# GMAT Math Mock Test Questions and Answers

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## Mock Test Questions and Answers on Math for GMAT

**Directions for questions 1 to 21: Answer the questions independently of each other.**

1. A cone is placed in a X-y-2 plane such that, its tip is placed on (0, 0, 0) i.e., the origin and its base is parallel to x-y plane and towards positive direction of z axis. This cone is then dropped such that its tip remains on origin and its slant height is on x-y plane and is at 45° to positive x axis and positive y axis. What are the co-ordinates of the upper most point of the cone. (radius of the base of cone is 3 units and height is 4 units)

(a) (\frac{5}{7\sqrt{2}},\frac{5}{7\sqrt{2}},\frac{24}{5})

(b) (\frac{7}{5\sqrt{2}},\frac{24}{5},\frac{7}{5\sqrt{2}})

(c) (\frac{7}{5\sqrt{2}},\frac{7}{5\sqrt{2}},\frac{24}{5})

(d) Cannot be determined

2. The average weight of a class of x students is 40 kg. If 5 students weighing between 35 to 40 kg left the class and 5 students weighing over 37 kg were admitted to the class, ﬁnd the minimum possible new average weight of the class in kg. (Assume that the weight of a student is always an integer.)

(a) \frac{10}{x} less than the previous average

(b) \frac{78}{x} less than the previous average

(c) \frac{28}{x} more than the previous average

(d) None of these

3. 130 packets have to be ﬁlled with candies such that number of candies in a packet vary from 125 to 148. These packets are then packed into boxes such that a box contains maximum number of packets with different number of candidates. If maximum number of such boxes are formed, ﬁnd the minimum number of packets containing equal number of candies.

(a) 5

(b) 6

(c) 10

(d) Cannot be determined

4. Amar buys 5 oranges, 2 mangoes and 3 apples for Rs.37. Akbar buys 6 apples, 10 oranges and 4 mangoes for Rs.74. Anthony buys 5 mangoes, 9 apples and 15 oranges for Rs.105. Which of the following is deﬁnitely true?

I. Cost of a mango is Rs.6/-

II. Cost of an apple is Rs.3/-

III. Cost of an orange is Rs.5/-

(a) Only I

(b) I and II

(c) I, II and III

(d) None of these

5. The sum of all possible 4 digit numbers formed by digits of 3556, using each digit only once is:

(a) 64427

(b) 63327

(c) 65297

(d) 43521

6. In how many ways can a group of 6 friends A, B, C, D, E and F stand in a queue such that A and E are standing in the corners and B and C are never together?

(a) 36

(b) 27

(d) 24

(d) 42

7. If f(x,y)=3x^{2}-2xy-y^{2}+4, then f(f(2, 3), f(-1, 1)) = ?

(a) -68

(b) 95

(c) 251

(d) 232

8. In a regular octagon ABCDEFGH, ﬁnd the area of rectangle ACEG, if side of the octagon is 2 cm.

(a) 13.24 cm^{2}

(b) 12.97 cm^{2}

(c) 14.18 cm^{2}

(d) 13.66 cm^{2}

9. In a sequence of numbers, the sum of the ﬁrst n terms is equal to 11n^{2}+10n. What is the sum of the 2nd, 4rd and 6th terms in the sequence?

(a) 250

(b) 300

(c) 261

(d) Cannot be determined

10. A dog is tied outside a hexagonal room to a rope whose other end is tied to the centre of one of the side of that hexagonal room. Initially, the two ends of the rope and the centre of the hexagonal room are collinear. Now the dog starts moving with stretched rope in clockwise direction. After completing one round such that the position of the dog is collinear with the centre of the room and its initial position, only 30 cm of unwounded rope’s left. Find the approximate distance covered by the dog if the side of the hexagonal room is 30 cm.

(a) \frac{395}{2}\Pi cm

(b) \frac{595}{2}\Pi cm

(c) 200\Pi cm

(d) Cannot be determined

11. There are 1004 black balls and 1002 white balls in a box. Two balls are drawn at random without replacement from the box.

Let Ps = Probability that two balls are of same colour

and Pd = Probability that two balls are of different colours.

