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) f

18 (B)

f2

(C) 3 fs (D)18 f (E) 18 fs

(2) If 'n' is an even integer and a multiple of 7, which of the following cannot be an Even Integer?

(A)n

14 (B)

n7

(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) ab (B) a+b (C) a−b

(D) a+b−1 (E) 2 (a+b )−1

(4) If d=a×b×c , 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<a<b<c. Which of the following could be a+b+c ?

(A) 4 (B) 5 (C) 11 (D) 13 (E) 16

(6) A number when divided by 510 gives a Remainder 102 what remainder will be obtained by dividing the same number by 17?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

(7) How many numbers between 1 and 200 are of the form 7n+5 where 'n' is a positive integer?

(A) 32 (B) 25 (C) 30 (D) 28 (E) 27

(8) How many times should the keys of type Writer be pressed in order to write first 300 counting numbers?

(A) 789 (B) 792 (C) 795 (D) 798 (E) 789

(9) Let P be a collection of consecutive positive integers. If the sum of all the numbers in p is 91, what is the largest number of positive integers in p?(A) 10 (B) 11 (C) 13 (D) 15 (E) 16

(10) If when a certain integer 'a' is divided by 5 the remainder is 2, then each of the following could also be an integer except(A) a/17 (B) a/11 (C) a/10 (D) a/6 (E)a/3

(11) How many integers between 100 and 150, inclusive can be evenly divided by neither 3 nor 5.(A) 33 (B) 28 (C) 27 (D) 26 (E) 29

(12) Which of the following could be the remainders when four consecutive positive integers are each divided by 3?

(A) 1,2,3,1 (B) 1,2,3,4 (C) 0,1,2,3(D) 0,1,2,0 (E) none

(13) A number 'a' when divided by 75 leaves a remainder 30. What will be the remainder if 5a is divided by 75?(A) 30 (B) 0 (C) 15 (D) 45 (E) 60

(14) If the product of the integers w ,x , y , and z is 770, and if 1<w<x< y<z, what is the value of w+z ?

(A) 10 (B) 13 (C)16 (D)18 (E)21

(15) On the number line, if r<s , if p is halfway between r and s, and if t is halfway

between p and r, then s−tt−r

=

(A) 14

(B) 13

(C) 43

(D) 3 (E) 4

1

(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) If p is an even integer and q is an odd integer, which of the following must be an odd integer?

(A) pq

(B) pq (C) 2 p+q

(D)2 (p+q ) (E)3 pq

(20) If positive integers x and y are not both odd, which of the following must be even?

(A) xy (B) x+ y (C) x− y (D) x+ y−1 (E) 2(x+ y)-1

2

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+a )c

(B) acb

(C) cab

(D) (c+a )b

(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) 0 (B) 1 (C) 2 (D) 3 (E) 4

(4) If the integer m is a multiple of both 10 and 12, then all of the following must be factors of m EXCEPT(A) 15 (B) 12 (C) 10 (D) 8 (E) 6

(5) If a ,b ,and c are positive integers such that a is divisible by b, and c is divisible by a, which of the following is NOT necessarily an integer?

(A) a+cb

(B) c−ab

(C) cab

(D) c+ba

(E) cba

(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 integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?

(I)ab+b2

(II)(a+b)2

(III) a+b

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

(8) Two positive integers are “compatible” if their greatest common factor is a prime number. For instance, 15 and 25 are compatible because their greatest common factor is 5, which is prime. If m and 98 are compatible, and m is an odd number, then what is the greatest common factor of mand 98? (A) 2 (B) 5 (C) 7 (D) 14 (E) 49

(9) Three different containers contain Petrol 420 gallons, 220 gallons and 620 gallons. Which of the following is the biggest measure that can measure all the different quantities exactly? (A) 10 (B) 20 (C) 30 (D) 40 (E) 80

(10) Chime A and Chime B ring simultaneously at Noon. Afterwards, chime A rings every 72 minutes and chime B rings every 54 minutes. What time is it when they 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 & 204 green marbles. He distributes them amongst a group of kids such that each kid gets equal number of marbles and no kid has marbles of more than one color. Find the number of kids?

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

(12) A computer is programmed to generate a list of multiples of Prime Numbers 2,3 and 5 as shown below Program I __ List of Multiples of 2 Program II____ List of Multiples of 3 Program III ___ List of Multiples of 5

3

How many integers between 1 and 100 will appear on all three of the lists of the programs produced above?

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

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) If n is a positive integer less than 200

and 14n60

is an integer, then n has how

many different positive prime factors?(A) 2 (B) 3 (C)5 (D)6 (E) 8

(17) Simplify 30-54+(7-3)2 8(A) 10 (B) 13 (C) 12 (D) 16 (E) none

(18) ( 15 )

2

- ( 15 )( 1

4 ) =

(A) - 1

20 (B) -

1100

(C) 1

100 (D)

120

(E) 15

(19) √ (16 ) (20 )+(8 )(32) =

(A)4√10 (B) 24 (C) 25 (D) 4√20 +8√2 (E)32

(20)

12+[( 2

3×3

8 )÷4]− 916

=

(A)

2916 (B)

1916 (C)

1516 (D)

913 (E) 0

4

Exercise -03

(1) Peter traveled 1317

miles by Taxi , 1713

miles by Bus and 14 miles by Train. In the

return journey he traveled 1117

miles by

Train, 1914

miles by Taxi and the rest of the

distance by Bus. How much distance did he travel by Bus in the return Journey?

(A) 12 14

(B) 14 112

(C) 13 112

(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 consisting of 36 students, some boys and some girls, exactly 1/3 of boys and 1/4 of girls walk to school. What is the greatest possible number of students in this class who walk to school?(A) 9 (B) 10 (C) 11 (D) 12 (E) 13

(8) During the four years that Mr. John owned his car, he found that his total car expenses were $18000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the remainder. The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total. If the only other expenses were taxes and license fees, then the cost of financing was how much more or less than the cost of taxes and license fees?

(A) $1,500 more (B) $1,200 more (C)$ 100 less (D) $ 300 less (E) $1,500 less

(9) In a nationwide poll, N people were interviewed. If 1/4 of them answered "yes" to question 1, and of those,1/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who DID NOT answer "yes" to both questions?

(A) N7

(B)6 N7

(C) 5N12

(D) 7N12

(E) 11N12

5

(10) A restaurant buys fruit in cans

containing 312

cups of fruit each. If the

restaurant uses 12

cup of the fruit in each

serving of its fruit compote, what is the least number of cans needed to prepare 60 servings of the compote.

