### Quantitative Section : GMAT Sample Problem Solving Ability

**Directions: ** Solve each gmat sample quantitative ability problem and indicate the best of the answer choices given..

**Numbers:** All numbers used are real numbers.

**Figures: **A figure accompanying a gmat sample quantitatove ability problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie on a plane unless otherwise indicated.

Following are some gmat sample quantitative ability questions.

1. A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square then its area changes by :

1. 4

2. 144

3. 12

4. 2

5. None of the above.

Ans : A

2. A motorcycle stunts man belonging to a fair, rides over the vertical walls of a circular well at an average speed of 54 kph for 5 minutes. If the radius of the well is 5 meters then the distance traveled is:

1. 2.5 kms

2. 3.5 kms

3. 4.5 kms

4. 5.5 kms

5. None of the above

Ans : C

3. If 1 cm on a map corresponds to an actual distance of 40 kms. And the distance on the map between Bombay and Calcutta is 37.5 cms., the actual distance between them is :

1. 375 kms

2. 3750 kms

3. 1500 kms

4. 1375 kms

5. None of the above

Ans : C

4. A box contains 90 mts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is :

1. 10 kg

2. 10.5 kg

3. 11 kg

4. 11.5 kg

5. None of the above

Ans : D

5. If the radius of a circle is increased by 20% then the area is increased by :

1. 44%

2. 120%

3. 144%

4. 40%

5. None of the above

Ans : A

6. Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $409. They got a bill for $104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is

1. 120

2. 200

3. 60

4. 24

5. 36

Ans : E

7. A plot of land is in the shape of a trapezium whose dimensions are given in the figure below :

Hence the perimeter of the field is

1. 50 m

2. 64 m

3. 72 m

4. 84 m

5. None of the above

Ans : c

8. Four concentric ( having the same center ) circles with radii, x, 2x, 3x and 4x are drawn to form two rings A and B as shown in the figure.

Ratio of the area of inner ring A to the area of outer ring B is

1. 1 : 2

2. 1 : 4

3. 2 : 3

4. 3 : 7

5. None of the above

Ans : D

9. If 3/p = 6 and 3/q = 15 then p – q = ?

1. 1/3

2. 2/5

3. 3/10

4. 5/6

5. None of the above

Ans : C

10. A father is three times as old as his son. After fifteen years the father will be twice as old as his son’s age at that time. Hence the father’s present age is

1. 36

2. 42

3. 45

4. 48

5. None of the above

Ans : C

* (1/4) 3 + (3/4) 3 + 3(1/4)(3/4)(1/4 + 3/4) =?

1. 1/64

2. 27/64

3. 49/64

4. 0

5. 1

Ans : E

* If the area of two circles are in the ratio 169 : 196 then the ratio of their radii is

1. 10 : 11

2. 11 : 12

3. 12 : 13

4. 13 : 14

5. None of the above

Ans : D

* A semi-circle is surmounted on the side of a square. The ratio of the area of the semi-circle to the area of the square is

1. 1 : 2

2. 2 : p

3. p : 8

4. 8 : p

5. None of the above

Ans : C

* Which of the following is the greatest ?

1. 40% of 30

2. 3/5 of 25

3. 6.5% of 200

4. Five more than the square of 3

5. 1/2 -4

Ans : E

* Two identical taps fill 2/5 of a tank in 20 minutes. When one of the taps goes dry in how many minutes will the remaining one tap fill the rest of the tank ?

1. 5 minutes

2. 10 minutes

3. 15 minutes

4. 20 minutes

5. None of the above

Ans : C

* If the value of XYZ Company stock drops from $25 per share to $21 per share, what is the percent of the decrease?

1. 4

2. 8

3. 12

4. 16

5. 20

Ans : D

* If a building b feet high casts a shadow f feet long, then, at the same time of day, a tree t feet high will cast a shadow how many feet long?

1. ft/b

2. fb/t

3. b/ft

4. tb/f

5. t/fb

Ans : A

* If x, y, and z are consecutive negative integers, and if x > y > z, which of the following must be a positive odd integer?

1. xyz

2. (x – y) (y – z)

3. x – yz

4. x(y + z)

5. x + y + z

Ans : B

* At a certain ice cream parlor, customers can choose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. Considering both ice cream flavor and cone type, how many distinct triple-scoop cones with three different ice cream flavors are available?

1. 12

2. 16

3. 20

4. 24

5. 30

Ans : C

* What is the greatest value of a positive integer n such that 3n is a factor of 1815?

1. 15

2. 18

3. 30

4. 33

5. 45

Ans : C

1. If .2t = 2.2 – .6s and .5s = .2t + 1.1, then s =

1. 1

2. 3

3. 10

4. 11

5. 30

Ans : B

2. Five years ago, Beth’s age was three times that of Amy. Ten years ago, Beth’s age was one half that of Chelsea. If C repre- sents Chelsea’s current age, which of the following represents Amy’s current age?

1. c/6 + 5

2. 2c

3. (c-10)/3

4. 3c-5

5. 5c/3 – 10

Ans : A

3. A portion of $7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?

1. $160

2. $320

3. $400

4. $720

5. $1,600

Ans : B

4. An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity?

1. 4

2. 4.5

3. 5

4. 5.5

5. 6

Ans : E

5. If r = (3p + q)/2 and s = p – q, for which of the following values of p would r2 = s2?

1. 1q/5

2. 10 – 3q/2

3. q – 1

4. 3q

5. 9q/2 – 9

Ans : A

6. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?

1. 38

2. 40

3. 44

4. 48

5. 50

Ans : C

7. On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle’s diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?

1. (3, 3/2)

2. (1, 2/2)

3. (0, -4)

4. (2/2, 1)

5. (-1, -2/2)

Ans : C

8. If a rectangle’s length and width are both doubled, by what percent is the rectangle’s area increased?

1. 50

2. 100

3. 200

4. 300

5. 400

Ans : D

9. A rectangular tank 10″ by 8″ by 4″ is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?

1. 9

2. 12

3. 16

4. 21

5. 39

Ans : B

10. Point Q lies at the center of the square base (ABCD) of the pyramid pictured above. The pyramid’s height (PQ) measures exactly one half the length of each edge of its base, and point E lies exactly halfway between C and D along one edge of the base. What is the ratio of the surface area of any of the pyramid’s four triangular faces to the surface area of the shaded triangle?

1. 3 :v2

2. v5:1

3. 4v3:3

4. 2v2:1

5. 8:v5

Ans : D

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