Then |Ps – Pd] is: –

(a) \frac{1001}{1003\times 2005}

(b) \frac{1002\times 1004}{2006\times 2005}

(c) \frac{1}{2003\times 2005}

(d) 0

12. A honeybee ﬂies from one point to another on the XY plane. It moves in such a way that, if it is at a point (x, y) at any time, the next point it can move to, can only be (x + 3, y + 3) or (x + 3, y – 1). If the honeybee starts moving from the origin, then what is the minimum number of steps that the honeybee takes to land on the point (7272, 1626)?

(a) 1012

(b) 1134

(c) 2025

(d) It will never land on that point.

13. If m and n are real and positive numbers and m\ times.......\sqrt[n]{\sqrt[n]{\sqrt[n]{m}}}=n, then which of the following is true?

(a) \log_{n}m=m-n

(b) \log_{n}m=mn

(c) \log_{n}m=n^{m}

(d) \log_{n}m=m^{n}

14. The ratio of the height to the radius of a hollow cylinder is 2:\sqrt{3}. In it two indentical solid cones are kept tip to tip such that their bases coincide with the bases of the cylinder. Two solid spheres are then kept such that they occupy maximum possible volume that remains unoccupied in the hollow cylinder. If the volume of each cone is 27π:, ﬁnd the volume of

the empty space.

(a) 40.14π

(b) 94.14π

(c) 54π

(d) Data insufﬁcient

15. Given a five digit number, what is the probability that it will contain atleast one zero?

(a) 0.411

(b) 0.344

(c) 0.403

(d) 0.314

16. The inequality \left| x-1 \right|\lt \left| \sqrt{13-x^{2}} \right| is true for what percentage of the interval [-5, 5]? Consider only integral values. .

(a) 36.4%

(b) 70.1%

(c) 50%

(d) 42.5%

17. The cost function (C) for a certain company for the production of output x is given by C=\frac{1}{3}a^{2}x^{2}+3ax^{2}-2a , where a is a constant and x is the quantity produced. The revenue (R) that the company generates from its sales is given by R=a^{2}x^{2}+4ax^{2}-4x. What should be the proﬁt maximizing quantity that the company should produce? (a < 0)

(a) \frac{3a}{2}

(b) -\frac{2}{a}

(c) \frac{1}{a}

(d) None of these

18. Aamir and Armaan decided to invest some amount of money in the ratio 5 : 4 for the same period in a business. It was decided that at the end of a year, x% of the profit was to be given to charity. Out of the remaining profit, 70% was to be reinvested as capital and the remaining was to be shared among themselves in the ratio of their capitals. If the total profit, was Rs.12000 and the difference in the shares of Aamir and Armaan was Rs.360. What is the value of x?

(a) 10%

(b) 73%

(c) 22%

(d) 40%

19. What is the probability that 10 different numbers arranged linearly are in a strictly decreasing or strictly increasing order?

(a) \frac{1}{10!}

(b) \frac{2}{10!}

(c) \mathrm{C}_{10}^{100}\left( \frac{1}{(10!)^{10}} \right)

(d) 2\times \mathrm{C}_{10}^{100}\left( \frac{1}{(10!)^{10}} \right)

20. Two friends Ramesh and Suresh go to a shop to buy pens. Ramesh wants to buy 13 pens, but is short of money equal to the cost of a pen. Suresh wants to buy 5 pens, but he has Rs.5 extra. If Ramesh has double the money that Suresh has, then how much money does each one has? p

(a) Rs.90, Rs.45

(b) Rs.30, Rs.15

(c) Rs.60, Rs.30

(d) Rs.50, Rs.25

21. An alien spaceship’s velocity is given by: v=x^{4}-x^{3}+x^{2}-1, where x is the distance of the ship from the home planet (displacement). The acceleration of the ship is given by a=x^{5}-4x^{4}+4x^{3}-3x^{2}-x+3. If the spaceship is out in space at a distance ‘d’ from the home planet, and there is an inﬁnitesimal change (S) in the displacement of the ship, then what will be the corresponding change (infinitesimal) in the ship’s velocity?

Note: Velocity is the rate of change of displacement with respect to time. Acceleration is the rate of change of velocity with respect to time.

(a) S^{3}-d+1

(b) (S-3)d

(c) (d-3)S

(d) d^{5}-4d^{4}+4d^{3}-3d^{2}-d+3