# GMAT Math Typical Questions and Answers

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## Typical Questions and Answers on Math for GMAT

**Directions for questions 1 to 4: Answer the questions on the basis of the information given below.**

a # b = a + 2b; if |a+b| is even.

= 2a ! 2b; if |a+ b| is odd.

a ! b = 3a – b; if |a+b| is even.

= 2a # 2b; if |a + b| is odd.

1. Evaluate 2 # ((7 ! (4 # 5 )) ! 3).

(a) 306

(b) 142

(c) 188

(d) 204

2. Which of the following is/are deﬁnitely true?

i. If a x b is odd, a # b always evaluates to a ! b.

ii. If a x b is even, a ! b always evaluates to 2(a # 2).

m. If b > a and |a + b| is odd, then a # b will be negative.

(a) iii only

(b) ii and iii only

(c) i, ii and iii

(d) None of these

3. Which of the following is/are true?

i. If b = 2a and a+b is even, then a#b=b#a.

ii. If b = 3a, a ! b will always be zero.

iii. If b = 2a and a is odd, then a ! b will be even.

(a) ii only

(b) iii only

(c) i and iii only

(d) ii and iii only

4. Which of the following is/are true?

i. 6 ! 2 = 12 # 2

ii. 6#3=(14 ! 12) + (2 ! 6)

iii. (6 ! 2) + (6 # 3) = (12#2) + (14 ! 12) – (2 ! 6)

(a) i and ii only

(b) i & iii only

(c) ii & iii only

(d) i, ii, & iii

**Directions for questions 5 and 6: Answer the questions on the basis of the information given below**

P, Q and R start a joint venture, where in they make an annual proﬁt. P invested one-third of the capital for one-fourth of the time, Q invested one-fourth of the capital for one-half of time while R invested the remainder of the capital for the entire year. P is a working partner and gets a salary of Rs.10000 per month. The proﬁt after paying P’s salary is directly proportional to the sum each one has put and also to the square of the number of months for which each has put their sum in the venture. P earns Rs.60000 more than Q in a year.

5. How much does P earn?

(a) Rs.30000

(b) Rs.120000

(c) Rs.60000

(d) Rs.150000

6. Find the total profit made by them?

(a) Rs.840000

(b) Rs.720000

(c) Rs.730000

(d) Rs.830000

**Directions for questions 7 and 8: Answer the questions on the basis of the information given below.**

Four pipes A, B, C and D can fill a cistern in 20, 25, 40 and 50 hours respectively.

6. The ﬁrst pipe A was opened at 10 a.m., B at 12p.m., C at 1 p.m. and D at 2 p.m. When will the cistern be full?

(a) 2:42 p.m.

(b) 5:37 p.m.

(c) 7:09 p.m.

(d) 8:03 p.m.

7. If the first and third pipes are opened as inlet pipes into the cistern and the second and fourth pipes are opened as outlet pipes from the cistern and all the four pipes are opened simultaneously, how many hours will it take to fill the cistern completely?

(a) 24 hours

(b) 48 hours

(c) 69 hours

(d) None of these

**Directions for questions 8 to 15: Answer the questions independently of each other.**

8. Find die remainder when x^{4}+2x^{3}-3x^{2}+4x-5 is divided by x^{2}-x-2.

(a) 12x

(b) 4x – 1

(c) -1

(d) x – 1

9. In 24 hours, how many times is the hour hand either 90° or 180° to the minute hand?

(a) 44 times

(b) 66 times

(c) 96 times

(d) 72 times

10. What is the area of the square, all four vertices of which lie on the circumference of a circle if the area of the circle is twice its diameter in magnitude?

(a) \frac{8}{\Pi^{2}}

(b) \frac{16}{\Pi^{2}}

(c) \frac{32}{\Pi^{2}}

(d) \frac{64}{\Pi^{2}}

11. If \log_{16}9\times 3\log_{27}64=\log_{x^{4}}80^{3} then x = ?

(a) 3\sqrt[4]{2}

(b) 4\sqrt[4]{3}

(c) 2\sqrt[4]{5}

(d) 4\sqrt[]{2}

12.

In the figure CC’ is a chord parallel to tangent O’T.

If O’T’ and radius of the circle with centre O are in ratio 17 : 10, then the approximate value of 9 in degrees will be:

(a) 30°

(b) 63.26°

(c) 59.53°

(d) 43.24°

13. The number of isosceles/equilateral triangles, which can be drawn with integral sides and perimeter equal to 45 is:

(a) 9

(b) 10

(c) 11

(d) 12

14. The probability that Machin scores a century in a match is 0.4. He is 3 centuries away from breaking the world record. He has to announce his retirement. After how many minimum possible number of matches should he announce in order to ensure a 30% probability of scoring atleast 3 centuries?

(a) 4

(b) 5

(c) 6

(d) 7

15. f(x)=\frac{2x-1}{3} for (x\gt 0)

f(x)=3x+\frac{1}{2} (otherwise)Find f(x) if x is a nonzero multiple of 3 and x^{2}+4x-12\lt 0.

(a) \frac{5}{3}

(b) -0.5(2^{4}+1)

(c) -0.5(2^{5}+3)

(d) None of these

**Directions for questions 16 and 17: Answer the questions on the basis of the information given below.**

85 children went to an amusement park, where they could ride on the merry-go-round, roller coaster, and wheel. It was known that 20 of them took all the three rides, and 55 of them took at least two of the three rides. Each ride cost Re,1, and the total receipt of the amusement park from these children was Rs.145.

16. How many children did not try any of the rides?

(a) 5

(b) 10

(c) 15

(d) 20

17. How many children took exactly one ride?

(a) 5

(b) 10

(c) 15

(d) 20

**Directions for questions 18 to 20: Answer the questions on the basis of the information given below.**

The product of the “first three terms of a G.P. is 27. Also the sum of the ﬁrst two terms of the series is 4.

18. The ﬁrst term of the series will be:

(a) 1

(b) 2

(c) 3

(d) 4

19. The ﬁfth term of the series will be:

(a) 81

(b) 27

(c) 64

(d) 32

20. The sum of the ﬁrst ﬁve terms of the series is:

(a) 120

(b) 121

(c) 99

(d) 115