# GMAT Math Important Questions and Answers

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## Important Questions and Answers on Math for GMAT

1. The market price of an article was 40% more than its cost price. I was going to sell it at market price to a customer, but he showed me some defects in the article, due to which I gave him a discount of 28.57%. Next day he came again and showed me some more defects, hence I gave him another discount that was equal to 12.5% of the cost price. What was the approximate loss to me?

(a) Loss of 10%

(b) Loss of 12.5%

(c) Loss of 15%

(d) None of these

2. Kiran buys 5 kgs of rice and 7 kgs of dal for Rs.339 and Kishore buys 5 kgs of dal and 7 kgs of rice for Rs.321. Find the cost of rice and dal in Rs. per kg.

(a) 23, 32

(b) 11, 44

(c) 17, 38

(d) Data insufficient

3. In \Delta ABC, L(AB) = C, L(BC) = a, L(AC) = b. If this triangle is inscribed in a circle, then ﬁnd the ratio of arc(AB) : arc(BC) : arc(AC) if a : b : c = 1 : 1 : \sqrt{3}

(a) 1 : 4 : 1

(b) \sqrt{3} : 1 : 1

(c) 1 : \sqrt{3} : 1

(d) 4 : 1 : 1

4. Find the sum of the series \frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+ ..... up to 99 terms.

(a) \frac{99}{199}

(b) \frac{198}{199}

(c) \frac{98}{99}

(d) Cannot be determined

5. Stefan, a class 3 student at Sudarshan Public School is learning geometry. He draws a triangle with sides 15, 20 and 25 cm. He wants to draw a circle, such that all the three corners of the triangle touch the circle and the circle has the maximum possible area. Then he shades the triangle in crimson red colour. What is the area of the unshaded part?

(a) 150 cm^{2}

(b) 490 cm^{2}

(c) 640 cm^{2}

(d) 340 cm^{2}

6. A committee is to be formed from amongst.9 boys and 6 girls. In how many ways can the boys and girls divide themselves into groups of three so that no group has more than 2 girls and no group has all boys?

(a) 2025 x 6!

(b) 2145 x 9!

(c) \frac{15}{4} x 9! x 3!

(d) None of these

7. z varies as (px^{2}+qy^{2}). z = 26 when x = 1 and y = 2, and z= -16, when x = 2, y = 1. p+q=1,find p.

(a) 4

(b) 3

(c) -3

(d) -4

8. Two solid pyramids are melted together. These pyramids had number of edges equal to length of each of their edges =’ 8 units. They are moulded to form a hexagonal pyramid with length of each side of base 8 units. Find the slant height of the new pyramid.

(a) \frac{8}{3}\sqrt{\frac{35}{3}} units

(b) \sqrt{\frac{35}{3}} units

(c) \frac{8}{3}\sqrt{\frac{2}{3}} units

(d) 8\sqrt{\frac{2}{3}} units

9. In a certain coding system, letters of the English alphabet are written as A ≡ 2, B ≡ 5, C ≡ 10, and so on. In that coding system, how is VARSHA Written (codes for letters are written next to each other to form a word)?

(a) 4851335362652

(b) 4852325362652

(c) 48523225361652

(d) 4852322362662

**Directions for questions 10 and 11: The graphs of some functions are given below.**

Choose (a) if f(x)=if(-x), x\ge 0

Chose (b) if f(x)=\frac{1}{2}+\frac{1}{2}f(-x), x\ge 0

Choose (c) if f(x)=\left| f(x) \right|,x\ge 0

Choose (d) , otherwise

10.

11.

**Directions for questions 12 to 19: Answer the questions independently of each other.**

12. f is a real valued function such that f(x)-3f(\frac{72}{x})=4x(x\neq 0). Find the value of f(3).

(a) -\frac{52}{3}

(b) -\frac{75}{2}

(c) \frac{75}{4}

(d) \frac{52}{3}

13. If y=\frac{n^{4}+256+4n(16+n^{2})}{n^{2}+8n+16} and 27\le n^{3}\le 512, then

(a) 13 ≤ y ≤ 48

(b) 13 ≤ y ≤ 48

(c) 37 y < 97

(d) 13 ≤ < 92

14. A six digit number is formed by using digits 1, 2, 3, 4, 5 and 6 without repeating any of them. What is the sum of all such possible numbers?

(a) 279999720

(b) 299997290

(c) 379999720

(d) 379999900

15. A money lender lent a total amount of Rs.47000 to A, B and C at an interest rate of 5%, 3% and 4% per annum respectively. If the same amount of interest is paid by three persons at the end of 7 years, 10 years and 5 years respectively, find the amount borrowed by C.

(a) Rs.14000

(b) Rs.12000

(c) Rs.15000

(d) Rs.21000

16. Out of 4 strikers A, B, C and D, 5 midﬁelders E, F, G, H and I, 5 defenders J, K, L, M and N and 3 goalkeepers O, P, and Q, a team of 11 has to be chosen such that atleast 3 strikers and exactly l goalkeeper always play. A and D never play together while Q will be a goal keeper only if M and N are defenders. In how many ways can the team be selected?

(a) 256

(b) 368

(c) 480

(d) 592

17. Nine people, A, B, C, D, E, F, G, H and I go for a party in a restaurant. They sit around an octagonal table which has a chair at each of its vertices and also one at the midpoint of each of its sides. Exactly 3 people A, B and C sit adjacent to each other. Also, G and H sit opposite to each other but not adjacent to A, B or C. In how many ways can all of them be seated if nobody sits near G, H or the triplet A, B, C?

(a) 11520

(b) 28800

(c) 25220

(d) 20160

18. A series is formed in such a manner that the ﬁrst term is the first natural number, the second term is the cube of the first term, the third term is the third natural number while the fourth term is the cube of the third term and so on ……..

What is the sum of the ﬁrst 50 terms of the series?

(a) 51234

(b) 56139

(c) 121768

(d) 781250

19. A cylindrical vessel 80 cm in diameter is partly filled with water. If a sphere of diameter 60 cm is dropped into the vessel then the water level will increase by:

(a) 30.5 cm

(b) 35.2 cm

(c) 22.5 cm

(d) 32.5 cm