30 kg is replaced

by new boy. What is the weight of the new

boy (in kg)?

(A) 25 (B) 25.5 (C) 34.5 (D) 35 (E) none

(6) Average of 9 members is 30. The average

of first 5 members is 27 and the average of

last 5 members is 31. Find the 5th number?

(A) 20 (B) 22 (C) 25 (D) 28 (E) 34

(7) Bob s average score for five math tests

was 150 out of possible 200. His scores on

three of the tests were 182, 147 and 171

respectively. Lowest of his other scores

could have been?

(A) 45 (B) 50 (C) 70 (D) 75 (E) 95

(8) The average of 20 observatio

calculated as 40, it was found la

of the observations was mis

instead of 34, the correct mean

(A) 38 (B) 39 (C) 40 (D) 41 (E) 42

(9) A man purchased two varietie

in equal weight, the prices of

wheat are $12 per kg and $ 15 per kg,

the average price (in $) (per Kg)

(A) 12.5 (B) 13 (C) 13.5 (D) 14 (

(10) The average of 5 numbers is

number is multiplied by 5, the aver

new set of numbers is

(A) 55 (B) 60 (C) 80 (D) 225 (E) 27

(11) The average of 6 numbers is

one number is discarded, the av

remaining numbers becomes 7

the discarded number?

(A) 7.8 (B) 9.8 (C) 10.0 (D) 12.4 (E

(12) Ifbooks cost $5 each andbooks co

$8 each, then the average cost, in

book, is equal to

(A) (B) (C)

(D) (E)

(13) If , then which of

following represents the

in terms of?

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


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10

(14) A Club sold an average of 92 raffle

tickets per member. Among the female

members, the average number sold was 84,

and among the male members, the average

number sold was 96. What was the ratio of

the number of male members to the number

of female members in the club?

(A) 1:1 (B) 1:2 (C) 1:3 (D) 2:1 (E) 3:1

(15) On 3 sales John has received

commission of $240, $80, and $110, and he

has 1 more sale pending. If John is to receive

an average commission of exactly $150 on

the 4 sales, then the fourth commission

must be

(A) $164 (B) $170 (C) $175 (D) $182 (E) $185

(16) If the average ofandis 60 and the

average ofandis 80, what is the value of

?

(A)70 (B) 40 (C) 20 (D) 10

(E) It cannot be determined from the

information given

(17) A certain college has a student-to-

teacher ratio of 11 to 1. The average annual

salary for teachers is $26000. If the college

pays a total of $3380000 in annual salaries

to its teachers, how many students does the

college have?

(A) 130 (B) 169 (C) 1300 (D) 1430 (E) 1560

(18) Last year John received 26 pay checks.

Each of his first 6 paychecks was $750; each

of his remaining paychecks was $30 more

than each of his first 6 paychecks. To the

nearest dollar, what was the average

amount of his paychecks for the year?

(A) $752 (B) $755 (C) $765 (D) $773 (E) $775

(19) If 3 pounds of dried aprico

dollars per pound are mixed wit

of prunes that costdollars per po

what is the cost, in dollars, pe

mixture?

(A) (B) (C)

(D)( ) (E)

(20) The manager of a theater no

every 10 admission tickets sol

sells 3 bags of popcorn at $2

sodas at $1.50 each, and 2 cand

1.00 each. To the nearest cent,

average amount of these snac

ticket sold?

(A) $1.18 (B) $1.48 (C) $1.60

(D)$1.64 (E) $1.7


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11

Exercise -06

(1) The boys and girls in a school are in the

ratio 15:8 .If the 20% of boys and 25 % of

girls are adults, the percentage of students

who are adults is

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

(E) 33

(2)Last year Peter s annual salary was $

25,000.This years raise brings his annual

salary to $ 30,000 .If he gets the same

percent raise every year, what will his salary

be next year?

(A)$ 33,000 (B) $ 35,000 (C) $ 36,000

(D) $ 38,000 (E) $ 40,000

(3) If the total expenses of certain businessin year 2012 was $60,000, which was 20%

more than in year 2011 what was the total

expenses in year 2011 ?

(A) $48,000 (B) $50,000 (C) $51,000

(D) $52,000 (E) $72,000

(4) If 60% of students in a school are boys

and the number of boys exceeds that of girls

by 140. Find the total girl students in the

school?

(A) 200 (B) 240 (C) 280 (D) 320 (E) 360

(5) Of the 4800 employees of company z,

are non technicians. If the non- technicians

staff were to be reduced by, what percent

of the total number of the remaining

employees would then be non- technicians?

(A) 40 (B) 50 (C) 56 (D) 60 (E) 62

(6) In an examination, there are 3 papers of

math, science and English of 100 markseach. A boy secures 90% in math, and 78% in

the Science paper. In order to secure 85% in

the aggregate, the percentage of marks he

should secure in English will be

(A) 80 (B) 82 (C) 84 (D) 85 (E) 87

(7) A union contract specif

salary increase plus a $ 450 bon

employee. For a certain emplo

equivalent to an 8 percent sala

What was this employee's salary

new contract?

(A)$21500 (B)$22500 (C)$23500

(D)$24300 (E)$25000

(8) If the length and width of a r

garden plot were each increa

percent, what would be the percen

in the area of the plot?

(A) 20 (B) 24 (C) 36 (D) 40 (E) 4

(9) Tickets for all but 100 s

10000seat stadium were sold. Of

sold, 20 percent were sold at ha

the remaining tickets were so

price of $2? What was the total r

$) from the tickets sales?

(A) 15840 (B) 17820 (C) 18000

(D) 19800 (E) 21780

(10) In a shipment of 120 machi

percent were defective. In a shi

machine parts, 10 percent were

For the two shipments combi

percent of the machine part

defective?

(A) 6.5 (B) 7 (C) 7.5 (D) 8 (E) 8.5

(11) Of the 3600 employees of com

are clerical. If the clerical st

reduced by, what percent of the

number of the remaining emplo

then be the clerical?

(A) 25 (B) 22.2 (C) 20 (D) 12.5 (E


12

12

(12) In countrya returning tourist may

import goods with a total value $500 or less

tax free, but must pay a 8 percent tax on the

portion of the total value in excess of $500.

What tax must be paid by a returning tourist

who imports goods with a total value of

$730?

(A) $58.40 (B) $40.00 (C) $24.60

(D) $18.40 (E) $16.00

(13) A tank contains 10, 000 gallons of a

solution that is 5 percent sodium chloride by

volume. If 2,500 gallons of water evaporate

from the tank, the remaining solution will be

approximately what percent sodium

chloride?

(A) 1.25% (B) 3.75% (C) 6.25%

(D) 6.67% (E) 11.7%

(14) In 2005, 45 percent of a document

storage facility s 60 customers were banks,

and in 2007, 25 percent of its 144 customers

were banks. What was the percent increase

from 2005 to 2007 in the number of bank

customers the facility had?

(A) 10.7% (B)20% (C)25% (D) 33% (E) 58%

(15) During a certain season, a team won 80

percent of its first 100 games and 50 percent

of its remaining games. If the team won 70

percent of its games for the entire season,

what was the total number of the games

that the team played?

(A) 180 (B) 170 (C) 156 (D)150 (E) 105

(16) In a poll of 66000 physicians, only 20

percent responded; of these, 10 percent

disclosed their preference for pain reliever X.

how many of the physicians who responded

did NOT disclose a preference for pain

reliever X?

(A) 1320 (B) 5280 (C) 6600 (D) 10560

(E)11880

(17) Thirty percent of the memb

swim club have passed the lifesa

Among the members who have no

the test, 12 have taken the prep

course and 30 have not taken

How many members are there in th

club?

(A) 60 (B) 80 (C) 100 (D) 120 (E) 14

(18) The organizers of a fair p

percent increase in attendan

over that of last year, but atte

year actually decreased by 20 perce

percent of the projected attend

actual attendance?

(A) 45% (B) 56%(C) 64%(D) 75% (E

(19) A part-time employee whos

wage was increased by 25 percent

to reduce the number of hours w

week so that the employee s tot

income would remain unchan

percent should the number of ho

be reduced?