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

(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) 34

(B) 56

(C) 1112

(D) 76

(E) 116

(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) 1

10 (B)

33100

(C) 25

(D) 12

(E) 35

(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) 1

625 (B)

256625

(C) 61

125 (D)

64125

(E) 369625

(14) Company Z spent 14

of its revenue last

year on marketing and 17

of 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) 5

14 (B)

12

(C) 1728

(D) 9

14 (E)

911

15) Which of the following fractions has the greatest value?

(A) 6

(22 ) ( 52 ) (B) 1

(23 ) (52 ) (C) 28

(22 ) ( 53 )

(D) 62

(23 ) (53 ) (E) 122

(24 ) (53 )

16) At a certain pizzeria, 18

of the pizzas sold

in one week were mushrooms and13

of the

remaining pizzas sold were pepperonis. If n of the pizzas sold were pepperoni, how many were mushroom?

(A) 3n8

(B) 3n7

(C) 7n16

(D) 7n8

(E) 3n

(17) of the final grades received by the

students in a certain math course, 15

are A’s,

14

are B’s, 12

are C’s, and the remaining 10

grades are D’s. What is the number of students in the course?

(A) 80 (B) 110 (C) 160 (D) 200 (E) 400

(18) If 12

of the air in a tank is removed with

each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 4 strokes?

6

(A) 1516

(B) 78

(C) 14

(D) 18

(E) 1

16

(19) Equal amounts of water were poured into two empty jars of different capacities,

which made one jar 14

full and the other jar

13

full. If the water in the jar with the lesser

capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water?

(A) 17

(B) 27

(C) 12

(D) 712

(E) 23

(20) In company X, no employee is both a technician and an Accountant. Also in

company X, 25

of the employees are

technicians and 5

16 of the remaining

employees are Accountants. What fraction of the total number of employees at company X are neither technicians nor Accountants.

(A) 2380

(B) 3380

(C) 37

(D)4780

(E) 5780

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 that three secretaries worked on a special project are in the ratio of 1 to 2 to 5 . If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project?

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

(8) In a certain class, the ratio of the number of mathematics majors to the number of students who are not mathematics majors is 2 to 5. If 2 more mathematics majors were to enter the class, the ratio would be 1 to 2. How many students are in the class?

7

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

(9) If ab=2

3 , which of the following is NOT

true

(A) a+bb

=53

(B) b

b−a=3 (C)

a−bb

=13

(D) 2a3b

=49

(E) a+3b

a=11

2

(10) In a certain company, the ratio of the number of managers to the number of production line workers is 5 to 72. If 8 additional production line workers were to be hired, the ratio of the number of managers to the number of production line workers would be 5 to 74.How many mangers does the company have?

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

(11) The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two quantities?

(A) 3 :4 (B) 8 : 9 (C) 18 : 19 (D) 23 : 24(E) It cannot be determined from the information given

(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 theshipment

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 shipments to 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 of m buses uses g gallons of gasoline every two days, how many gallons of gasoline will be used by 4 buses every 5 days?

(A) 10gm

(B) 10 gm (C) 10mg

(D) 20gm

(E)

5 g4m

(16) A machine can produce 50 computer chips in 2 hours. At this rate, how many computer chips can the machine produce in 7 hours.

8

(A) 175 (B) 200 (C) 225 (D) 250 (E) 275

(17) To make a purple dye, red dye and blue dye are mixed in a ratio of 3:4. To make a certain orange dye, red dye and yellow dye are mixed in a ratio of 3:2. If equal amounts of the purple and orange dye are mixed, what fraction of the new mixture is red dye?

(A) 9

20 (B)

12

(C) 1835

(D) 2740

(E) 3635

(18) If 4 cows produce 4 cans of milk in 4 days, how many days does it take eight cow to produce 8 cans of milk?(A) 1(B) 2 (C) 4 (D) 8 (E) 16

(19) In a class of 160 seniors, the ratio of boys to girls is 3 to 5. In the junior class, the ratio of boys to girls is 3 to 2. When the two classes are combined, the ratio of boys to girls is 1 to 1. How many students are in the junior class?

(A) 160 (B) 180 (C) 200 (D) 360 (E) 400

(20) If 1 pound of grain can feed 5 chickens or 2 pigs, then 10 pounds of grain can feed 20 chickens and how many pigs?

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

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 these four 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 observations was calculated as 40, it was found later that one of the observations was misread as 54 instead of 34, the correct mean is(A) 38 (B) 39 (C) 40 (D) 41 (E) 42

9

(9) A man purchased two varieties of wheat in equal weight, the prices of respective wheat are $12 per kg and $ 15 per kg, then the average price (in $) (per Kg)(A) 12.5 (B) 13 (C) 13.5 (D) 14 (E) 14.5

(10) The average of 5 numbers is 55 if each number is multiplied by 5, the average of the new set of numbers is(A) 55 (B) 60 (C) 80 (D) 225 (E) 275

(11) The average of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8 (B) 9.8 (C) 10.0 (D) 12.4 (E) 15.0

(12) If x books cost $5 each and y books cost $8 each, then the average cost, in dollars per book, is equal to

(A) 5x+8 yx+ y

(B) 5x+8 y

xy (C)

5x+8 y13

(D) 40 xyx+ y

(E) 40 xy

13

(13) If x+ y=8 z, then which of the following represents the average of x , y ,∧z ,in terms of z?

(A) 2 z+1 (B) 3 z (C) 5 z (D) z3

(E) 3 z2

(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 of x and y is 60 and the average of y and z is 80, what is the value of z−x?

(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 apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?

10

(A) 3x+2 y

5 (B)

3x+2 yx+ y

(C) 3x+2 y

xy

(D) 5 (3 x+2 y ) (E) 3 x+2 y

(20) The manager of a theater noted that for every 10 admission tickets sold, the theater sells 3 bags of popcorn at $2.25 each, 4 sodas at $1.50 each, and 2 candy bars at $ 1.00 each. To the nearest cent, what is the average amount of these snack sales per ticket sold?

(A) $1.18 (B) $1.48 (C) $1.60 (D)$1.64 (E) $1.7

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) 211723

(B) 221723

(C) 231723

(D)241723

(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 business in 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, 23

are non–technicians. If the non- technicians

staff were to be reduced by 14

, 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 marks

each. 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 specifies a 6 percent salary increase plus a $ 450 bonus for each

11

employee. For a certain employee this is equivalent to an 8 percent salary increase. What was this employee's salary before the new contract?

