Mathematical Aptitude Test

1. One hundred Students took math and physics tests. 25 students got scores higher than or equal to 80 for both tests. 42 students’ math score was higher than or equal to 80. The numbers of the students whose scores of both tests were less than 80 is 48. Let x and y be the numbers of the students with only math score higher than or equal to 80, and with physics score higher than or equal to 80, respectively. What are x and y?

(A) x = 17, y = 35 (B) x = 10, y = 17 (C) x = 10, y = 23 (D) x = 23, y = 10 (E) x = 35, y = 17

2. Three lottery winners, X, Y, and Z share the lottery jackpot. X’s share equals to 1/5 of Y’s share, and also equals to 1/7 of Z’s share. If the total jackpot is 195,000 Rs., What is the amount of Z’s share?

(A) 15,000 Rs. (B) 35,000 Rs.

(C) 75,000 Rs. (D)105,000 Rs.

(E) 115,000 Rs.

3. A farmer uses 140 meter fencing to enclose a rectangular field. The ratio of the two different sides is 3:4. What is the distance between the two corners diagonally apart from each other?

(A) 40m (B) 253m (C) 45m (D) 50m (E)(653)/2 cm

4. Two types of notebooks are sold. The price of type A is 12 Rs. and that of type B is 15 Rs. for each. John bought 10 notebooks in mixture of both types, and paid 126 Rs.. How many notebooks of type A did he buy?

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

5. If -1 <>

(A) X square (B)X cube (C) 1 (D) -x (E)1/x

6. Suppose x^2 – y^2 = 155 ( x square minus y square is equal to 155) and x - y = 5. What is the value of x + y?

(A) 15 (B) 31 (C) 35 (D) 100 (E) 150

7. One printer prints a sheet in 0.5 seconds, and the other does it in 0.75 seconds. If we use both printers simultaneously, what is the minimum time to print 200 sheets?

(A) 40 sec. (B) 45 sec. (C) 50 sec. (D) 55 sec. (E) 60 sec

8. Let series an =n^2 – 2n (n = 0, 1, 2,   ). What is the value of (a100 - a99 - a98 + a97)?

(A) 2 (B) 4 (C) 10 (D) 40 (E) 400

9. How many 3-digit positive odd integers that do not contain 5 in any places exist?

(A) 256 (B) 288 (C) 320 (D) 324 (E) 360

10. Darsh and Tathya independently try to decode a coded message. The probabilities that Darsh and Tathya are successfull are 0.8 and 0.7, respectively. What is the probability that at least one of them decodes the message?

(A) 0.10 (B) 0.47

(C) 0.56 (D) 0.80 (E) 0.94

11. When throwing two fair dice, what is the probability that the sum of their numbers is equal to or greater then 11?

(A) 1/18 (B) 1/12

(C) 1/8 (D) 1/6

(E) 1/3

12. Let gcd(m, n) be the greatest common divisor of integers m and n. Which of the following is the largest?

(A) gcd(14, 144) (B) gcd(24, 144) (C) gcd(49, 144) (D) gcd(70, 144) (E) gcd(91, 144)

13. The price of a Seiko watch is 1/3 the price of Omega watch. The shop sold 45 Seiko watches and 60 Omega watches, and the total receipt is 90,000 Rs. What is the price of one Omega watch?

(A) 1200 Rs (B) 1500 Rs(C) 1850 Rs(D) 2000 Rs (E) 2200 Rs

14. There is a circular railroad track for miniature train models. The space between the two rails is

3cm. How much longer is the outer rail than the inner rail?

(A) 2p cm (B) 3p cm (C) 4p cm (D) 6p cm (E) 8p cm

15. Let S = {a, b, c, d, e}. What is the number of subsets with two elements of set S?

(A) 4 (B) 8 (C) 10 (D) 16 (E) 20

16. Let f(x) = x^2 - 1. Which of the following satisfies equation f(f(x)) = 0?

(A) 1 (B) 2 (C) 2 (D) 3 (E) 3

For suggestions or queries contact alpesh.bhalala@gmail.com

Answers

1. B

2. D

3. D

4. D

5. B

6. B

7. E

8. B

9. B

10. E

11. B

12. B

13. A

14. D

15. C

16. B

{2006/11/15}

Mathematical Aptitude Test

1. A recipe serves 4 people and calls for 1.5 cups of milk. If you want to serve 6 people, how much milk do you need?

a) 7/3 cups b) cups c) 2.25 cups d) 2.75 cups

2. Tony's car used 19.5 liters of gasoline on a 318 kilometers trip. How many kilometers per liter did the car get?

a) 6.2 km/h b) 13.6 km/h c) 16.3 km/h d) 14.8 km/h

3. Find the best price of a brand from following

Brand 1: 36 grams for 10.8 Rs

Brand 2 : 42 grams for 13.44 Rs.