(A) 12.5% (B) 20% (C) 25%

(D) 50% (E) 75%

(20) Of the researchers in a wo

percent will be assigned to tea

remaining 60 percent to team B

70 percent of the researchers pr

and 30 percent prefer tem B. wha

least possible number of res

will NOT be assigned to the te

prefer?

(A) 15 (B) 17 (C) 20 (D) 25 (E) 30


13

13

Exercise -07

(1) The price of a cell phone is discounted by

5 percent and the reduced price is further

discounted by 3 percent, this is equal to a

single discount (%)

(A) 8 (B) 7.85 (C) 7.5 (D) 7.25 (E) 7

(2) A certain customer paid $81 for a pair of

shoes. If the price represented a 10%

discount on the original price of the shoes.

The original price of the shoes is?

(A) $ 72 (B) $ 90 (C) $ 91 (D) 71(E) $ 98

(3) A man sells two watches for $ 20 each,

on one he gained 5% and on the other he

losses 5%. Find his gain % or Loss % ?

(A) 0.5% Loss (B) 0.25 % Loss (C) 0.5% gain

(D) 1% Gain (E) 0.25% gain

(4) If the selling price of 10 oranges is the

same as the cost price of 8 oranges. Find the

gain or loss percentage?

(A) 20% gain (B) 25% gain (C) 20% Loss

(D) 25% Loss (E)16(2/3) % gain

(5) The cost of a sweater to a merchant was

$ 50. The merchant fixes the marked price. Ifthe marked price were later discounted by

25%, the Selling Price would be 10% greater

than cost of the sweater. What is the

marked price (in $) of the sweater?

(A) 70 (B) 73(1/3) (C) 80 (D) 83(1/3) (E) 30

(6) A businessman allows two successive

discounts of 10% and 4% on his goods, still

he gets a profit of 8%. Find by what % the

goods were marked up?

(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

(7) Peter sold a camera at a profit of 15% If

he has sold it for $ 6 more than its SP, he

would have gained 25% profit, what was the

Cost price of the camera?

(A) 50 (B) 60 (C) 80 (D) 100 (E) 12

(8) At a selling price of $920, a c

20% Profit on the cost. What s

will yield a 5% profit on the cos

(A) $805 (B) $815 (C) $825 (D) $845 (

(9) A bookseller bought 200 bo

each and spent $ 0.25 for bindi

them. He then sells the books at

Find his gain percent?

(A) 15 (B) 16 (C) 19 (D) 21 (E) 25

(10) A man sells an article at a

had he sold it for $20 more, he w

gained 10%. Find Cost Price of t

(A) $50 (B) $100 (C) $200 (D) $400

(11) An article is offered $

customer pays $ 576 for it, after

two discounts. If the rate o

discount is 20%, find the secon

(A) 5 (B) 8 (C) 10 (D) 12 (E) 20

(12) A toy store regularly sell

discount of 20% to 40%. If an ad

were deducted from the discou

during a special sale, what wo

lowest possible price of a to

before any discount

(A) $5.6 (B) $7.2 (C) $8.8 (D) $9.6 (

(13) During a floral shop sal

roses purchased, one rose is

If the cost of one rose is $1.

money is saved by buying 2 dozen

Ans:

(14) A sports jacket marked $48 is

a discount of 25 percent duri

this reduced price the dealer make

of 20 percent on the cost. The

dealer is

(A) 29 (B) 30(C) 32 (D) 36 (E) 40


14

14

(15) A lamp is manufactured to sell for $35,

which yields a profit of 25percent of cost. If

the profit is to be reduced to 15 percent of

cost, the new retail price will be?

(A) 21 (B) 28(C) 31.50 (D) 32.2 (E) 43

(16)A furniture store sells only two models

of desks, model A and model B. The selling

price of model A is $120, which is 30 % of

the selling price of model B. If the furniture

store sells 2000 desks, 3/4 of which are

model B, what is the furniture stores total

revenue from the sale of desks?

(A) $660000 (B) $186000 (C) $294000

(D) $380000 (E) $114000

(17) A dealer originally purchased 100

identical batteries at a total cost ofdollars.

If each battery was sold at 50 percent above

the original cost battery, then, in terms of,

for how many dollars was each battery sold?

(A) (B) (C) 150 (D) +50

(E)

(18) Ms. Adams sold two properties, X and Y,

for $30000 each. She sold property X for 20

percent more than she paid for it and sold

property Y for 20 percent less than she paid

for it. If expenses are disregarded, what was

her total net gain or loss, if any, on the two

properties?

(A) Loss of $1250

(B) Loss of $2500

(C)Gain of $1250

(D) Gain of $2500

(E)There was neither a net gain nor a net

loss

(19) Envelopes can be purchase

per pack of 100, $1.00 per pack o

$0.03 each. What is the greatest n

envelopes that can be purchased

(A) 426 (B) 430 (C) 443 (D) 460 (

(20) A shipment of 1500 heads o

each of which was approximately

size, was purchased for $600. T

shipment arrived,of the heads were so

each at 25 percent above the cost

The following day the rest wer

price per head equal to 10 percent

the price each head sold for o

before. What was the gross pro

shipment?

(A) $100 (B) $115 (C)$125(D)$13


15

15

Exercise -08

(1) Albert takes half as long as Bush to do a

piece of work. Albert and Bush together can

complete a work in 12 days. In how many

days can, Albert does it separately?

(A) 10 (B) 14 (C) 15 (D) 18 (E) 20

(2) Two pipes A and B can separately fill a

tank in 10 minutes and 15 minutes

respectively. If both the pipes are opened

simultaneously, how much time will be

taken to fill the 2/3 of the tank?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

(3) If 5 printing machines can print 500 leaf

lets in 5 hours. How many hours are

required for 10 printing machines to print1000 leaflets?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 10

(4) If 5 people working together at the same

rate can do a job in 5 days, what fraction of

that job can two of these people do in one

day

(A)(B) (C) (D) (E) 5

(5) When three taps are kept open, the tank

is filled in 10 hours. If one tap can fill it in 5

hours and the second in 15 hours, In how

many hours can the 3rdtap empty it?

(A) 4 (B) 6 (C) 8 (D) 10 (E) none

(6) One inlet pipe fills an empty tank in 5 hrs.

A second inlet pipe fills the same tank in 3

hrs. If both pipes are used together, then

how long (hrs) will it takes to fill 2/3 of the

tank?

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

(7) Machine A produces bolts a

rate of 120 every 40 seconds, an

produces bolts at a uniform

every 20 seconds. If the two ma

simultaneously, how many sec

take for them to produce a tot

bolts.

(A) 22 (B) 25 (C) 28 (D) 32 (E) 56

(8) Three machines, individua

certain job in 4, 5 and 6 hours

What is the greatest part of the jo

be done in one hour by two of t

working together at their respe

(A) 11/30 (B) 9/20 (C) 3/5 (D) 11/1

(9) Machine A produces 100 partsfast as machine B does. Machine

100 parts in 40 minutes. If eac

produces parts at a constant ra

parts does machine A produce in

(A) 30 (B) 25 (C) 20 (D) 15 (E) 7.5

(10) Machines 'A' and 'B 'alw

independently and at their

constant rates. When wor

machine 'A' can fill a product

hours, and machine 'B' can fill the sam

hours. When the two machine

simultaneously to fill the pro

takes them 2 hours to complete

What is the value of 'x'

(A) 3 (B) 3 (C) 2(D) 2(E)1

(11) Working alone printers

a certain printing job in 12,1

respectively. What is the ratio o

takes printer X to do the Job, w

at its rate, to the time it takes pr

Z to do the job, working toge

individual rates.

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


16

16

(12) Running at the same constant rate, 6

identical machines can produce a total of

270 bottles per minute. At this rate, how

many bottles could 10 such machines

produce in 4 minutes?

(A)648 (B) 1800 (C)2700 (D)10800 (E) 64800

(13) Three machines, individually, can do a

certain job in 4, 5, and 6 hours, respectively.

What is the greatest part of the job that can

be done in one hour by two of the machines

working together at their respective rates?

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

(14) An automobile tyre has two punctures.