(A)$21500 (B)$22500 (C)$23500(D)$24300 (E)$25000

(8) If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20 (B) 24 (C) 36 (D) 40 (E) 44

(9) Tickets for all but 100 seats in a 10000seat stadium were sold. Of the tickets sold, 20 percent were sold at half price and the remaining tickets were sold at the full price of $2? What was the total revenue (in $) from the tickets sales?(A) 15840 (B) 17820 (C) 18000 (D) 19800 (E) 21780

(10) In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

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

(11) Of the 3600 employees of company X, 13

are clerical. If the clerical staff were to be

reduced by 13

, what percent of the total

number of the remaining employees would then be the clerical?

(A) 25 (B) 22.2 (C) 20 (D) 12.5 (E) 11.1

(12) In country x a 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) 3313

% (E) 5813

%

(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

12

(17) Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

(A) 60 (B) 80 (C) 100 (D) 120 (E) 140

(18) The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance?

(A) 45% (B) 56%(C) 64%(D) 75% (E) 80%

(19) A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee’s total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

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

(D) 50% (E) 75%

(20) Of the researchers in a workgroup, 40 percent will be assigned to team A and the remaining 60 percent to team B. However, 70 percent of the researchers prefer team A and 30 percent prefer tem B. what is the least possible number of researchers who will NOT be assigned to the team they prefer?(A) 15 (B) 17 (C) 20 (D) 25 (E) 30

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. If the 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

13

(8) At a selling price of $920, a car yields a 20% Profit on the cost. What selling price will yield a 5% profit on the cost?

(A) $805 (B) $815 (C) $825 (D) $845 (E) $865

(9) A bookseller bought 200 books at $ 25 each and spent $ 0.25 for binding each of them. He then sells the books at $ 30 each. Find his gain percent? (A) 15 (B) 16 (C) 19 (D) 21 (E) 25

(10) A man sells an article at a loss of 10%, had he sold it for $20 more, he would have gained 10%. Find Cost Price of the article.(A) $50 (B) $100 (C) $200 (D) $400 (E) $600

(11) An article is offered $ 800 and a customer pays $ 576 for it, after a series of two discounts. If the rate of the first discount is 20%, find the second discount.(%) (A) 5 (B) 8 (C) 10 (D) 12 (E) 20

(12) A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount (A) $5.6 (B) $7.2 (C) $8.8 (D) $9.6 (E) $15.2

(13) During a floral shop sale, for every 5 roses purchased, one rose is free of charge. If the cost of one rose is $1.20, how much money is saved by buying 2 dozen roses Ans:

(14) A sports jacket marked $48 is offered at a discount of 25 percent during a sale. At this reduced price the dealer makes a profit of 20 percent on the cost. The cost to the dealer is (A) 29 (B) 30(C) 32 (D) 36 (E) 40

(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 of q dollars. If each battery was sold at 50 percent above the original cost battery, then, in terms of q, for how many dollars was each battery sold?

(A) 3 q200

(B) 3q2

(C) 150q (D) q

100 +50

(E) 150q

(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

14

(19) Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.30?(A) 426 (B) 430 (C) 443 (D) 460 (E) 486

(20) A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the

shipment arrived, 23

of the heads were sold,

each at 25 percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for on the day before. What was the gross profit on this shipment?

(A) $100 (B) $115 (C)$125(D)$130 (E) $135

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 print 1000 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) 1

25 (B)

225

(C)3

25 (D)

425

(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 3rd tap 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) 8

15 (B)

34

(C) 54

(D) 158

(E) 83

15

(7) Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts.

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

(8) 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) 11/30 (B) 9/20 (C) 3/5 (D) 11/15(E) 5/6

(9) Machine A produces 100 parts, twice as fast as machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does machine A produce in 6 minutes.

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

(10) Machines 'A' and 'B 'always operate independently and at their respective constant rates. When working alone machine 'A' can fill a production lot in 5 hours, and machine 'B' can fill the same in 'x’ hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of 'x'

(A) 313

(B) 3 (C) 212

(D) 213

(E)112

(11) Working alone printers X,Y, and Z can do a certain printing job in 12,15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the Job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates.

(A) 411

(B) 12

(C) 1522

(D) 2215

(E) 114

(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) 1130

(B)9

20 (C)

35

(D) 1115

(E) 56

(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) 335

(B) 4 (C) 514

(D) 712

(E) 15

(15) A cistern has two pipes, pipe A and pipe B. 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

16

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 57

(B) 12 57

(C) 14 (D) 14 57

(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 reaches the 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 65 miles 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

17

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 simultaneously

from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate, completed the 100 mile trip in 5 hours ; train Y travelling at a constant rate, completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y?

(A) 37.5 (B) 40.0(C) 60.0 (D) 62.5 (E) 77.5

(8) A Car travels at an average speed of 10mph through Urban area in 0.8 hours,50 mph through Suburban area in3 hours, and 70 mph through rural areas in 6.2 hours, What is the Car’s average speed for the entire trip?

(A) 52.2 (B) 56.2 (C) 59.2 (D) 60 (E) 62.2

(9) Thirty minutes after Peter started walking from A to B distance of 14 miles, Paul started walking from along the same road from B to A. if Peter’s walking speed was 4 miles per hour and Paul’s was 2 miles per hour, how many miles had Paul walked when they met

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

(10) Two trains start from two stations ‘x’ and ‘y’ with speeds 60 miles per hour and 40 miles per hour in the opposite direction at 11 a.m. Find at what time they will meet each other, if the distance between the two stations is 350 miles?

(A) 2:30p.m. (B) 3: 30 p.m. (C) 3 p.m. (D) 2 p.m. (E) None

(11) Two motorcyclists do the same Journey by traveling at 40 miles per hour and 50 miles per hour respectively. Find the distance traveled when one of them takes one hour longer than the other?

(A) 200(B) 300 (C) 400 (D) 600 (E) 2000

(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

212

hours later. The second flight leaves

airport B every 20 minutes, beginning at

8:00a.m and arrives at airport C 116

hours

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

18

(16) A train travels from New York city to Chicago a distance of 840 miles, at an average rate of 60 mph and arrives in Chicago at 6:00 in the evening, Chicago Time. At what hour in the morning, New York city time did the Train depart for Chicago?(Note : Chicago time is 1 Hour earlier than New York city time)

(A) 4:00 (B) 5:00 (C) 6:00 (D) 7:00 (E) 8:00

(17) During a car trip Maria stopped to rest after she traveled half of the total distance to her destination. She stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination and then she drove the remaining 120 miles to her destination. What was the Total distance in miles from Maria's starting point to her Destination?

(A) 280 (B) 320 (C) 360 (D) 420 (E) 480

(18) One hour after Yolanda started walking from X to Y, a distance of 45miles; Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles had Bob walked when they met?

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

(19) A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed in miles per hour, for the round trip?