a) Brand 2 b) Brand 1

c) Both are equal values

d) Not enough information provided

4. Anil gets 13776 Rs per week at a shop when he works for 28 hours. What is his per hour rate ?

a) 482 b) 490 c) 491 d) 492

5. If @ is defined for all positive numbers a and b by a @ b = 2ab - b2, then 5 @ 2 =

a) 8 b) 12 c) 16 d) 20

6. What is the total amount of your purchases if you bought 5 shirts at m and 2 more shirts at 50% off.

a) 5m b) 6m c) 7.5m d) 10m

7. Which of the following proportions is correct if 12 = pq ?

a) 2:p = 6:q b) 4:p = 3:q c) 6:p = 2:q d) 4:q = p:3

8. A car travels across Ahmedabad m miles at the rate of t miles per hour. How many hours does the trip take?

a) m / t b) t / m. c) m – t d) t – m

9. What is the value of (x + y)(x + y) if xy = -3 and x2 + y2 = 10?

a) 1 b) 2 c) 3 d) 4

10. Telephone calls cost 0.20 Rs. per minute for the first 15 minutes and 0.10 Rs. per minute thereafter. Which of the following represents the amount of money needed (in rupee) to talk x minutes (x greater than 15)?

a) $3.00 + $0.10x

b) $3.00 + $0.10(x-15)

c) $3.00 + $0.10(15-x)

d) $3.00 + $0.15x

11. Which of the following numbers is divisible by 3 and 5, but not by 2?

a) 975 b) 955 c) 990 d) 995

12. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

a) 1/8 b) 2/9 c) 2/7 d) 3/8

13. If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?

a) k+5 b) k+20 c) k+30 d) k+45

14. A rectangular rug has an area of 84 square feet and a length of 14 feet. What is its width?

a) 70 feet b) 6 feet c) 28 feet d) 176 feet

15. 12 people enter a room. Two more than two-thirds of these people then leave. How many people remain in the room?

a) 2 b) 1 c) 3 d) 4

You can reach to the author at alpesh.bhalala@gmail.com for your queries or suggestions

Answers

1. c

2. c

3. b

4. d

5. c

6. b

7. d

8. a

9. d

10. b

11. a

12. d

13. c

14. b

15. a

{2006/10/11}

Mathematical Aptitude Test

Mathematics Test

1. The L.C.M. (Lowest (or Least) Common Multiple) of two numbers is 45 times to their H.C.F (Highest Common Factor). If one of the numbers is 125 and sum of L.C.M. and H.C.F. is 1150, the other number is:

a) 215 b) 220

c) 225 d) 235

2. Six bells commence tolling together and toll at intervals 2,4,6,8,10 and 12 seconds respectively. In 30 minutes how many times they toll together.

a) 4 b) 10

c) 15 d) 16

3. The value of (0.625 * 0.0729 * 28.9)/(0.0017 * 0.025 * 8.1) is

a) 0.3825 b) 3.825

c) 38.25 d) 3825

4. The number of coins 1.5 cm in diameter and 0.2cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is:

a) 380 b) 450

c) 472 d) 540

5. The size of a wooden block is 5 * 10 * 20 cm3. How many whole such blocks you will take to construct a solid wooden cube of minimum size?

a) 6 b) 8

c) 12 d) 16

6. Find the odd man out - 1050, 510, 242, 106, 46, 16, 3

a) 510 b) 242

c) 106 d) 46

7. If x and y are the two digits f the number 653xy such that this number is divisible by 80, then x+y is equal to:

a) 2 b) 3

c) 4 d) 6

8. If 1.5x=0.04y then the value of (y-x)/(y+x) is

a) 730/77 b) 73/77

c) 7.3/77 d) None

9. The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class?

a) 1:2 b) 3:4

c) 3:5 d) None of these

10. If one-seventh of a number exceeds its eleventh part by 100 then the number is…

a) 770

b) 1100

c) 1825

d) 1925

11. The ratio of Darsh's age to her mother's age is 3:8. The difference of their ages is 35 years. The ratio of their ages after 4 years will be:

a) 7:12 b) 5:12

c) 38:43 d) 42:47

12. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

a) 1:1 b) 2:3

c) 1:2 d) 3:2

Answer

1. c Let L.C.M. be l and H.C.F. be h. Then l = 45h

l + h =1150

This gives h =25 and l = 1125

Thus the second number = (25 * 1125)/125 = 225

2. d Solution: L.C.M. of 2,4,6,8,10,12 = 120

So they toll together after every 120 seconds i.e. 2 minutes. So in 30 minutes they toll together 30/2 + 1 = 16 times

