# GMAT Math Practice Questions and Answers

## Practice Questions and Answers on Math for GMAT

Directions for questions 1 to 10: Answer the questions independently of each other.

1. A murderer was subjected to ‘n’ whip lashes. Also for every r th whip lash if the murderer groans, he will be subjected to (r – 1) lashes after the first n lashes. If for the n lashes, the murderer  groaned on all the lashes except one and the total number of lashes summed up to 111, find the serial number of the lash on which the murderer did not groan.

(a) 14

(b) 15

(c) 5

(d) 10

2. A circle of radius 3 cm circumscribes a square. The square has another circle inscribed in it, which again circumscribes a square and so on. What is the total area of all such circles and squares in  cm^{2}?

(a) 18π

(b) 18(π+2)

(c) 9π

(d) 4.5π

3. Two non-negative integers are choosen at random. The probability that their sum is divisible by 6 is:

(a) \frac{1}{18}

(b) \frac{1}{9}

(c) \frac{1}{6}

(d) \frac{4}{9}

4. A two digit odd number is such that the sum of its digits is 7 less than \frac{1}{3}rd of the number. The number is:

(a) 30

(b) 51

(c) 57

(d) 69

5. A square PQRS is constructed inside a triangle ABC having sides 110, 17 and 21 as shown in the figure. Find the perimeter of the square PQRS.

(a) 28

(b) 23.2

(c) 25.4

(d) 28.8

6. If a(x)=4x,b(y)=3y^{2}, the value of b[a(3)] is:

(a) 48

(b) 108

(c) 148

(d) 432

7. A hollow cube having side 8 cm is filled with solid cylinders whose height is same as that of the cube and radius is \frac{1}{8}th the side of the cube. After fitting the cylinders in  the cube, milk is poured into the cube. What is the volume of the milk that is poured?

(a) 210.6 cc

(b) 310.4 cc

(c) 512 cc

(d) 110.1 cc

8. Milk India Ltd. is a government owned milk distribution center. Earlier they used to distribute milk in bottles as shown in the figure for Rs.8 per bottle. Now, they have decided to reduce the price per bottle by 50 paise, by reducing the size of the bottle. However, they do not Want their old customers to notice this change in the size of the bottle, so they plan to reduce the circumference  of the opening of the bottle without changing the height of the bottle. What is the new circumference of the opening?

(a) 6π cm

(b) 8π cm

(c) 3.5π cm

(d) Cannot be determined

9. A detergent manufacturer used soda ash and acid slurry for its manufacture in the ratio 5 : 1. If their respective costs are in the ratio 2 : 5, calculate his cost price per kg of slurry, if the labour cost  is Rs.0.25 per kg of detergent, and the detergent costs him Rs.8.50 per kg. (inclusive of labour cost)

(a) Rs.16.50

(b) Rs.21.00

(c) Rs.10.50

(d) Rs.12.30

10. The volume of a sphere varies directly as the cube of its radius. Two solid spheres of diameter l0 cm and 8 cm are melted and cast into a hollow sphere of outer radius 6 cm. Find the thickness of the sphere.

(a) 1 cm

(b) 2 cm

(c) 1.5 cm

(d) 3 cm

 Practice Set Important Question Advance Questions Previous Papers Mock Test Sample Paper Typical Questions Model Set

11. Find the equation of the tangents from origin to the parabola y^{2}-8x+16=0.

(a) y=x

(b) y-x=0

(c) y=|x|

(d) None of these

Directions for questions 12 to 14: Answer the questions on the basis of the information given below.

Consider a cylinder of height n cm and radius \frac{4}{π} cm. A string of width h cm, when wound around the cylinder Without keeping any space between two turns, covers the  lateral surface of the cylinder completely.

12. What is the required length of the string?

(a) \frac{4n}{h} cm

(b) \frac{8n}{h} cm

(c) \frac{2n}{h} cm

(d) 8n cm

13. The same string is wound on the exterior four walls of a cube, making equally spaced 9 turns starting from point A and ending at point B exactly above. A. If ‘a’ is the side of the cube, then find  the relation between ‘a’ and ‘n’. (Take h = 1)

(a) a=\frac{1}{3}n^{2}

(b) a=\sqrt{n}

(c) n=\frac{a^{2}}{\sqrt{3}}

(d) a=\frac{2}{9}n

14. Find the ratio of the lateral surface area of the cylinder to the total surface area of the cube?

(a) 27 : n

(b) 64 : 3n

(c) 3n : 64

(d) None of these

Directions for questions 15 to 20: Answer the questions independently of each other.

15. Two non-negative integers are chosen at random. The probability that the sum of their squares is divisible by 6 is:

(a) \frac{1}{18}

(b) \frac{1}{9}

(c) \frac{4}{9}

(d) \frac{1}{6}

16. A sum of money at a compound interest is doubled in 8 years. In how many years will it become 16 times?

(a) 60 years

(b) 64 years

(c) 32 years

(d) 72 years

17. Deep and Jagat contribute \frac{1}{2} and \frac{1}{3} of the capital and Pramod contributes the remaining capital. Deep, Jagat and Pramod will share the profits  in the proportion:

(a) 2:3:1

(b) 3;2:5

(c) 2:3:6

(d) 3:2:1

18. A canary lies asleep at the centre of the base of a hemispherical cage. It wakes up, flies to the topmost point in the cage, then in a straight line to the cage door at the intersection of the curved  surface and the base. It covers a total distance of 241 yards. ‘What is the radius of the hemisphere?

(a) 40 yards

(b) 50 yards

(c) 100 yards

(d) 120.5 yards

19. Two circles having radii 17 cm and 10 cm have centres 21 cm apart. Calculate the length of the common chord.

(a) 6 cm

(b) 16 cm

(c) 10 cm

(d) Data insufficient

20. If roots of the equation x^{3}+ax^{2}+bx+c=0 are α, β and γ, then the equation with roots \alpha^{2},\beta^{2} and\gamma^{2} is:

(a) x^{5}+(2c-a)x^{4}+(c^{2}-2ac)x^{2}-a^{2}=0

(b) x^{6}+a^{2}x^{4}+bx+c=0

(c) x^{6}+(2c-b)x^{4}+(a^{2}-2bc)x^{2}-b^{2}=0

(d) x^{2}+(2b-a^{2})x^{4}+(b^{2}-2ac)x^{2}-c^{2}=0