(A) 32.0 (B) 33.0(C) 34.3(D) 35.5(E) 36.5

(20) Starting at town S, Fred rode his bicycle 8 miles due east, 3 miles due south, 2 miles due west, and 11 miles due north, finally stopping at town T. if the entire region is flat, what is the straight line distance, in miles, between town S and T?

(A) 10 (B) 8√2 (C) √157 (D) 14 (E) 24

Exercise -10

(1) If 4x2 -12x +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 odd integers where y>x which of the following is equal to y2 −x2

(A) 2x (B) 4x (C) 2x+2 (D) 2x+4 (E) 4x+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+2b

) = 0 and b≠ 3, then b =

(A) -8 (B) -2 (C) −12

(D) 12

(E) 2

(5) If 4−x2+x

= x, what is the value of

x2+3x−4

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

(6) If x= -1, then x4−x3+x2

x−1 =

(A) - 32

(B) – 12

(C) 0 (D) 12

(E) 32

(7) If the quotient ab

is positive, which of the

following must be true?

(A) a>0 (B) b>0 (C) ab>0 (D) a−b>0 (E) a+b>0

(8) If 3x=2 and

y4=3 then

3+ yx+4

=¿

19

(A) 109

(B) 32

(C) 2011

(D) 3011

(E) 5

(9) If 1.5

0.2+x = 5, then x =

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

(10) If x = 1-3t and y = 2t -1, then for what value of t does x= y?

(A) 52

(B) 32

(C) 23

(D) 25

(E) 0

(11) If x is an integer and y=3 x+2, which of the following CANNOT be a divisor of y?

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

(12) If 12+ 1

3+ 1

4=13

x, which of the following

must be an integer?

I.x8

II.x

12

III.x

24

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

(13) If 2x+5=4y and 3x+2=27x− y then what is the value of x.

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

14) If 82 x+3=23 x+6 then x=¿

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

(15) If 0.0015×10 m = 5×107 then m-k = 0.03×10k

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

(16) 292+2929

=

(A) 870 (B) 841 (C) 58 (D) 31 (E) 30

(17) If 13x +

16x +

19x =33 , then what is

the value of x.

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

(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 then x miles from home, what is the range of possible values for ?

(A) 2≤ x≤10 (B) 4 ≤x ≤10 (C) 4 ≤x ≤12(D) 4 ≤x ≤16 (E) 6≤ x≤16

(19) If x2 -9 0 which of the following is true?

(a) x -3 (b) x 3 (c) x 9 (d) x -3 or x 3 (e) -3x x 3

(20) How many integers n are there such that 1<5n+5<25(A) Five (B)Four (C) Three (D) Two (E) One

20

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

21

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 competition, the total Weight of Joe’s two lifts was 750 pounds. If twice the weight of his first lift was300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift.(A) 225 (B) 275 (C) 325 (D) 350 (E) 400

(7) Which of the following has a root in common with x2−6 x+5=0?

(A) x2+1=0 (B) x2−x−2=0(C)x2−10 x−5=0(D) 2 x2−2=0(E) x2−2 x−3=0

(8) Elena purchase brandx pens for $4 a piece and brand y for $2.80 a piece. If Elena purchased a total of 12 of these pens for $42, how many brand x pens did she purchase?

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

(9) Marion rented a car for $18.00 plus $0.10 per mile driven. Craig rented a car for $25.00 plus $0.05 per mile driven. If each drove d miles and each was charged exactly the same amount for the rental, then d equals

(A) 100 (B ) 125 (C) 135 (D) 140 (E ) 150

(10) Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Sam and Tina are all alive 4 years from today, which of the following must be true on that day?

I Rose is twice as old as Sam

II Sam is 3 years younger than Tina.

III Rose is older than Tina.

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

(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 lives x floors 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, then x equals

(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?

22

(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 number n of calculators sold per week varies with the price p in dollars according to the equation n=300−20 p, what would be the total weekly revenue from the sale of $10 calculators?(A) $100 (B) $300 (C) $1000 (D) $2800 (E) $3000

(17) An optometrist charges $150 per pair for soft contact lenses and $85 per pair of hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1690, what was the total number of pairs of contact lenses that she sold.

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

(18) The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

(A) x6

(B) x

10 (C)

x16

(D) 3x40

(E) 3x80

(19) If Sam were twice as old he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

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

(20) The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?

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

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)

If ∠XYZ in the figure above is a right angle, what is the value of x?

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

(3)

Note: Figure not drawn to scale.

23

m

n

Y

X

Z

qp

l

150 (4a+2)b

m

n

c d

be

a

In the figure above, the value of y 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 line m is parallel to line k and s = t + 30 then, what is the value of t. (A) 30 (B) 60 (C) 75 (D) 80 (E) 105

(6)

In the figure above, what is the average of

a ,b , c , and d?

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

(7)

In the figure above, what is the value of ? (A) 30 (B) 80 (C) 100 (D) 130 (E) 160

(8)

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?

24

ba

cd40

m

n

l

y

z x

m

n

l

xmy

z

q

R

Qx

15

(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 is the value of y+z?

(A) 80 (B)120 (C) 160 (D) 180 (E)220

(12)

In the figure above l is parallel to m. If x=50, what is the value of z+q?

(A) 25 (B)50 (C) 100 (D) 125 (E)130

(13)

In the figure above line m is parallel to line n, find the value of a+b?

(A) 160 (B)180 (C) 195 (D) 200 (E)can’t say

(14) Lines mand n are parallel. If line m and n are cut by three different transversals, what is the least number of points of intersection that can occur among the five lines

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

(15)

110

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, lines r and s are drawn such that r is parallel to s. If third line t is drawn such that t is perpendicular to s, and a fourth line u is drawn such that u ‖t , which of the following statements must be true?

(I) t⊥r

(II) s⊥u

(III) r ‖u25

m

n95105

a b

S

P

C

A D

B

E30X

B6 mile

6 mile

A

Y

X Z

e

b

bb

c d

a

(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 y?

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

(19)

In the figure above, l is parallel to m and m is parallel to n then what is the value of a+2c+d?

(A) 180 (B) 270 (C) 360 (D) 450(E) can’t be determined.

(20)

Three lines intersect in a point as shown in the figure above. Which of the following pairs of angle measures is NOT sufficient for determining all six angle measures?

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

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

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

26

C D2mile

y

2 x

x 30

l

m

n

d

cb

a

t xy

sr z

A

B

C

2105

R

Q

S

Q

80

R

S

105

30

B

A D C

2630

4a 5a

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) √3 (B) 2 (C) 1+ √2 (D) 1+√3 (E) 2+√3

(4)

In triangle PQR below, angle RPQ is greater than angle RQP, and the bisector of angle P and angle Q meet in S. which of the following must be true?