3. d Solution: The sum of decimal places in numerator and denominator being the same, decimal point can be removed

(625*729*289) / (17*25*81) = 3825

4. b Solution: Volume of 1 coin = 22/7 *(1.5)/2*(1.5)/2 * 0.2 = 99/280 cm3

Volume of large cylinder = 22/7 *(4.5)/2*(4.5)/2 * 10 = (99*45)/28cm3

Number of coins = (99*45)/28 * 280/99 = 450

5. b Solution: Size of each cube = 5 cm

So number of blocks = (5 * 10 * 20)/(5*5*5) = 8

6. c Solution:

2nd term = (Ist term - 30) / 2 = (1050-30)/2 = 510

3rd term = (2nd term - 26) / 2 = (510-26)/2 = 242

4th term = (3rd term - 22) / 2 = (242-22)/2 = 110

So 106 is the answer.

7. a Solution:

Since 653xy is divisible by 2 as well as by 5, so y = 0

Now 653x0 is divisible by 8 so 3x0 is also divisible by 8.

By hit and trial x=2 and x+y = 2

8. b Solution: x/y = 0.04/1.5 = 2/75

So (y-x)/(y+x) = (1 - x/y)/(1 + x/y) = (1 - 2/75)/ (1 + 2/75) = 73/77

9. d Solution:

Let the ratio be k:1.

Then k*16.4+1*15.4 + (k+1)*15.8 (16.4-15.8)k = 15.8 - 15.4 k=0.4/0.6 = 2/3 so required ratio = 2:3

10. d Solution:

Let the number be x. Then X/7 - x/11 =100 11x-7x = 7700 x=1925.

11. b Solution:

Let their ages be 3x and 8x

8x - 3x =35

x =7

Their present ages are 21 and 56 years.

Ratio of their ages after 4 years are 25:6 = 5:12

12. d Solution:

Let 1gm of gold be mixed with x gm of copper to give (1+x)gm of the alloy.

1G=19W, 1C = 9W and alloy = 15W 1gm gold + xgm Copper = (1+x)gm alloy 19W+9Wx = (1+x)*15W x = 4W/6W = 2/3

So ratio of gold and copper is 1:2/3 or 3:2

{2006/08/09}

Mathematical Aptitude Test

1. If a ladder touches a 15 ft high pole on top. The bottom part of the ladder is 8 ft away from the bottom of the pole. What is the height of the ladder .

A. 4.8 ft. B. 7 ft.

C. 17 ft. D. 23 ft.

2. Mr. Darsh purchased 20 concert tickets for a total of Rs. 225. The concert tickets cost Rs. 15 for adults and Rs. 10 for children under 12. How many tickets for children under 12 did Mr. Darsh purchase?

A. 5 B. 9

C. 15 D. 18

3. The force needed to stretch a spring is directly proportional to the amount the spring is to be stretched. If a force of 100 kg stretches a certain spring 8 inches, how much force is needed to stretch the spring 12 inches?

A. 25 kg

B. 50 kg

C. 100 kg

D. 150 kg

4. What is the measure angle B in the triangle ABC? Where angle A measures 56 degree, and sides AB and BC are equal.

A. 340

B. 560

C. 620

D. 680

5. A right circular cylindrical can is 6 inches high, and the area of its top is square inches. What is the minimum number of square inches of construction paper it would take to cover the lateral surface of this can?

A. 72 sq. in.

B. 72 sq. in.

C. 432 sq. in.

D. 432p sq. in.

6. Kavya noticed that many of the students at her school had red hair. She randomly chose 25 of the students in her school and found that 2 of them had red hair. If Kavya’s sample is representative, which of the following is closest to the number of the 2200 students at her school who have red hair?

A. 44

B. 88

C. 176

D. 200

7. Krisha and her family visit her grandparents once a month. Krisha recorded the driving time to her grandparents’ house for 6 trips in the chart below. Based on the data in the chart, what is the mean driving time to Krisha’s grandparents’ house?

Driving Times

Month Time

January 3 hours, 23 minutes

February 3 hours, 5 minutes

March 3 hours, 50 minutes

April 3 hours, 52 minutes

May 3 hours, 15 minutes

June 3 hours, 35 minutes

A. 3 hours, 23 minutes

B. 3 hours, 26 minutes

C. 3 hours, 30 minutes

D. 3 hours, 35 minutes

8. Two rectangles, ABCD and WXYZ, are as described. The measure of each side of WXYZ is 5 times the measure of each corresponding side of ABCD. Which statement is true of the areas of these two rectangles?

