# GMAT Math Sample Questions and Answers

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## Sample Questions and Answers on Math for GMAT

**Directions for questions 1 to 3: Answer the questions on the basis of the information given below.**

In a class of 40 students, who study Mathematics, Physics and Chemistry, the number of students studying Mathematics is 2 more than 40% of those studying Chemistry, while 20 of the students study Physics. Three less than one fifth of total students in class study all the three subjects. The number of students studying only Physics is 2 less than the number of students studying Mathematics. The number of students ‘studying only Mathematics and only Chemistry is 3 and 15 respectively. The number of students studying Mathematics as well as Physics is same as number of students studying Mathematics as well as Chemistry.

1. Find the number of students who study both Physics and Chemistry but not Mathematics?

(a) 2

(b) 3

(c) 5

(d) 4

2. How many students study both Mathematics and Chemistry but not all three subjects?

(a) 5

(b) 4

(d) 1

(d) 2

3. The number of students studying only Physics is:

(a) 13

(b) 15

(c) 14

(d) None of these

**Directions for questions 4 to 10: Answer the questions independently of each other. **

4. A solid metallic cuboid with sides in the ratio 2 : 3 : 4 is melted to form smaller cubes with sides 2 cm (assume no wastage). If the sum of the length of edges of the cuboid is 108 cm, then ﬁnd the ratio of the surface area of the original cuboid to the total surface area of the smaller cubes?

(a) \frac{13}{16}

(b) \frac{13}{2592}

(c) \frac{3}{2592}

(d) \frac{13}{54}

5. Ram invests in 5% and 8% stocks buying them at x% premium and at a discount of x% respectively. The total amount of premium paid is 70% of the total discount received. The dividend from the 5% stock forms x% of dividend from the 8% stock. Find x.

(a) 34.5%

(b) 35.37%

(c) 43.75%

(d) 56.8%

6. A dart board of 3 x 3 m is divided into six regions A, B, C, D, E and F as shown below:

In a certain game, the following points are awarded:

1. If the dart hits A, 4 points are awarded.

2. If the dart hits B, 3 points are awarded.

3. If the dart hits C, D or E, 2 points are awarded.

4. If the dart hits F, 6 points are awarded.

If the dart misses the target, no points are awarded.

What is the probability of getting a score of 12 in three consecutive throws without a miss?

(a) \frac{237}{729}

(b) \frac{40}{243}

(c) \frac{40}{81}

(d) \frac{125}{729}

7. Estimate the maximum volume of a cylinder, if the sum of its radius and height is 6 cm.

(a) 16π cm3

(b) 24π cm3

(c) 18π cm3

(d) 32π cm3

8. If the selling price of a mat is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price?

(a) 11:30

(b) 2:5

(c) 1:6

(d) 7:30

9. A football team of 11 players is posing for a photograph along with its coach. The football players are standing in two rows in groups of six, one behind the other. The coach and the vice captain stand together in the centre in the first row while the captain stands behind the vice captain. The goalkeeper stands in the corner, while exactly two out of three defenders stand next to each other. In how many ways can it be done?

(a) 18720

(b) 34560

(c) 95040

(d) 129600

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10. Harsh kicks a football and starts running after the ball at a speed of 9 mps. The path taken by the ball is semicircular and the distance covered by the ball in every subsequent bounce is \frac{1}{8} times of that covered in the previous bounce. The initial velocity that the ball gains from the kick is 24 mps and the horizontal distance covered by the ball in the ﬁrst bounce, had it travelled in a straight path, would be 81.52 m. The deceleration caused to the ball due to friction, is 2 mps2. (Distance travelled by the ball in time ‘t’, s=xt-\frac{1}{2}at^{2} where ‘x’ is initial velocity, ‘a’ is deceleration, velocity at time ‘t’, v = u + at.) The ball bounces at least once before Harsh catches it. How far is Harsh from the ball, when the ball bounces for the ﬁrst time?

(a) 0.2 m

(b) 9.52 m

(c) 8 m

(d) Cannot be determined

**Directions for questions 11 to 13: Answer the questions on the basis of the information given below.**

Given in the above figure is a game of boxes. Two blank boxes are shown in the figure and the other boxes can move horizontally or vertically in the blank box. a_{ij} represents’ the alphabet in i^{th} row and j^{th} column (a_{12}=B_{1}, a_{32}=I) shifting of every box by one step is counted as a move, and each box can make only one move at a time.

11. What is the minimum number of moves required for F to reach a_{43}?

(a) 7

(b) 8

(c) 9

(d) 10

12. D takes at least __________ moves to reach a_{23}.

(a) 6

(b) 7

(c) 8

(d) 9

13. What is the minimum number of moves required for A to reach a_{14}?

(a) 7

(b) 9

(c) 10

(d) 11

**Directions for questions 14 to 19: Answer the questions independently of each other.**

14. Company A has ten Computer Engineers, eight Electronics Engineers, seven Chemical Engineers and three Mechanical Engineers. The total monthly salary of all these engineers is Rs.235900. In Company B, five Chemical Engineers, seven Mechanical engineers, twelve Computer Engineers and six Electronics Engineers draw Rs.262100 monthly. Company C has four Electronics Engineers, four Chemical Engineers, ﬁve Mechanical engineers and seven Computer Engineers. These Engineers draw Rs.178800 monthly. If all the respective engineers are paid equally in all the companies then ﬁnd the total monthly salary often Mechanical Engineers, ten Chemical engineers, eleven Electronics Engineers and eighteen Computer Engineers from Company D.

(a) Rs.498000

(b) Rs.328500

(c) Rs.427800

(d) Data Insufficient

15. (436)_{8}+(537)_{8}=(?)_{8}

(a) 1175

(b) 1036

(c) 1145

(d) 1215

16. Two frustums having base radius of 20 m are joined together. One of the frustums has height 3 m and top radius 16 in. The other frustum has height 6 m and top radius 12 m. Find the cost of painting for the total. surface of composite frustum, if the cost of painting is Rs.21 per sq. m.

(a) Rs.54400

(b) Rs.59400

(c) Rs.50400

(d) Cannot be determined

17. The proﬁt of a firm is given by \frac{\sqrt{2}}{3}x^{3}-(2\sqrt{2}+\frac{1}{2})x^{2}+4x-13, where x is the cost of the product. For what value of x will the proﬁt be maximum?

(a) 4

(b) \frac{1}{\sqrt{2}}

(c) Both of these

(d) None of these

18. A tangent is drawn to a circle with centre O(5, -4), touching it at the point P(7, -6). Find the X-intercept of the tangent.

(a) 13

(b) 1

(c) -13

(d) The tangent will not intercept the X-axis.

19. A sells his house to B at a proﬁt of 10% who in turn sells it to C at a proﬁt of 15% who in turn sells it to D at a profit of 25% and D sells it to E at 35% profit. If cost price of E’s house is Rs.3500000 then what is approximate cost price of A’s house?

(a) Rs.1540000

(b) Rs.1510000

(c) Rs.1500000

(d) Rs.l640000