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

(D) SQ ≥ SP (E) Can’t say

(5) Peter lives 12 miles west of his school and Bill lives north of the school. Peter finds that the direct distance from his house to Bill’s is 6 miles shorter than the distance by way of school. How many miles north of the school does Bill live?

(A) 6 (B) 9 (C) 10 (D)6√2 (E) 6√3

(6)

In triangle PQR, QS and SR are angle bisectors and the measure of angle p is 80o. How many degrees are there in angle QSR?

(A) 115 (B) 120 (C) 125 (D)130 (E) 135

(7) A ladder is placed against a building such that the top of the ladder forms an angle of 30o with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?

(A) 5 (B) 10 (C) 15 (D) 20√2 (E) 20√3

(8) If an equilateral triangle with sides x has the same perimeter as another triangle with sides 6, 8 and x, what is the value of x?

(9)

What is the area of the triangle in the figure above?(A) 2+2√3 (B) 4√3 (C) 8 (D) 8√3 (E) 12

(10)

What is the length of BC in the figure above?

27

P

P

2√2

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

(11)

In ΔPQS above, if PQ =3 and PS = 4, then find the value of PR?

(A) 94

(B) 125

(C) 16

5 (D) 15

4 (E) 20

3

(12)

If each side of ΔACD above has length 3 and if AB has length 1, what is the area of region BCDE?

(A) 9

4 (B) 7

4√3

(C) 9

4√3

(D) 72√3 (E) 6+√3

(13)

In △ABC above, what is x in terms of z ?

(A) z + 73 (B) z – 73 (C) 70 – z (D) z – 70 (E) 73 – z

(14)

In the figure above, if AB is parallel to CE, and CE = DE, and y = 45, then what is the value of x?

(A) 45 (B) 60 (C) 67.5 (D) 112.5 (E) 135

(15)

The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?(A) 24 (B) 30 (C) 48 (D) 60 (E) 96

(16)

In the figure above, M, N, and P are midpoints of the sides of an equilateral triangle whose perimeter is 18. What is the perimeter of the triangular region MNP?

28

C

B

(A) 2 (B) 3(C) 412

(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 triangle whose perimeter is 36 and whose sides are x, x+3, and x+6?

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

(19) The three sides of a triangle have lengths of 9, 16 and k. which of the following could equal K?(Indicate that all apply)

(I) 6(II) 16

(III) 25

(20) If the hypotenuse of isosceles right triangle ABC is 6√2, then what is the area of triangle ABC?

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

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√5 (C) 5√3 (D) 10 (E) 15

29

P

D

A

w

140

R

Q

35 40

(4) A diagonal of a rectangle forms an angle of measure 60o 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) 2√2 (B) 2√3 (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 figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?

(A) 9√2 (B) 32

(C) 9

√2 (D) 9

2 (E) none

(7)

In the figure above, the two square regions have areas 16 and 25, respectively. What is the area of the shaded triangular region? (A) 6 (B) 8 (C) 9 (D) 12 (E) 15

(8)

In the figure above, the areas of square regions X and Y are 1 and 4, respectively. What is the area of the triangular region?

(A) 2 (B) 1 (C) 34

(D) 12

(E) 14

(9)

What is the value of h in the trapezoid above?

(A) 6√2 (B) 4 √3 (C) 8 (D) 6 (E) 4

(10)

30

In the figure above, M, N, and P are the midpoints on the respective sides of equilateral triangle ABC. If the perimeter of triangle ABC is 24, what is the perimeter of quadrilateral AMNP?

(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√3 (B) 6 (C) 6√2 (D) 6√3 (E) 12

(12) If the perimeter of a regular polygon of six sides is 48. What is its area?

(A) 96√3 (B)384 (C) 288 (D) 108√3 (E) 96

(13)

Note: Figure is not drawn to scale

The figure above shows the lengths of sides of an equiangular polygon. What is the area of the polygon.

Ans:

(14)

If the area of the square in the figure is 81 and the perimeter of each of the 4 triangles is 30. What is the perimeter of figure outlined by dashed line?

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

(15)

Note: Figure is not drawn to scale

What is the perimeter of the figure?

Ans:

31

J

K

P ®

6

120

1

1

30 30

6 6

6

(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 of A, B, C, and X as shown. If A = 144, B=81, and C=225, then X =

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

(18)

In the figure above, CE = 5, BD = 8, and the area of quadrilateral ABCD is 36. What is the

area of △ABD ?(A) 4 (B) 9 (C) 16 (D) 20 (E) 56

(19)

In the figure above, if PQRS is a square and QT = TR, which of the following statements is NOT true? (A) PT = TS (B) x = y (C) u = v (D) r = y

(E) The area of ΔPQT is equal to the area of ΔSRT.

(20)

In the figure above, what is the value of x ? (A) 50 (B) 70 (C) 80 (D) 90 (E) 100

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)

32

AB••

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

made by placing 34

of 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) 3 Π+3√3 (B) 3 Π+6√3 (C) 3 Π+2√33(D) 4Π+3√3 (E) 4Π+6√3

(3)

In the diagram above, if the circle with centre A has an area of 32𝜫, what is the area of the circle with centre B?(A) 4𝜫 (B) 6𝜫 (C) 8𝜫 (D) 12𝜫 (E) 16𝜫(4)

In the figure above, circles A and B are tangent. The circumference of circle A is 6𝜫, and the circumference of circle B is

4𝜫. If point P(not shown ) lies on the circle A and point Q(not shown) lies on circle B, what is the greatest possible distance between points P and Q?

(A) 5 (B) 5√2 (C) 10 (D) 5𝜫 (E) 10𝜫(5)

Square ABCD is inscribed in the circle with center O. if the area of the square is 36, what is the area of the circle?

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

In the figure above, two circles with the same area are inscribed rectangle ABCD. If the area of the rectangle is 32, what is the area of one of the circles?

(A) 4𝜫 (B) 5𝜫 (C) 6𝜫 (D) 8𝜫 (E) 10𝜫 (7)

33

A B• •

A

D

B

C

A

B

D

C

y

y+4

If A is the center of the circle shown above and AB=BC=CD, what is the value of x?

(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

34

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) 9π (B) 12π (C) 9 π √2

(D)18π (E) 9π

√2

(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) 210π (B) 210π+ 280 (C) 280π (D) 280π + 80 (E) 280π+ 280

(10)

The rectangular region above contains two circles and a semicircle, each with a radius of

7. If 227

is used as an approximation for π,

then the area of the shaded region is approximately(A) 105 (B) 210 (C) 380 (D) 385 (E) 405

(11)

If O is the center of the circle above and the length of arc RSP is twice the length of arc PQR, then x equals(A) 60 (B) 100 (C) 120 (D) 150 (E) 240

(12)

The curve above consists of three semicircles: AB, BC, and CD. The diameter of AB is 2, the diameter of BC is twice the diameter of AB, and the diameter of CD is twice the diameter of BC. What is the total length of the curve?