A. The area of WXYZ is 5 times the area of ABCD.

B. The area of WXYZ is 10 times the area of ABCD.

C. The area of WXYZ is 20 times the area of ABCD.

D. The area of WXYZ is 25 times the area of ABCD.

9. A group of 36 people from the Gova Recreation Center plans to purchase tickets for a cruise to Maldives. The standard fare for an individual ticket is shown below.

The group is informed that, because of the size of the group, the standard fare will be reduced by 30%. With the discount of 30%, how much does each member of the Nantucket Recreation Center have to pay for a cruise ticket?

Cruise Price : Individual Ticket costs Rs 12000

A. Rs 3600

B. Rs 4320

C. Rs 7680

D. Rs 8400

10. Which of the following is equivalent to the expression below?

(4)(-x)(-y)

A. 4xy

B. -4xy

C. (-4)(x)(y)

D. (-4)(-x)(-y)

Answers:

1. C

2. C

3. D

4. D

5. B

6. C

7. C

8. D

9. D

10. A

{5th March 2008 }

Mathematical Aptitude Test

1. A vehicle rents for Rs. 220 per week plus Rs. 0.25 per mile. Find the rental cost for a 2-week trip of 500 miles for a family of 5.

A. Rs. 345.00 B. Rs. 565.00 C. Rs. 2200.00 D. Rs. 2825.00

2. Find the greatest common factor of 42 and 70.

A. 2 B. 4 C. 7 D. 14

3. Simplify:

8 - 4 ÷ 2 - 10 ÷ 2

A. 4 B. 1 C. - 3 D. - 4

4. Darsh wants to paint the walls and ceiling in a room that is 14 feet x 16 feet with an 8-foothigh

ceiling. He will not paint the double door, which has a measurement of 6 feet x 7 feet.

One gallon of paint will cover 350 square feet. The paint is sold in gallon containers only. How many gallons of paint will he need to buy?

A. 2 gallons B. 3 gallons C. 4 gallons D. 5 gallons 5. On a map, the distance between two cities is 8.5 inches. If ½ inch represents 25 miles, how

far, in miles, is it between the two cities (to the nearest mile)?

A. 106 miles B. 213 miles C. 425 miles D. 850 miles 6. Ansh wants to buy a carpet that is 12 feet x 15 feet. The cost of the carpet, including installation, is Rs. 29.90 per square yard. Without including tax, how much does Ansh have to

spend to carpet his room?

A. Rs. 598.00

B. Rs. 807.30

C. Rs. 1614.60 D. Rs. 5322.00

7. A radio station is going to construct a 12-foot tower for a new antenna on top of a tall

building. The tower will be supported by three cables, each attached to the top of the tower

and to points on the roof of the building which are 5 feet from the base of the tower. What is the total length of these three cables?

A. 13 feet B. 39 feet C. 42 feet D. 51 feet

8. Find the missing number in the following sequence.

2, ___, 18, - 54, 162

A. 6 B. 3 C. -3 D. -6

9. Kinetic Energy (KE) is calculated by the formula KE = ½ mv(square) where m is mass and v is

velocity. Translate the expression ½ mv(square) into words.

A. half the product of m times v times v

B. the quantity of half the mass times velocity, all squared

C. half the square root of mass times velocity

D. half the square of the quantity of mass times velocity

10. Solve for x : 3(x + 4) = 6

A. - 2 B. 2/3 C. 10/3 D. 6

11. Determine which of the ordered pairs listed below satisfies the given system.

x + 2y = 3

2x + y = 6

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

12. Given below are students' scores on an essay (possible score range is from 0 to 10). What is the median of the set of scores?

Student Essay Score

A 8

B 5

C 4

D 2

E 4

F 1

G 7

H 8

A. 3 B. 4.5 C. 4.9 D. 5

13. Given a bag of 20 marbles containing 8 green, 4 red, 2 blue, and 6 yellow, if a person picks

out a single marble from the bag without looking, what is the probability that it will be a red marble?

A. 1/20 B. 1/10 C. 1/5 D. 14

14. A man has a choice of a white, yellow, or blue shirt. He also may select a red tie or a green tie.

How many different outfits can he make of 1 shirt and 1 tie?

A. 5 B. 6 C. 8 D. 9

Answers:

1. C

2. B

3. C

4. D

5. D

6. B

7. C

8. A

9. D

10. A

11. A

12. C

13. C

14. D

October 31, 2007

Jai Sardar !