The first puncture by itself would make the

tyre flat in 9 minutes. The second puncture

by itself would make the tyre flat in 6

minutes. How long will it take(in minutes)

for both punctures together to make the

tyre flat?

(A) (B) 4 (C) (D) 7 (E) 15

(15) A cistern has two pipes, pipe A and pipeB. if both pipes are opened; the cistern is

drained in 20 minutes. If pipe A is closed and

pipe B is open, the cistern will be drained in

30 minutes. If pipe B is closed and pipe A is

opened, how long (in minutes) will it take to

drain the cistern?

(A) 10 (B) 30 (C) 60 (D) 90 (E) 120


17

17

Exercise -09

(1) A bus departed from New York at 10: 47

a.m. and arrived in New Jersey at 3: 37 p.m

on the same day, the distance between

above cities is 290 miles. What was the

approximate average speed of the bus?

(A) 20 (B) 40 (C) 60 (D) 70 (E) 80

(2) A boy rode his bicycle from home to

school, a distance of 16 miles, at an average

speed of 16 miles per hour. He returned

from school (same route) at an average

speed of 12 miles per hour. What was his

average speed for the round trips?

(A) 13 (B) 12 (C) 14 (D) 14 (E) 15

(3) Two motor cyclist leave a signal point at

11 a.m., with one motor cyclist Traveling

North at 75 miles per hour and other south

at 55 miles per hour along a Straight road .At

what time (P.M) they will be 390 miles

apart?

(A) 1 (B) 2 (C) 3.30 (D) 3.50 (E) 4

(4) If a man walks at 5 miles per hour, He

reaches the bus stop 7 minutes too late and

if he walks at 6 miles per hour, he reachesthe stop 8 minutes too early. The bus stop is

at a distance of?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7.5

(5) A train covers a distance in 40 minutes if

it runs at a speed of 60 mph. How much

speed will be required to cover the same

distance in 50 minutes

(A) 42 (B) 46 (C) 48 (D) 50 (E) 75

(6) A train travels at average speed of 65miles per hour for the first 5 hours of a trip

and averages 55 miles per hour for each

additional hour of travel time if the average

speed for the entire trip 60 miles per hour,

how many hours long is the trip?

(A) 2.5 (B) 5 (C) 7.5 (D) 8 (E) 10

(7) Two trains X and Y started si

from opposite ends of a 100 mil

travelled toward each other o

tracks. Train X travelling at a

completed the 100 mile trip in 5 ho

Y travelling at a constant rate

100 mile trip in 3 hours. How m

had train X travelled when it met t

(A) 37.5 (B) 40.0(C) 60.0 (D) 62.

(8) A Car travels at an average

10mph through Urban area in 0.

mph through Suburban area in3

70 mph through rural areas in

What is the Car s average speed

entire trip?

(A) 52.2 (B) 56.2 (C) 59.2 (D) 60 (

(9) Thirty minutes after Peter st

from A to B distance of 14 miles,

walking from along the same ro

A. if Peter s walking speed was 4

hour and Paul s was 2 miles per

many miles had Paul walked when th

(A) 1 (B) 2 (C) 3 (D) 4 (E) 6

(10) Two trains start from tw

and y with speeds 60 miles per homiles per hour in the opposite

11 a.m. Find at what time they wi

each other, if the distance betw

stations is 350 miles?

(A) 2:30p.m. (B) 3: 30 p.m. (C) 3 p.

(D) 2 p.m. (E) None

(11) Two motorcyclists do the

by traveling at 40 miles per ho

miles per hour respectively.

distance traveled when one o

one hour longer than the othe

(A) 200(B) 300 (C) 400 (D) 600 (E)


18/

18

(12) Two hundred gallons of fuel oil are

purchased at $0.91 per gallon and are

consumed at a rate of $0.70 worth of fuel

per hour. At this rate, how many hours are

required to consume the 200 gallons of fuel

oil?

(A) 140 (B) 220 (C) 260 (D) 322 (E)330

(13) An airline passenger is planning a trip

that involves three connecting flights that

leave from Airports A, B and C respectively.

The first flight leaves airport A every hour,

beginning at 8:00a.m and arrives at airport B

2 hours later. The second flight leaves

airport B every 20 minutes, beginning at

8:00a.m and arrives at airport C 1hours

later. The third flight leaves airport C every

hour beginning at 8:45 a.m. What is the least

Total Amount of Time the passenger must

spend between flights if all flights keep to

their schedules.

(A) 25 min (B) 1 hr 5 min (C) 1 hr 15 min

(D) 2 hr 20min (E) 3 hr 40 min

(14) A certain car increased its average speed

by 5 miles per hour in each successive 5-

minute interval after the first interval. If in

the first 5- minute interval its average speed

was 20 miles per hour, how many miles did

the car travel in the third 5- minute interval?

(A) 1.0 (B) 1.5 (C) 2.0 (D) 2.5 (E) 3.0

(15) A hiker walked for two days. On the

second day the hiker walked 2 hours longer

at an average speed 1 mile per hour faster

than he walked on the first day. If during the

two days he walked a total of 64 miles and

spent a total of 18 hours walking, what was

his average speed (mph) on the first day?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

(16) A train travels from New Y

Chicago a distance of 840 mil

average rate of 60 mph and arr

Chicago at 6:00 in the evenin

Time. At what hour in the morn

York city time did the Train d

Chicago?(Note : Chicago tim

earlier than New York city time)

(A) 4:00 (B) 5:00 (C) 6:00 (D) 7:0

(17) During a car trip Maria sto

after she traveled half of the to

to her destination. She stopp

she traveled 1/4 of the distanc

between her first stop and her

and then she drove the remainin

to her destination. What wa

distance in miles from Maria's

to her Destination?

(A) 280 (B) 320 (C) 360 (D) 420 (E) 4

(18) One hour after Yolanda st

from X to Y, a distance of 45

started walking along the same

to X. If Yolanda s walking ra

per hour and Bob s was 4 miles

how many miles had Bob walked wh

met?

(A) 24 (B) 23 (C)22 (D) 21 (E) 19.5

(19) A car travels from Mayville

an average speed of 30 miles per h

returns immediately along the s

an average speed of 40 miles per

the following, which is close

speed in miles per hour, for the r

(A) 32.0 (B) 33.0(C) 34.3(D) 35.

(20) Starting at town S, Fred r

8 miles due east, 3 miles due south

due west, and 11 miles due nor

stopping at town T. if the ent

flat, what is the straight line

miles, between town S and T?

(A) 10 (B) 8 (C) (D) 14 (E) 24


19

19

Exercise -10

(1)If 42-12+k is a perfect square find

the numerical value of k?

(A) 3 (B) 6 (C) 9 (D) 12 (E) none

(2) If x and y are positive consecutive oddintegers where> which of the following is

equal to2

2

(A) 2 (B) 4 (C) 2+2

(D) 2+4 (E) 4+4

(3) If (a2- 3a)(a+3) =0 then a = ?

(A) { 3 } (B) { -3} (C) { 3,-3}

(D) { 0,3,-3 } (E) {0,-1,3,-3}

(4) If (b-3) (4+) = 0 and b3, then b =

(A) -8 (B) -2 (C) (D) (E) 2

(5) If = , what is the value of

(A) -4 (B) -1 (C) 0 (D) 1 (E) 2

(6) If= -1, then =

(A) - (B) (C) 0 (D)(E)

(7) If the quotientis positive, which of the

following must be true?

(A) (B) (C)

(D) (E)

(8) If and then

(A) (B) (C) (D) (E) 5

(9) If = 5, then=

(A) -3.7 (B) 0.1 (C) 0.3 (D) 0.5 (E) 2.8

(10) If= 1-3and= 2 -1, then for w

value ofdoes ?

(A) (B) (C) (D) (E) 0

(11) Ifis an integer and, which

of the following CANNOT be a div?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

(12) If , which of the foll

must be an integer?

I.

II.

III.

(A ) I only (B) II only (C) I and

(D) II and III only (E) I, II an

(13) If and then

what is the value of x.