(A) 2π (B) 4π (C) 6π (D) 7π (E) 8π

(13)

Fig not drawn to scale.

34

The figure above shows a semicircle with center O and a quarter circle with center R. If OQ = 4 and QR = 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) p2+πp (C) 7 p+ π

2p

(D) 73p+ π

3p (E)

43p+ π

6p

(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) √3 (C) 2 (D) 2√2 (E) 2√3

(16)

In the figure above, the circle with center A and the circle with center C are tangent at point D. If the circles each have radius 10, and if line l is tangent to the circle with center A at point B, what is the value of x?

(A) 55 (B)60 (C) 63 (D) 65 (E) It cannot be determined from the information given.

(17)

In the figure above, inscribed triangle ABC is equilateral. If the radius of the circle is r, then the length of arc AXB is

(A) 2πr

3 (B)

4 πr3

(C) 3πr

2 (D) π r2

3 ( E)

2π r2

3

(18) Jane customized her bicycle by exchanging the front wheel for a wheel that had one half the diameter of the back wheel. Now when Jane rides the bicycle, how many revolutions does the front wheel make for each revolution of the back wheel?

35

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

(E) 14

(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) 3√3 (B) 4 √3 (C) 6√3 (D) 9 (E) 12

(20)The radius of circle A is twice the radius of circle B. if the sum of their circumferences is 36𝜫, then what is the radius of circle A?

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

36

A

B

C

21

1

A B

C

F

H

D

G

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) 1+√5 (B) 1+2√5 (C) 6

(D) 1+√5+√6 (E) 2√5+6

(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 above, AB = 3, BC =4, and FC=12. What is the area of triangle ACF?

Ans:

(6) If a cylindrical can with radius of 2 feet and a volume of 30𝜫 cubic feet is filled up half way with water, how high (in feet) up the side of the can will the water reach

(A) 15/4 (B) 5 (C) 15/2 (D) 19/2 (E) 10

(7) Milk is poured from a rectangular container with dimensions 4 inches by 10 inches by 9 inches into a cylindrical container with a diameter of 6 inches. Assuming the milk does not overflow, how many inches high will the milk raise?

(A) 60∏

(B) 24 (C) 40∏

(D) 10 (E) 3∏

(8) A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base is placed in the cylinder such that each of the corners of the solid is tangent to the cylinders walls. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?(A) 500(Π−3) (B) 500(Π−2.5)

37

E

(C) 500(Π−2) (D) 500(Π−1.5)

(E) 500(Π−1)

(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√2 (E) 10√3

(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 of cylinder 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 than the volume of the original sphere?(A) 3 (B) 8 (C) 27 (D) 64 (E) 208

(14) A rectangular fish tank 25 inches by 9 inches has water in it to a level of 2 inches. This water is carefully poured into a cylindrical container with a diameter of 10 inches. How high will the water reach in the cylindrical container?

(A) 18 ∏ (B) ∏18

(C) 18∏

(D) 9

2∏ (E)

9∏2

(15) A rectangular box is 24 inches long, 10 inches wide and 15 inches high. If exactly 60 smaller identical rectangular boxes can be stored perfectly in this larger box, then which of the following could be the dimensions in inches of these smaller boxes?

(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 rectangular solid is a square of area 4. If the surface area of the solid 32, what is the volume of the solid?

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

(17) How many cubical blocks, each with edges of length 4 are needed to fill a rectangular box that has inside dimensions 20 by 24 by 32?

(A) 38 (B) 96 (C) 192 (D) 240 (E) 384

(18) A right circular cylinder with radius 5 and height 4 has volume V. in terms of V, what is the volume of a right circular cylinder with radius 5 and height 8?

(A) V+4 (B) 2V (C) 4V (D) 6V (E) 8V

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) √2 :1 (D) 2:1 (E) 4:1

39

O

O O

A(2,4)

C(2,-2) B

Exercise -17

1) Which of the following lines is perpendicular to y=−2x+3 and has the same y intercept as y=2x−3?

(A) y=−12

x+3 (B) y=12x−3

(C)y=12x+3 (D) y=2x+3

(E) y=2x−3

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 the xy coordinate system, if (m ,n ) and (m+2 , n+k ) are two points on the line with equation x=2 y+5, then k= ?

(A) 12

(B) 1 (C) 2 (D)52

(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 points C (2,5) D (-1,2) and E (x,y) lie on the line l, which of the following could be the coordinates of point E?

(A) (0,1) (B) (1,1) (C) (0,2) (D) (1,3) (E) (1,4)

(6) In the rectangular coordinate system, what is the area of a square with vertices (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 contains the point (4,-3), which of the points is also on the line L?

(A) (2,1) (B) (3,0) (C) (3,1) (D) (4,8) (E) (6,2)

(8) The area of a circle whose centre is at (0,0) is 25𝜫. The circle passes through all of the following points EXCEPT?

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

(9) Find the equation of a line parallel to 2x + 5y = 7 and passing through the midpoint of the line joining points (2, 7) and (-4, 1).

(A) 5y+2x = 18 (B) 5y+2x = -22 (C) 2y+5x = 13

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

(10) The vertices of rectangle ABCD are A(0,0) B(8,0) C(8,k) D(0,9). Value of k is?(A) 1 (B) 4 (C) 8 (D) 9 (E) 17

(11)

40

x

xO

R•

•S(9,6)

What is the area of the shaded region in the figure above ?

(A) 72 (B) 57 (C) 55 (D) 5412

(E)4912

(12)

The circle with center C shown above is tangent to both axes. If the distance from O to C is equal to k, what is the radius of the circle, in terms of k ?

(A) k (B) k

√2 (C)

k

√3 (D)

k2

(E) k3

(13)

What are the coordinates of point B in 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 segment PQ have coordinates that are both integers? (A) 5 (B) 8 (C) 10 (D) 11 (E) 20

(15)

In the rectangular coordinate system above, if point (a, b), shown, and the two points (4a, b) and (2a, 2b), not shown, were connected by straight lines, then the area of the resulting triangular region, in terms of a and b, would be

(A) ab2

(B) ab (C) 3ab2

(D) 2ab (E) 4ab

(16)

In the figure above, ABCE is a square. What

are the coordinates of point B?(A) (-4,2) (B) (-2,4) (C) (-2,6)(D) (4, -6) (E) (6,-2)

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(17) The vertices of triangle ABC are (4,3) (4,7) and (8,3). What is the area of triangle ABC?

