# GMAT Math Model Questions and Answers

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## Model Questions and Answers on Math for GMAT

1. Two circles intersect each other such that the tangents drawn at a point of intersection are mutually perpendicular. What is the length of the line segment of a common tangent between the points where it touches the two circles, if the radii of circles are 10 and 5 respectively?

(a) 10

(b) 12

(c) 2(50)^{1/2}

(d) 15

2. If \frac{(a-x)\sqrt{a-x}-(b-x)\sqrt{x-b}}{\sqrt{a-x}+\sqrt{x-b}}=a-b, then x=?

(a) a

(b) b

(c) a and b

(d) None of these

3. A rectangular garden is surrounded by a path of width 2 m on all sides. Now if the length of the garden is reduced by 2 m the garden becomes a square garden and the area of path becomes \frac{13}{11} times, find the length of the original rectangular garden.

(a) 6m

(b) 8m

(c) 10m

(d) 12m

4. If x=\cos^{2}\theta and f(x)=x^{3}-\frac{5}{2}x^{2}+\frac{5}{2}x-\frac{3}{4}>0, which of the following best represents x?

(a) -\infty \lt x\le -\frac{1}{2}

(b) \frac{1}{2}\lt x\lt \infty

(c) \frac{1}{2}\lt x\le 1

(d) 0\le x\le \frac{1}{2}

5. A box contains a number of apples. When the apples are divided into groups of 5, 4 apples are left, when divided into groups of 4, 3 are left, when divided into groups of 3, 2 are left and when divided into groups of 2, 1 is left. What is the minimum possible number of apples?

(a) 49

(b) 59

(c) 64

(d) 39

6. The roots of the equation x^{2}-2\sqrt{3}x+3=0 are:

(a) rational and unequal

(b) irrational and unequal

(c) rational and equal

(d) real and equal

7. Sixteen added to the product of four consecutive odd natural numbers is always:

(a) a prime number

(b) a perfect square

(c) a cube

(d) None of these

8. Glass spheres of radius 7 mm, dropped into a cylindrical vessel containing some water, are fully submerged. The diameter of the vessel is 14 cm. How many spheres have been dropped in the vessel if the water level rises by 3.5 cm?

(a) 300

(b) 37

(c) 375

(d) Data insufficient

9. Rajendra sells out Rs.20000 stock at Rs.93\frac{5}{8} at 3% dividend. He invests the proceeds in 4% at Rs.101\frac{7}{8}. Find his change in income.

(a) Rs.162\frac{1}{4}

(b) Rs.142\frac{1}{3}

(c) Rs.135\frac{1}{2}

(d) Rs.151\frac{2}{3}

10. What is the area of the solution region of |x| + ]y ≤ 1?

(a) 2 sq. units

(b) 1 sq. units

(c) Inﬁnite, as one side is unbounded

(d) Indeterminate

11. If \log_{8}m+\log_{8}\frac{1}{6}=\frac{2}{3}, then m is equal to:

(a) 1

(b) 6

(c) 24

(d) 4

12. Ramesh leaves his office at 5:00 p.m. everyday and his driver (who starts from Ramesh’s house) picks him up, at his office, at 5:00 p.m. They normally reach home at 6:00 p.m. Today, however, Ramesh left early and started walking towards his house, at the same time the driver started from his house towards the office. The driver picked him up on the way. However, in all this, Ramesh’s travel time increased by half an hour from his normal travel time. How long did Ramesh walk? (Assume constant speeds)

(a) 45 minutes

(b) 1 hr

(c) 30 minutes

(d) 15 minutes

13. Ashish sells sugar at 20% more than the cost of purchase. He also cheats on weight and weighs only 950 gm per kg of sugar.–Girish being a regular customer is offered a discount of 5% and pays only Rs.l8 for a kg of sugar. The profit of Ashish when Girish purchases 1 kg of sugar from him is:

(a) Rs.3.60

(b) Rs.3

(c) Rs.2.85

(d) Rs.2.70

14. Simplify \frac{0.7x0.7x0.7-0.3x(0.3)^{2}}{0.7x0.7-0.3x0.3}-\frac{0.7x0.7x0.7x 0.7}{0.7-0.3}+\frac{0.3x0.3x0.3x0.3}{0.7-0.3}

(a) 0.26

(b) 0.21

(c) 0.32

(d) 0.36

15. Due to a phenomena called refraction, the sun is visible before it appears on the horizon because rays get bent in air. If the bent rays form an angle of 5°, what would be the increase in the time for which the sun is visible, for one day? ‘

(a) 20 minutes

(b) 40 minutes

(c) 1 hour and 20 minutes

(d) 1 hour and 40 minutes

16. Eight mice are selected at random and they are divided into two groups A and B of four each. Each mouse in group A is given a dose of certain poison P which is expected to kill one in four; and each mouse in group B is given a dose of certain poison Q which is expected to kill one in two. Find the probability that there are fewer deaths in group B than in group A.

(a) \frac{615}{4096}

(b) \frac{525}{4096}

(c) \frac{425}{4096}

(d) \frac{315}{4096}

17. A alone takes twice as long as B and C together to do a peice of work. B alone takes thrice as long as C and A take to do the work together. If all the three of them: work together, they can complete the work in 36 days. In how many days can C, working alone, complete the work?

(a) 73

(b) 87

(c) 117

(d) 144

18. If px = p + 10x, then the number of positive integral values of x is:

(a) 3

(b) 4

(c) 2

(d) 1

19. Just before elections, \frac{2}{5}th of the voters promised to vote for P and the rest promised to vote for Q. However, during the elections, 15 of P’s supporters deserted him and voted for Q, and 25 of Q’s supporters voted for P. If P won by a margin of 2 votes, what is the total number of voters?

(a) 90

(b) 100

(c) 140

(d) None of these

20. Product A is manufactured in a series of three operations – Cutting, Finishing and Assembling respectively. Total manpower is 100, which is in the ratio of 2 : 3 : 5 in Cutting, Finishing and Assembling operations respectively. There is skilled and unskilled manpower for each of the operations. A Skilled worker is twice as good as an unskilled worker. The ratio of skilled to unskilled workers is 3 : 1, 2 : 1 and 2 : 3 for Cutting, Finishing and Assembling operations respectively. The operations are done in shifts of 8 hours. Product A requires 3.5 man hours of Cutting, l man hour of Finishing and 1.4 man hours of Assembling of skilled manpower.

What is the number of shifts required to complete the order of 200 units of product A if the next operation begins only after the entire earlier operation is completed?

(a) 5

(b) 7

(c) 8

(d) None of these