(A) 12 (B) 19 (C) 24 (D) 28 (E) 38

14) If then

(A) -3 (B) -1 (C) 0 (D) 1 (E) 3

(15) If 0.0015 10m = 5 10

7then m-k =

0.03 10k

(A) 9 (B) 8 (C) 7 (D) 6 (E) 5

(16) =

(A) 870 (B) 841 (C) 58 (D) 31 (E

(17) If+ + =33 , then what is t

value of.

(A)33 (B) 54 (C)44 (D) 22 (E)11


20

20

(18) Bill s school is 10 miles from his home.

He travels 4 miles from school to football

practice and then 2 miles to a friend s house.

If he is thenmiles from home, what is the

range of possible values for ?

(A) 2

(B)

(C)

(D)

(E) 6

(19) If2-9 0 which of the following is

true?

(a) -3 (b) 3 (c) 9

(d) -3 or 3 (e) -3 3

(20) How many integersare there such

that

(A) Five (B)Four (C) Three (D) Two (E) One


21

21

Exercise -11

(1) The amount of fat in an ounce of food A

plus the amount of protein in an ounce of

food A is 100 grams. The amount of protein

in an ounce of food A minus twice the

amount of fat in an ounce of food A is 10

grams. How many grams of protein are there

in an ounce of food A ?

(A) 210 (B) 105 (C) 70 (D) 35 (E) 190

(2) Eight persons are planning to share

equally the cost of a rental car. If one person

withdraws from the arrangement and the

others share equally, the entire cost of the

car, then the share of each remaining person

increased by what fraction.

(A)7 (B) 1/7 (C) 1/56 (D) 1/8 (E) 8

(3) A labor is engaged for 30 days on the

condition that he receives $25 for each day

he works and he is fined $7.5 for each day

he absents from work. He gets $ 425 in all

for how many days was he absent?

(A) 20 (B) 10 (C) 15 (D) 25 (E) 5

(4) A father s Age is three times the sum of

the ages of his two children. In four years, he

will be twice as old as the sum of their ages.

How old is the Father?

(A) 12 (B) 24 (C) 36 (D) 48 (E) 40

(5) There is the same number of boys and

girls on a school bus when it departs from

school. At the first stop, four boys get off the

bus and no body gets on. After the first stop

there are twice as many girls as boys on the

bus. How many girls are on the bus?

(A) 8 (B) 4 (C) -4 (D) 0 (E) can't determine

(6) In a weight lifting competit

Weight of Joe s two lifts was 7

twice the weight of his first l

pounds more than the weight of

lift, what was the weight, in pou

first lift.

(A) 225 (B) 275 (C) 325 (D) 350 (E)

(7) Which of the following h

common with ?

(A)

(B)

(C)

(D)

(E)

(8) Elena purchase brand pens for $4

piece and brandfor $2.80 a piece. If E

purchased a total of 12 of thes

$42, how many brandpens did she

purchase?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

(9) Marion rented a car for $18.

per mile driven. Craig rented a c

plus $0.05 per mile driven. If ea

miles and each was charged exac

same amount for the rental, theequals

(A) 100 (B ) 125 (C) 135 (D) 140 (E )

(10) Today Rose is twice as old

Sam is 3 years younger than Tin

Sam and Tina are all alive 4 ye

today, which of the following

on that day?

I Rose is twice as old as Sam

II Sam is 3 years younger than Ti

III Rose is older than Tina.

(A) I only (B) II only (C) III o

(D) I and II (E) II and III


22

22

(11) Jack is now 14 years older than Bill. If in

10 years Jack will be twice as old as Bill, how

old will Jack be in 5 years?

(A) 9 (B) 19 (C) 21 (D) 23 (E) 33

(12) A rope 40 feet long is cut into two

pieces. If one piece is 18 feet longer than the

other, what is the length, in feet, of the

shorter piece?

(A) 9 (B) 11 (C) 18 (D) 22(E) 29

(13) Jan livesfloors above the ground floor

of a high rise building. It takes her 30

seconds per floor to walk down the steps

and 2 seconds per floor to ride the elevator.

If it takes Jan the same amount of time to

walk down the steps to the ground floor as

to wait for the elevator for 7 minutes and

ride down, thenequals

(A) 4 (B) 7 (C) 14 (D) 15 (E) 16

(14) A certain manufacturer produces items

for which the production costs consists of

annual fixed costs totaling $130000 and

variable costs averaging $8 per item. If the

manufacturer s selling price per item is $15,

how many items must the manufacturer

produce and sell to earn an annual profit of

$150000?

(A)2858 (B)18667 (C)21429

(D) 35000 (E)40000

(15)Sales person A s compensation for any

week is $360 plus 6 percent of the portion of

A s total sales above $1000 for that week.

Salesperson B s compensation for any week

is 8 percent of B s total sales for that week.

For what amount of total weekly sales would

both salespeople earn the same

compensation?

(A) $21000 (B) $18000 (C) $15000

(D) $4500 (E) $4000

(16) If the numberof calculators s

week varies with the pricein dolla

according to the equation,

what would be the total weekly r

from the sale of $10 calculator

(A) $100 (B) $300 (C) $100

(D) $2800 (E) $3000

(17) An optometrist charges $

for soft contact lenses and

hard contact lenses. Last week

more pairs of soft lenses than

her total sales for pairs of co

week were $1690, what was the t

number of pairs of contact le

sold.

(A) 11 (B) 13 (C) 15 (D) 17 (E) 19

(18) The cost to rent a small bus

dollars, which is to be shar

among the people taking the tr

people take the trip rather than

many more dollars, in terms o, will it co

per person?

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

(19) If Sam were twice as old he is,

be 40 years older than Jim. If Jim

younger than Sam, how old is Sa

(A) 20 (B) 30 (C) 40 (D) 50 (E) 60

(20) The contents of a certain

14 apples and 23 oranges. Ho

oranges must be removed from

that 70 percent of the pieces of f

box will be apples?

(A) 3 (B) 6 (C) 14 (D) 17 (E) 20


23

23

Exercise -12

(1) If the number of points of intersection of

a set of 10 lines lying in a plane is denoted

by 'n' , what will be the greatest possible

number of points of intersection when

eleventh line is added to the set?

(A) n+10 (B)n+11 (C) 2n (D) 10n (E) n2

(2)

IfXYZ in the figure above is a right angle,

what is the value ofx ?

(A) 155 (B) 145 (C) 135 (D) 125 (E) 110

(3)

Note: Figure not drawn to scale.

In the figure above, the value ofy is

(A) 6 (B) 12 (C) 24 (D) 36 (E) 42

(4)

Find the value of x?

(A) 80 (B) 100 (C) 120 (D) 240 (E) none

(5)

In the figure above, if linem is parallel to

k ands=t+ 30 then, what is the value o.

(A) 30 (B) 60 (C) 75 (D) 80 (E) 105

(6)

In the figure above, what is the av

and?

(A)60 (B) 70 (C) 80 (D) 90 (E) 50

(7)

In the figure above, what is the va

(A) 30 (B) 80 (C) 100 (D) 130 (E) 1

(8)

m

n

Y

X

Z

q

p

l

d


24

24

In the above line m and n are parallel and l

bisects angle XYZ. If p=105, what is the value

of q?

(A) 52.5 (B)37.5 (C) 75(D) 105(E) 30

(9)

In the figure above, what is the value of a-b?

(A) 7 (B)30 (C) 37 (D) 107 (E)148

(10)

If m is parallel to n in the figure above,

which of the following expressions must

equal 180?

(I) a+b

(II) c+e

(III) c+d+e

(A) I only (B) II only (C) III only

(D) II and III only (E) I, II, and III

(11)

In the figure above, if x=40, what

value of y+z?

(A) 80 (B)120 (C) 160 (D) 180 (E)22

(12)

In the figure above l is parallel

what is the value of z+q?

(A) 25 (B)50 (C) 100 (D) 125 (E)13

(13)

In the figure above line m is par

n, find the value of a+b?