(A) 8 (B) 4 √3 (C) 4 (D) 16 (E) 12.5

(18) If A is point (-4, 1) and B is point (2, 1). What is the area of the circle that has AB as a diameter? (A) 3∏ (B)6∏ (C)9∏ (D) 12∏ (E) 36∏

(19) What is the area of the circle whose centre is at the origin and that passes through point (3,-3)?(A) 3√2 𝜫 (B) 3𝜫 (C) 9𝜫 (D) 18𝜫 (E) 36𝜫

Exercise -18

(1) If the range of the six measurements 140, 125, 180, 110, 165, and x is 80, which of the following could be the value of x? (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 the median, what is the value of x?

(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 greater than 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; x, 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 ofx?

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

(7) The mean ofx, 2, 6 and 10 is 8. What is the median of x, 2, 6 and 10.

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

(8) 2, 4, 6, 8, n, 3, 5, 7, 9 In the list above, if n is an integer between 1 and 10, inclusive, then the median must be

(A) Either 4 or 5 (B) Either 5 or 6(C) Either 6 or 7 (D) n (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 are ordered from greatest standard deviation to least standard deviation in which of the following?(A) I, II, III (B) I, III, II (C) II, III, I(D) III, I, II (E) III, II, I

(10) If a certain sample of data has a mean of 20 and a standard deviation of 3, which of the following values is more than 2.5 standard deviations from the mean?(A) 12 (B) 13.5 (C) 17 (D) 23.5 (E) 26.5

(11) If m is the average of first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M−m ?

42

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

(12) 3, k , 2, 8, m, 3

The arithmetic mean of the list of numbers above is 4. If k and m are integers and k ≠m, what is the median of the list?

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

(13) The average of seven integers is 11. If each of these integers is less than 20, then what is the least possible value of any one of these integers?(A) -113 (B) -77 (C) -37 (D) -22 (E) 0

(14) S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

(A) The mean of S is equal to the mean of T(B) The median of S is equal to the median of T

(C)The range of S is equal to the range of T (D) The mean of S is greater than the mean of T

(E) The range of S is less than the range of T

(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) number of passengers on a subway car is 60. If the number of passengers on a car has a normal distribution with a standard deviation of 20, approximately what percent of subway cars carry more than 80 passengers?(A) 16% (B) 48% (C) 68% (D) 88% (E) 98%

(18) In both rural and urban areas of country G, the average annual number of holidays taken by citizens is 8, and the annual number of holidays follows a normal distribution. In rural areas, 2% of the citizens take more than 12 holidays per year. In urban areas, 2% of the citizens take more than 16 holidays per year. How much greater is the standard deviation of the annual number of holidays taken by urban citizens than that of rural citizens?

(19) At Rock Town College, the 400 students taking statistics received an average score of 76 on the final exam, and the scores had a normal distribution. Students who received a score of 66 or lower on the exam will fail the course and only 8 students earned a score of

43

96 or higher. How many of the students will fail the course?

(20) The fourth grade at School x is made up of 300 students who have a total weight of 21,600 pounds. If the weight of these fourth graders has a normal distribution and the standard deviation equals 12 pounds, approximately what percentage of the fourth graders weighs more than 84 pounds? (A) 12% (B) 16% (C) 36% (D) 48% (E) 60%

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 most podium, 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 out the starting line up for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goal keeper, 2 on defense, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?(A) 60 (B) 210 (C) 2580 (D)3360 (E) 151200

(8) Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?(A) 10 (B) 21 (C) 210 (D) 420 (E) 1260

(9) How many 4 digit numbers begin with a digit that is prime and end with a digit that is prime?(A) 16 (B) 80 (C) 800 (D) 1440 (E) 1600

44

(10) Of the 5 wires that lead into a apartment, 2 are for cable television service and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?(A) 6 (B) 9 (C) 8 (D) 7 (E) 10

(11) A company that ships boxes to a total of 12 distribution centers uses color coding to identify each centre. If either a single color or a pair of two different colors is chosen to represent each centre and if each center is uniquely represented by that choice of one color or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)(A)4 (B) 5 (C) 6 (D) 12 (E) 24

(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 basement. She is going to bring up 2 of them and hang 1 in her drawing room and 1 in her bedroom. In how many ways can she choose which painting go in each room?

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

(19) A cafeteria has a lunch special consisting of soup or salad, a sandwich, coffee or tea, and a dessert. If the menu lists 3 soups, 2 salads, 8 sandwiches, and 7 desserts, how many different lunches can you choose?(Note: Two lunches are different if they in any aspect?)

(A) 22 (B) 280 (C) 336 (D) 560 (E) 672

(20) Dr. Peri works on the second floor of a building . There are 10 doors to the building and 8 stair cases from the first to the second floor. Dr. Peri decided that each day he would enter by one door and leave by a different one, and go up one stair case and

45

A

B

C

D

E

F

down another. If Dr. Peri works 240 days a year, for how many years can he work without ever repeating the same path?

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) 1

900 (B)

536

(C)5

90 (D)

1125

(E) 12

(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) 9

16 (B)

45

(C) 14

(D)5

16 (E)

716

(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)79

(B) 1081

(C) 9

10 (D)

45

(E) 29

(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) 1724

(B) 8

25 (C)

57

(D) 27

(E) 5

25

(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) 1

36 (B)

118

(C)16

(D)1136

(E)13

(8) In his wardrobe, Alfred has three trousers, one of them is black, the second is blue and the third is brown. In his wardrobe, he also has four shirts one of them is black and the other three are white. He opens his wardrobe in the dark and picks out one shirt trouser pair without seeing the color. What is the likelihood that neither the shirt nor the trouser is black?

(A) 1217

(B)89

(C) 12

(D) 34

(E) 14

(9)

The fig. Shows the top view of an open

46

square box that is divided into six compartments with walls of equal height. Each of the rectangles D,E and F has twice the area of each of the equal squares A,B and C when a marble is dropped into the box at random, it falls into one of the compartments. What is the probability that it will fall into compartment F?

(A) 29

(B) 79

(C) 23

(D) 16

(E) 34

(10) A list of numbers consist of 'p' positive and 'n' negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5, what is the value of n/p?

(A) 25

(B) 15

(C) 23

(D) 35

(E)45

(11) There are eight job applicants sitting in a waiting room – 4 women and 4 men. If two of the applicants are selected at random, what is the probability that both will be women?

(A)12

(B) 37

(C) 14

(D)3

14 (E)

110

(12) Each person in room A is a student and 16

of the students in room A are seniors.

Each person in room B is a student and 57

of

the students in room B are seniors. If 1 student is chosen at random from room A, and 1 student is chosen at random from room B, what is the probability that exactly 1 of the students chosen is a senior?

(A) 5

42 (B)

3784

(C) 9

14 (D)

1621

(E) 3742

(13) A computer wholesaler sells eight different computers and each is priced differently. If the wholesaler chooses

three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?

(A)1556

(B) 3

28 (C)

128

(D)1

56 (E)

1168

(14) There are 5 marbles in a bag- 2 orange and 3 blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?

(A) 7

10 (B)

35

(C) 25

(D)3

10 (E)

110

(15) A student is to take her final exams in two subjects. The probability that she will pass the first subject is ¾ and the probability that she will pass the second subject is 2/3. What is the probability that she will pass one exam or the other exam?

(A) 512

(B) 12

(C) 712

(D) 5

17 (E)

1112

(16) A student is to take her final exams in three subjects. The probability that she will pass the first subject is ¾, the probability that she will pass the second subject is 2/3, and the probability that she will pass the third subject is ½ . What is the probability that she will pass at least one of these three exams?

(A)14

(B) 1124

(C) 1724

(D)34

(E)2324

47

17) What is the probability of tossing a coin five times and having heads appear at most three times?

(A)1

16 (B)

516

(C)1316

(D)25

(E) 2732

(18) A bag contains 4 red hammers, 10 blue and 6 yellow hammers. If three hammers are removed at random and no hammer is returned to the bag after removal, what is the probability that all three hammers will be blue?

(A)12

(B) 18

(C) 3

20 (D)

219

(E) 38

(19)A jar contains a number of jelly beans of which 58 are red, 78 are green and the rest are blue. If the probability of choosing a blue jelly bean from this jar at

random is 15

, how many blue jelly beans

are in the Jar?(A) 34 (B) 56 (C) 78 (D) 102 (E)152

(20) A bag contains only red marbles, blue marbles and yellow marbles. The probability of randomly selecting a red marble from this

bag is 14

, and the probability of randomly

selecting a blue marble is 16

. Which of the

following could be the total number of marbles in the bag?(Indicate all that apply)

(A) 10 (B) 12 (C) 18 (D) 24 (E) 36

Exercise -21To count how many quantities are there between two given quantities, follow these rules:

(i) If exactly one of the end quantity is included, subtract the end quantities.(ii) If both the end quantities are included, subtract the end quantities and add 1

(iii) If neither end quantity is included, subtract the end quantities and subtract 1.

(1) John started solving questions 6-20 in his Math’s paper at 1:13 hrs and finished by 1:43 hrs. At this rate, how long will it take him to complete questions between29-75?

(A) 90 min (B) 60 min (D) 45 min (D) 30 min

(2) Given an integer C, how many integers are greater than C and less than 2C?

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

(3) In a painting competition there are 35 participants. They use blue or green or both colors. If 26 participants use blue color and 19 participants use both colors. Find the number of participants who use the green color. (A) 28 (B) 18 (C) 38 (D) 16 (E) 0

(4) In a college team, there are 29 Athletes, 20 are field event athletes while 15 are track event athletes. Find the number of athletes in both the events. (A) 14 (B) 6 (C) 9 (D) 20 (E) 5

(5) In a group of 50 students, 25 play hockey, 30-play Football and 8 play neither game. Find the number of students who play both Hockey and Football. (A) 12 (B) 13 (C) 17 (D) 25 (E) 30

(6) Out of 50 students in a school, 15 students study English, 12 study Spanish, 8 study French, 7 study English and Spanish, 4 study English and French, 6 study Spanish and French, 3 students in all the three.

(a) How many study only English(b) Exactly in two Languages.(c) In more then one Language.

48

(A) 7,8,11 (B) 15,8,11 (C) 7,11,3(D) 15,17,3 (E) none

(7) In an examination 65% of the candidates passed in math, 30 % in science and 20% failed in both subjects. The pass percentage is (A) 10 (B) 15 (C) 20 (D) 25 (E) 30

(8) In an examination, 45 % of the students failed in math’s , 35 % of the students failed in science and 20% failed in both the subjects, the pass % is(A) 10 (B) 20 (C) 30 (D) 40 (E) 50

(9) If 75 % of all Americans own an automobile, 15% of all Americans own a bicycle and 20% of all Americans own neither an automobile nor a bicycle, what percent of Americans own both an automobile and a bicycle.(A) 0 (B) 1.33 (C) 3.75 (D) 5 (E) 10

(10) Of the 500 delegates attending a convention, 200 are Republicans and the rest are Democrats. One hundred of the delegates are vegetarians and, of those who are not vegetarians, 270 are Democrats. How many of the vegetarian delegates are Republicans?

(A) 30 (B) 40 (C) 50 (D) 60 (E) 70

(11) At a certain high school, 30 students study French, 40 study Spanish and 25 study neither. If there are 80 students in the school, how many study both French and Spanish?

(12) A certain company employs 25 women and 25 men. Some employees drive to work and the rest take public transportation. If 29 employees drive to work and exactly 6 men take public transportation, how many women drive to work?

(A) 6 (B) 8 (C) 10 (D) 11 (E) 13

(13) Of 30 applicants for a job, 14 had at least 4 years experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least 4 years experience and a degree?

(A) 14 (B) 13 (C) 9 (D) 7 (E) 5

(14) A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6.00 the time lapse between the beginning of the stroke and the end of the last stroke is 22 seconds. At 12.00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

(A) 72 (B) 50 (C) 48 (D) 46 (E) 44

(15) Of the 65 cars on a car lot, 45 have air conditioning, 30 have power windows, and 12 have both air conditioning and power windows. How many of the cars on the lot have neither air conditioning nor power windows? (A) 2 (B) 8 (C) 10 (D) 15 (E) 18

49

(16) If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?(A) 10% (B)20% (C)30%(D) 50% (E) 65%

(17) Every sophomore at hill side high school is required to study at least one language among Spanish, French and Latin, but no one may study more than 2. if 120 sophomores study Spanish, 80 study French, 75 study Latin and 50 study two of the three languages, how many sophomores are there at Hill side high school?

(A) 75 (B) 125 (C) 225 (D) 275 (E)325

(18) The Business News daily has 25 reporters covering Asia, 20 covering Europe and 20 covering America. 4 reporters cover Asia and Europe, but not America, 6 reporters cover Asia and America, but not Europe, and 7 reporters cover Europe and America, but not Asia. If The Business News daily has 38 reporters in total covering at least one of the three continents: Asia, Europe and America then how many reporters cover all of the 3 continents?

(A) 5 (B) 10 (C)11 (D) 15(E)cannot be determined

50