(A)160 (B)180 (C) 195 (D) 200 (E)ca

(14) Linesandare parallel. If linand

are cut by three different tra

what is the least number of p

intersection that can occur

lines

(A) 3 (B) 4 (C) 5 (D) 6 (E) 8

(15)

110

150 (4a+2)

b

m

n

c d

b

e

a

m

n

l

y

z x

m

n

l

x

m

z

q

m

n95105

a b

S

P

R

Q

x15


25

25

In the figure above, if PQ is parallel to RS,

then x=?

(A) 95 (B)85 (C) 75 (D) 65 (E)55

(16)

In the figure above, AB and CD intersect at

point X . If EX bisects angle BXD, what is the

degree measure of angle CXB?

(A) 60 (B) 90 (C) 100 (D) 110 (E) 120

(17) In a plane, linesandare drawn such

that is parallel to. If third lineis drawn

such thatis perpendicular to, and a

fourth lineis drawn such that, which

of the following statements must be true?

(I)

(II)

(III)

(A) I only (B) II only (C) III only (D) I and II

(E) I and II

(18)

In the figure above, what is the value of?

(A) 50 (B) 70 (C) 90 (D) 100 (E) 140

(19)

In the figure above, l is parallel to

is parallel to n then what is the val

of a+2c+d?

(A) 180 (B) 270 (C) 360 (D) 450

(E) can t be determined.

(20)

Three lines intersect in a poi

the figure above. Which of the

pairs of angle measures is NOT s

determining all six angle measu

(A) r and t (B) s and x (C) t and

(D) t and y (E) r and s

C

A D

B

E30

X

30

l

m

n

d

c

b

a

tx

y

s

r z


26

26

Exercise -13

(1)

The figure above shows the route of

John s trip from his house to his friend s

house. John travels 6 miles from A to B,

6 miles from B to C, and 2 miles from C to D.

If john were able to travel from A to D

directly, how much shorter in miles, would

the trip be ?

(A) 2 (B) 4 (C) 8 (D) 10 (E) 18

(2)

In Triangle XYZ above, what is the value

of a+c+d+e ?

(A) 60 (B) 45 (C) 240 (D)100 (E) 180

(3)

In the figure above, if AB=2, what is the area

of triangle ABC

(A) (B) 2 (C) 1+ (D) 1+ (E) 2+

(4)

In triangle PQR below, angle RP

than angle RQP, and the bisecto

and angle Q meet in S. which of th

following must be true?

(A) SQ> SP (B) SQ=SP (C) SQ


27

27

(8) If an equilateral triangle with sideshas

the same perimeter as another triangle with

sides 6, 8 and, what is the value of?

(9)

What is the area of the triangle in the figure

above?

(A) 2+2 (B) 4 (C) 8 (D) 8 (E) 12

(10)

What is the length of BC in the figure above?

(A) 10 (B)16 (C) 18 (D) 20 (E) 24

(11)

In PQSabove, ifPQ=3 andPS= 4,

then find the value of?

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

(12)

If each side of ACDabove has length 3

and ifAB has length 1, what is the ar

regionBCDE?

(A) (B) (C)

(D) (E)

(13)

InABCabove, what isx in terms ofz?

(A)z+ 73 (B)z 73 (C) 70 z

(D)z 70 (E) 73 z

(14)

In the figure above, if AB is para,

and CE = DE,andy = 45, then what is the

value ofx ?

(A) 45 (B) 60 (C) 67.5 (D) 112.5

105

30

2

B

A D C

26

30

4a 5a


28/

28

(15)

The figure above shows the dimensions of an

isosceles triangle in terms ofx . What is the

area of the triangle?

(A) 24 (B) 30 (C) 48 (D) 60 (E) 96

(16)

In the figure above,M, N, andP are

midpoints of the sides of an equilateral

triangle whose perimeter is 18. What is the

perimeter of the triangular region MNP?

(A) 2 (B) 3(C) (D) 6 (E) 9

(17)

In triangle PQR above, what is the value of

w?

(A) 50 (B) 55 (C) 60 (D) 65 (E) 75

(18) What is the area of a right

whose perimeter is 36 and whose

, , and ?

(A) 27 (B) 54 (C) 81 (D) 108 (E) 135

(19) The three sides of a tria

lengths of 9, 16 and k. which of t

could equal K?

(Indicate that all apply)

(I) 6

(II) 16

(III) 25

(20) If the hypotenuse of iso

triangle ABC is, then what is the are

triangle ABC?

(A) 6 (B) 9 (C) 12 (D) 18 (E) 36

P

w

140

R

Q

35 40


29

29

Exercise -14

(1) If a rectangle of perimeter 12 has a

width that is 2 less than its length, then what

is its area?

(A) 6 (B) 8 (C) 10 (D) 20 (E) 35

(2) A rectangle is cut in half, resulting in

squares each of area 25. What is the

perimeter of the original rectangle?

(A)10 (B)20 (C) 30 (D) 40 (E) 50

(3)

In quadrilateral ABCD above, if CD=6, BC= 8,

and AB= 5, what is the length of AD?

(A) 4 (B) 3(C) 5 (D) 10 (E) 15

(4) A diagonal of a rectangle forms an angle

of measure with each of the two

shorter sides of the rectangle. If the length

of a shorter side of the rectangle is 2,

what is the length of the diagonal?

(A) (B) (C) 3 (D) 4 (E) 5

(5)

In the figure above, all intersecting sides of

the polygon meet at right angles. What is

the area of the polygon?

(A) 108 (B) 104 (C) 102 (D) 98 (E) 96

(6)

The shaded region in the fig

represents a rectangular fram

18 inches and width 15 inches.

encloses a rectangular pictur

same area as the frame itself. If

and width of the picture have the s

as the length and width of the fra

the length of the picture, in inc

(A) (B) (C) (D) (E) none

(7)

In the figure above, the two squ

have areas 16 and 25, respective

the area of the shaded triangula

(A) 6 (B) 8 (C) 9 (D) 12 (E) 15

(8)

In the figure above, the areas

regions X and Y are 1 and 4, re

What is the area of the triangula

(A) 2 (B) 1 (C) (D)(E)

D

C

B

A


30

30

(9)

What is the value of h in the trapezoid

above?

(A) (B) (C) 8 (D) 6 (E) 4

(10)

In the figure above,M, N, andPare the

midpoints on the respective sides of

equilateral triangleABC. If the perimeter of

triangleABCis 24, what is the perimeter of

quadrilateralAMNP ?

(A) 8 (B) 16 (C) 32 (D) 48 (E) 64

(11)

In the figure above, the hexagon with centre

P has six sides, each of length 6, and six

angles that each measure 120o. What is the

length of JK?

(A) 3 (B) 6 (C) 6(D) 6 (E) 12

(12) If the perimeter of a regula

six sides is 48. What is its area?

(A) 96 (B)384 (C) 288 (D) 108(E) 96

(13)

Note: Figure is not drawn to s

The figure above shows the leng

of an equiangular polygon. W

of the polygon.

Ans:

(14)

If the area of the square in the fi

and the perimeter of each of the 4

is 30. What is the perimeter of fi

outlined by dashed line?

(A) 36 (B) 72 (C) 80 (D) 84 (E) 120

J

K

P

6

120


31

31

(15)

Note: Figure is not drawn to scale

What is the perimeter of the figure?

Ans:

(16) Harry wants to put up fencing around

three sides of his rectangular yard and leave

a side of 20 feet unfenced. If the yard has an

area of 680 square feet, how many feet of

fencing does he need?

(A) 34 (B) 40 (C) 68 (D) 88 (E) 102

(17)

In the figure above, three squares and a

triangle have areas ofA,B,C, andX as shown.

IfA = 144,B=81,andC=225,thenX =

(A) 150 (B) 144 (C) 80 (D) 54 (E) 36

(18)

In the figure above,CE= 5,BD = 8, and the

area of quadrilateralABCDis 36. What is th

area ofABD?

(A)4 (B) 9 (C) 16 (D) 20 (E) 56

(19)

In the figure above, ifPQRSis a square an

QT = TR,which of the following stNOT true?

(A)PT = TS (B)x = y (C)u = v (D)r = y

(E) The area of PQTis equal to the are

SRT.

(20)

In the figure above, what is the vax ?

(A) 50 (B) 70 (C) 80 (D) 90 (E) 100

30 30

6 6

6


32

32

Exercise -15

(1) A light house emits a light which can be

seen for 60 miles in all directions. If the

intensity of the light is strengthened so that

its visibility is increased by 40 miles in all

directions, by approximately how many

square miles is its region of visibility

increased?

(A) 6300 (B) 10000 (C) 10300

(D) 20000 (E) 31400

(2)

The outline of a sign for an ice-cream store is

made by placingof the circumference of a

circle with radius 2 feet on top of an

isosceles triangle with height 5 feet, as

shown above. What is the perimeter, in feet,

of the sign?

(A) (B) (C) (D) 4 (E) 4

(3)

In the diagram above, if the circle with

centre A has an area of 32, what is the

area of the circle with centre B?

(A) 4(B) 6(C) 8 (D) 12(E) 16

(4)

In the figure above, circles A

tangent. The circumference of,

and the circumference of circ. If

point P(not shown ) lies on

point Q(not shown) lies on

the greatest possible distan

points P and Q?

(A) 5 (B) 5 (C) 10 (D) 5(E) 10

(5)

Square ABCD is inscribed in the

center O. if the area of the squ

what is the area of the circle?

(A) 6(B) 12(C) 18 (D) 27(E) 36

(6)

In the figure above, two circ

same area are inscribed rectan

the area of the rectangle is 32,

area of one of the circles?

(A) 4(B) 5(C) 6(D) 8 (E) 10

A

B

A B

A

D

B

C

A

B

D

C


33

33

(7)

IfA is the center of the circle shown above

andAB=BC=CD, what is the value ofx?

(A) 15 (B) 30 (C) 45 (D) 60 (E) 75

(8)

The figure above shows the shape of a

tunnel entrance. If the curved portion is

4

3

of a circle and the base of the entrance is 12

feet across, what is the perimeter, in feet, of

the curved portion of the entrance'?

(A) 9 (B)12 (C)(D)18 (E)

(9)

The figure above shows a cord around two

circular disks. If the radii of the two disks are

80 centimeters and 60 centimeters,

respectively, what is the total length, in

centimeters, of the cord?

(A) 210 (B) 210 + 280 (C) 280

(D) 280 + 80 (E) 280 + 280

(10)

The rectangular region above c

circles and a semicircle, each w

7. Ifis used as an approximatio

then the area of the shaded re

approximately

(A) 105 (B) 210 (C) 380 (D) 385 (E)

(11)

IfO is the center of the circle abo

length of arcRSPis twice the length o

PQR, thenx equals

(A) 60 (B) 100 (C) 120 (D) 150

(12)

The curve above consists

semicircles:AB, BC,andCD. The diameter o

ABis 2, the diameter ofBCis twice the diamet

ofAB,and the diameter ofCD is twice the

diameter ofBC.What is the total len

the curve?

(A) 2 (B) 4 (C) 6 (D) 7 (E) 8


34

34

(13)

Fig not drawn to scale.

The figure above shows a semicircle with

centerO and a quarter circle with centerR. If

OQ = 4 andQR= 6, what is the ratio of the

area of the shaded region to the area of the

semicircular region?

(A) 2:3 (B) 4:3 (C) 8:9 (D) 9:4 (E) 9:8

(14)

An equilateral triangle with perimeter p, a

square and a semicircle were joined to form

the figure shown above. What is the

perimeter of this figure?

(A) 3p (B) (C)

(D) (E)

(15) A line segment joining two points on the

circumference of a circle is 1 inch from the

centre of the circle at its closest point. If the

circle has a 2 inch radius, what is the length

of the line segment?

(A) 1 (B) (C) 2 (D) (E)

(16)

In the figure above, the circle w

and the circle with center C are

point D. If the circles each hav

and if lineis tangent to the cir

center A at point B, what is the va?

(A) 55 (B)60 (C) 63 (D) 65

(E) It cannot be determined

information given.

(17)

In the figure above, inscribed

equilateral. If the radius of th

then the length of arc AXB is

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

(18) Jane customized her bi

exchanging the front wheel fo

had one half the diameter of the b

Now when Jane rides the bicycle,

revolutions does the front

each revolution of the back whe

(A) 8 (B) 4 (C) 2 (D) (E)


35

35

(19)

In the figure above, o is the center of the

circle and triangle ABO is equilateral. If the

sides of triangle ABO are of length 6, what is

the length of BC?

(A) (B) (C) (D) (E) 12

(20)The radius of circle A is twice the radius

of circle B. if the sum of their circumferences

is 36, then what is the radius of circle A?

(A) 9 (B) 12 (C) 14 (D) 16 (E)18


36

36

Exercise -16

(1) For a rectangular box to be shipped by a

courier, the sum of the height of the box and

the perimeter of the base of the box must be

no more than 60 inches. If a box that is

shipped by this courier has height 4 inches

and length 16 inches, what is the maximum

possible width of the box inches?

(A) 4.5(B) 9 (C) 12 (D) 15 (E) 16

(2) A can of soup completely fills a cylinder 5

inches tall and 3 inches in diameter. If one

can of soup can be poured into a cylindrical

pot with diameter of 6 inches, to what

depth, in inches, will it fill the pot?

(A) 1.25(B) 2 (C) 2.5 (D) 5 (E) 10

(3)

The figure above is a rectangular solid. What

is the perimeter of triangle ABC.

(A) (B) (C) 6

(D) (E) 2

(4) Some clay is shaped into a sphere with

radius of 2 inches. If more clay is added to

the original sphere so that the radius is

increased by 4 inches, then the volume of

the new sphere is how many times greater

than the volume of the original sphere?

(A) 3 (B) 8 (C) 27 (D) 64 (E) 208

(5)

In the rectangular solid abov

and FC=12. What is the area of tri

Ans:

(6) If a cylindrical can with ra

and a volume of 30cubic feet is fill

half way with water, how high (i

the side of the can will the water r

(A) 15/4 (B) 5 (C) 15/2 (D) 19/2

(7) Milk is poured from a re

container with dimensions

inches by 9 inches into a

container with a diameter o

Assuming the milk does not ov

many inches high will the milk ra

(A)(B) 24 (C) (D) 10 (E)

(8) A right circular cylinder has

and a radius of 5. A rectangula

height of 15 and a square base is

the cylinder such that each of the

the solid is tangent to the cyl

Liquid is then poured into the c

that it reaches the rim. What is t

of the liquid?

(A) ( )(B) (

(C) ( )(D) (

(E) ( )

A

B

C

2

1

1

E

A B

C

F

H

D

G


37

37

(9) A rectangular box is 10 inches wide, 10

inches long, 5 inches high. What is the

greatest possible (straight line) distance, in

inches, between any two points on the box?

(A) 15 (B) 20 (C) 25 (D) 10

(E) 10

(10) The inside dimensions of a rectangular

wooden box are 6 inches by 8 inches by 10

inches. A cylindrical canister is to be placed

inside the box so that it stands upright when

the closed box rests on one of its six faces.

Of all such canisters that could be used,

what is the radius, in inches, of the one that

has maximum volume?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 8

(11) The bottom of an underground

rectangular tank has an area of 12 square

feet and the depth of the tank is 10 feet. A

liquid is pumped into the empty tank at the

constant rate of 30 cubic feet per minute.

After how many minutes will the depth of

the liquid in the tank be 8 feet?

(A) 1.5 (B) 2.0 (C) 2.5 (D) 3.2 (E) 4.0

(12) If cylinder P has a height twice that ofcylinder Q and a radius half that of cylinder

Q, what is the ratio between the volume of

cylinder P and cylinder Q?

(A) 1:8 (B) 1:4 (C) 1:2 (D) 1:1 (E) 2:1

(13) Some clay is shaped into a sphere with

radius of 2 inches. If more clay is added to

the original sphere so that the radius is

increased by 4 inches, then the value of the

new sphere is how many times greater thanthe volume of the original sphere?

(A) 3 (B) 8 (C) 27 (D) 64 (E) 208

(14) A rectangular fish tank 2

inches has water in it to a level

This water is carefully pour

cylindrical container with a

inches. How high will the water r

cylindrical container?

(A) 18 (B) (C) (D) (E)

(15) A rectangular box is 24 in

inches wide and 15 inches high.

smaller identical rectangula

stored perfectly in this larg

which of the following co

dimensions in inches of thes

(A) 2 by 5 by 6

(B) 3 by 4 by 6

(C) 3 by 5 by 6

(D) 4 by 5 by 6

(E) 5 by 6 by 12

(16) One of the faces of a rectan

a square of area 4. If the surface

solid 32, what is the volume of th

(A) 8 (B) 12 (C) 16 (D) 24 (E) 128

(17) How many cubical blocks

edges of length 4 are needed t

rectangular box that has insi

20 by 24 by 32?

(A) 38 (B) 96 (C) 192 (D) 240 (

(18) A right circular cylinder

and height 4 has volume V. in te

what is the volume of a right

cylinder with radius 5 and heigh

(A) V+4 (B) 2V (C) 4V (D) 6V


38/

38

(19) How much greater is the combined

surface area of two cylinders each with a

height of 4 cm and a radius of 2 cm than the

surface area of a single cylinder with a

height of 8 cm and a radius of 2 cm.

(A) 8 (B) 4 (C) 12 (D) 2 (E) 0

(20) The volume of right cylinder A is twice

the volume of right cylinder B. if the height

of cylinder B is twice the height of cylinder A,

then what Is the ratio of the radius of

cylinder A to the radius of cylinder B?

(A) 1:2 (B) 1:1 (C):1 (D) 2:1 (E) 4:1


39

39

Exercise -17

1) Which of the following lines is perpendicular

to and has the same

intercept as ?

(A) (B)

(C) (D)

(E)

2)

In the rectangular coordinate system above,

of the area of the right triangle ACB is 24,

what are the coordinates of point B ?

(A)(10,-2) (B) (10,2) (C) (8,-2) (D) (2,6)

(E) It cannot be determined from the

information given.

3) In thecoordinate system, if()and

( )

are two points on the line

with equation , then k= ?

(A) (B) 1 (C) 2 (D) (E) 4

4)

In the figure above, line RS passes through

origin. If the x-coordinate of point R is -6,

what is the y coordinate of R?

(A) -9 (B) -6 (C) -4 (D) -3 (E) -2

(5) In a coordinate plane, if p

D (-1,2) and E (x,y) lie on the li

the following could be the co

point E?

(A) (0,1) (B) (1,1) (C) (0,2) (

(6) In the rectangular coor

what is the area of a square with

(0,0), (-2,2) , (0,4), and (2,2

(A) 2 (B) 4 (C) 6 (D) 8 (E) 16

(7) Line L has a slope of -2 and c

point (4,-3), which of the poi

the line L?

(A) (2,1) (B) (3,0) (C) (3,1) (D

(8) The area of a circle whose c

(0,0) is 25. The circle passes thro

the following points EXCEPT?

(A) (-5,0) (B) (5,0) (C) (0,5) (

(9) Find the equation of a line p

2x + 5y = 7 and passing throu

midpoint of the line joining

(-4, 1).

(A) 5y+2x = 18 (B) 5y+2x = -22 (C) 2y+5

(D) 5y+2x=10 (E) 5y+2x=50

(10) The vertices of rectangle A

A(0,0) B(8,0) C(8,k) D(0,9). Valu

(A) 1 (B) 4 (C) 8 (D) 9 (E) 17

(11)

What is the area of the shaded reg

the figure above ?

(A) 72 (B) 57 (C) 55 (D)(E)

O

A(2,4)

C(2,-2)B

x

xO

R

S(9,6)


40

40

(12)

The circle with centerCshown above is

tangent to both axes. If the distance from

O toCis equal tok, what is the radius of

the circle, in terms ofk?

(A)k (B) (C)

(D) (E)

(13)

What are the coordinates of pointBin the

xy -plane above ?

(A) (6, 12) (B) (6, 28) (C) (8, 20)

(D) (12, 20) (E) (14, 28)

(14)

In the figure above, how many of the points

on line segmentPQ have coordinates that

are both integers?

(A) 5 (B) 8 (C) 10 (D) 11 (E) 20

(15)

In the rectangular coordina

if point (a, b), shown, and the two p

(4a, b) and (2a,2b), not shown,

connected by straight lines, t

the resulting triangular regioa

andb, would be

(A) (B)ab (C) (D) 2ab(E) 4ab

(16)

In the figure above,ABCEis a square. Wha

are the coordinates of pointB?

(A) (-4,2) (B) (-2,4) (C) (-

(D) (4, -6) (E) (6,-2)

(17) The vertices of triangle

(4,7) and (8,3). What is the area

ABC?

(A) 8 (B) (C) 4 (D) 16 (E) 12.5

(18) If A is point (-4, 1) and B is

What is the area of the circle thaa diameter?

(A) 3 (B)6 (C)9 (D) 12 (E) 3

(19) What is the area of the cir

centre is at the origin and

through point (3,-3)?

(A) 3 (B) 3(C) 9 (D) 18 (E) 36


41

41

Exercise -18

(1) If the range of the six measurements 140,

125, 180, 110, 165, andx is 80, which of

the following could be the value ofx?

(A) 60 (B) 85 (C) 190 (D) 220 (E) 245

(2) Which of the following sets of number has

the greatest standard deviation?

(A) 2, 3, 4 (B) 2.5, 3, 3.5 (C) 1, 1.25, 1.5

(D) 2, 0, 2 (E) 20, 21, 21.5

(3)

3, 7, 9, 14,x

The numbers in the list above are ordered

from least to greatest. If the average

(arithmetic mean) is 2 greater than themedian, what is the value ofx ?

(A) 22 (B) 20 (C) 17 (D) 16 (E) 15

(4) The Arithmetic mean and standard

deviation of a certain normal distribution are

13.5 and 1.5, respectively. What value is

exactly 2 standard deviations less than the

mean?

(A) 10.5 (B) 11.0 (C) 11.5 (D) 12.0 (E) 12.5

(5) If S={0, 4, 5, 2, 11, 8}, how much greaterthan the median of the number in S is the

mean of the number in S?

(A) 0.5 (B) 1.0 (C) 1.5 (D) 2.0 (E) 2.5

(6) List I: 3, 6, 8, 19

List II;, 3, 6, 8, 19

If the median of the numbers in list I above

is equal to the median of the numbers in list

II above, what is the value of ?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

(7) The mean of , 2, 6 and 10 is 8. What is

the median of, 2, 6 and 10.

(A) 4 (B) 6 (C) 7 (D) 8 (E) 9

(8) 2, 4, 6, 8,, 3, 5, 7, 9

In the list above, ifis an integer betw

and 10, inclusive, then the medi

(A) Either 4 or 5 (B) Either 5 or

(C) Either 6 or 7 (D) (E) 5.5

(9)

I 72, 73, 74, 75, 76

II 74, 74, 74, 74, 74

III 62, 74, 74, 74, 89

The data sets I, II, and III above

from greatest standard deviat

standard deviation in whi

following?

(A) I, II, III (B) I, III, II (C(D) III, I, II (E) III, II, I

(10) If a certain sample of data

of 20 and a standard deviation

the following values is mo

standard deviations from the m

(A) 12 (B) 13.5 (C) 17 (D) 23.5 (

(11) If is the average of first 10

multiples of 5 and ifis the median of

first 10 positive multiples of

value of ?

(A) -5 (B) 0 (C) 5 (D) 25 (E) 27.5

(12) 3,, 2, 8,, 3

The arithmetic mean of the list

above is 4. Ifand are integers a

, what is the median of the lis

(A) 2 (B) 2.5 (C) 3 (D) 3.5 (E) 4

(13) The average of seven inte

each of these integers is less t

what is the least possible value o

these integers?

(A) -113 (B) -77 (C) -37 (D) -22 (


42

42

(14)is a set containing 9 different

numbers.is a set containing 8 different

numbers, all of which are members of.

Which of the following statements CANNOT

be true?

(A) The mean ofis equal to the mean of

(B) The median ofis equal to the median

of

(C)The range ofis equal to the range of

(D) The mean ofis greater than the mean

of

(E) The range ofis less than the range of

(15) The following table shows the hourly

wages earned by the employees of Peri &

company and the number of employees who

earn each wage.

Wage per

hour

Number of

employees

$6 3

$8 5

$10 4

$13 4

What is the average of the median and the

mode of this set of data?

(A) 4.5 (B) 8 (C) 8.5 (D) 9 (E) 9.5

(16) The standard deviation on a test was 12

points, and the mean was 70. If student X

scored 95 points, then student X scored

higher than approximately what percent of

students?

(A) 2% (B) 13% (C) 48% (D) 96% (E) 98%

17) The average (arithmetic mean

of passengers on a subway car

number of passengers on a car

distribution with a standard d

approximately what percent of su

carry more than 80 passengers?

(A) 16% (B) 48% (C) 68% (D) 88% (E) 98%

(18) In both rural and urban ar

G, the average annual number o

taken by citizens is 8, and t

number of holidays follow

distribution. In rural areas

take more than 12 holidays per

urban areas, 2% of the citizen

than 16 holidays per year. Ho

greater is the standard deviatannual number of holidays ta

citizens than that of rural cit

(19) At Rock Town College, the 4

taking statistics received an a

76 on the final exam, and the sc

normal distribution. Studen

a score of 66 or lower on the e

the course and only 8 student

score of 96 or higher. How ma

students will fail the course?

(20) The fourth grade at Schoolx is made up

of 300 students who have a tota

21,600 pounds. If the weight of t

graders has a normal distribu

standard deviation equals 1

approximately what percentage

fourth graders weighs more

pounds?

(A) 12% (B) 16% (C) 36% (D) 48% (E


43

43

Exercise -19

(1) Four points lie on a circle. How many

different triangles can be drawn with 3 of

these points as vertices?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

(2) 1,2,6,7 and 9

A three digit integer is to be formed from

the digits listed above. If the first digit must

be odd, either the second or third digit must

be 2, and no digit may be repeated, how

many such integers are possible?

(A) 6 (B) 9 (C) 18 (D) 24 (E) 30

(3)In a group of 8 semifinalists, all but 2 will

advance to the final round. If in the final

round only the top 3 will be awarded

medals, then how many groups of medal

winners are possible?

(A) 20 (B) 56 (C) 120 (D) 560 (E) 720

(4) Eight Alaskan Huskies are split into pairs

to pull one of four sleds in a race. How many

different assignments of huskies to sleds are

possible?

(A) 32 (B) 64 (C) 420 (D) 1680 (E) 2520

(5) The cooperative board of a certain

residential building must consist of two men

and three women. If there are six men and

seven women who want to be on the

committee, how many different make ups of

the committee exist?

(A) 65 (B) 525 (C) 1050 (D) 1287 (E) 1080

(6) At a prestigious dog show, six dogs of

different breeds are to be displayed on six

adjacent podiums. If the Springer spaniel

breed must be displaced on the left mostpodium, how many display arrangements of

the six dogs are possible?

(A) 5 (B) 6 (C) 30 (D) 120 (E) 240

(7) Coach John is filling ou

up for his indoor soccer team

boys on the team, and he must a

starters to the following po

keeper, 2 on defense, 2 in midf

forward. Only 2 of the boys

goalkeeper, and they cannot pl

positions. The other boys can

of the other positions. How m

groupings are possible?

(A) 60 (B) 210 (C) 2580 (D)3360 (E

(8) Judges will select 5 finalis

contestants entered in

competition. The judges will t

contestants and award prize

highest ranked contestants: afirst place, a red ribbon for

and a yellow ribbon for thir

many different arrangement

winners are possible?

(A) 10 (B) 21 (C) 210 (D) 420 (E) 1

(9) How many 4 digit numbers beg

digit that is prime and end with a d

prime?

(A) 16 (B) 80 (C) 800 (D) 1440 (E) 1

(10) Of the 5 wires that lead

apartment, 2 are for cable telev

and 3 are for telephone servic

wires, how many distinct comb

wires are there such that at leas

wires is for cable television?

(A) 6 (B) 9 (C) 8 (D) 7 (E) 10

(11) A company that ships boxes

of 12 distribution centers us

to identify each centre. If ei

color or a pair of two diffe

chosen to represent each cent

center is uniquely represen

choice of one color or two c

minimum number of colors ne

coding? (Assume that the order

in a pair does not matter.)

(A)4 (B) 5 (C) 6 (D) 12 (E) 24


44

44

(12) A certain class has 6 girls and 5 boys.

Four of these students are to line up in the

front of the room, with two girls on either

end, and two boys in between. How many

such arrangements are possible?

(A) 20 (B) 200 (C) 462 (D) 600 (E) 900

(13) How many different positive three digit

integers begin with an odd digit and end

with an even digit?

(A)125 (B) 180 (C) 200 (D) 225 (E) 250

(14) A bakery offers three different sizes of

cakes, two different types of flavor, and

eight different choices for toppings. How

many different one topping cakes are there

to choose from?

(A) 13 (B) 16 (C) 24 (D) 48 (E) 60

(15) Six students -3 boys and 3 girls are to

sit side by side in a row for a make up

exam. In how many ways could they

arrange themselves given that no two

boys and no two girls can sit next to one

another?

(A) 12 (B) 36 (C) 72 (D) 240 (E) 720

(16) For an upcoming charity event, a

famous singer has agreed to sing 4 out of

6 old songs and 2 out of 5 new songs. In

hoe many ways can the singer make his

selection?

(A) 25 (B) 50 (C) 150 (D) 480 (E) 600

(17) To use certain cash machine, you need a

personal identification code(PIC). If each PIC

consists of two letters followed by one of

the digits from 1 to 9( such as AQ7 or BB3)

or one letter followed by two digits (such as

Q37 or J88), how many different PICs can be

assigned?

(A) 2106 (B) 6084 (C) 8190

(D) 12168 (E) none of these

(18) Mary has 4 paintings in the

She is going to bring up 2 of th

1 in her drawing room and

bedroom. In how many ways can

which painting go in each roo

(A) 4 (B) 6 (C) 12 (D) 16 (E) 24

(19) A cafeteria has a lunch speci

of soup or salad, a sandwich,

and a dessert. If the menu lists

salads, 8 sandwiches, and 7 des

many different lunches c

choose?(Note: Two lunches a

they in any aspect?)

(A) 22 (B) 280 (C) 336 (D) 560 (

(20) Dr. Peri works on the seco

building . There are 10 doors to

and 8 stair cases from the first t

floor. Dr. Peri decided that e

would enter by one door and

different one, and go up one s

down another. If Dr. Peri wor

year, for how many years can

without ever repeating the same p


45

45

Exercise -20

(1) An integer between 100 and 999,

inclusive is chosen at random. What is the

Probability that all the digits of the number

are odd?

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

(2) A jar contains 20 marbles, 4 red 6 white

and 10 blue. If you remove marbles one at a

time, randomly, what is the minimum

number that must be removed to be certain

that you have at least 2 marbles of each

color?

(A) 6 (B) 10 (C) 12 (D) 18 (E) 20

(3) A box contains 5 Red balls, 4 Black balls

and 7 White balls. What is the probability,that a ball drawn is either Red or Black.

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

(4) One bag contains 4Red balls and 5Black

balls and another bag contains 7Red and

2Black balls. 2balls are drawn one from each

bag. What is the probability that both are

black?

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

(5) From 25 tickets, marked with first 25

numerals one is drawn at random. Find the

chance that it is a multiple of 5 or 7

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

(6) A town has two doctors A and B

operating independently with probabilities

of 0.8 and 0.7 of their availability. What is

the probability that at least one doctor is

available if a patient needs medical

attention?

(A) 1 (B) 0.6 (C) 0.06 (D) 0.94 (E) 0.56

(7) What is the probability of getting six

on either the first or second toss of a

normal six sided die?

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

(8) In his wardrobe, Alfred

trousers, one of them is black

blue and the third is brown. In

he also has four shirts one o

and the other three are

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GRTC GRE Quant Material - Corrections in Progree