# GMAT Math Advance Questions and Answers

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## Advance Questions and Answers on Math for GMAT

**Directions for questions I to 13: Answer the questions independently of each 0ther.**

1. If a four digit number is the sum of twice its reverse and half itself, and its first digit is 4 times its ‘last digit and the second digit is seven times the third, then the sum of the digits of the four digit number is:

(a) 12

(b) 14

(c) 16

(d) 18

2. Evaluate \frac{1}{2}\log_{10}25-2\log_{10}3+\log_{10}18.

(a) 3\frac{1}{2}

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

(c) 1\frac{3}{4}

(d) 1

3. Ram invests Rs.12805 in 4% stock at 98.5. When the value of the stock increased to 102.375, he sold it and invested in 4.5% stock at 105.625. Find the change in his income.

(a) Increase by Rs.31

(b) Decrease by Rs.47 7

(c) Decrease by Rs.31

(d) Increase by Rs.47

4. If a, aq, aq^{2} are the sides of a triangle, where a and q are real numbers and q ≥ 1, which of the following is the value that q cannot take? .

(a) 1

(b) 2

(c) 3/2

(d) 1.2

5. A ball dropped from a height X, bounces to one half of its height from the floor every time it strikes it. The total distance which the ball travels before coming to rest is:

(a) 2x

(b) 3x

(c) 6.6x

(d) 5x

6. Amar, Akbar and Anthony eat lunch at the same‘ restaurant everyday. If Amar orders a dosa, then Akbar also orders a dosa. Either Akbar or Anthony always orders a dosa, but never at the same lunch. Either Amar or Anthony or both always order a dosa. If Anthony orders a dosa, then Amar also orders a dosa. You can conclude that:

(a) Amar, Akbar and Anthony always order a dosa.

(b) Amar and Anthony sometimes order a dosa, Akbar never does.

(c) Amar and Akbar always order a dosa, Anthony never does.

(d) Amar and Anthony always order a dosa, Akbar never does.

7. If p th term of an harmonic progression (HP) is qr and q th term is pr, then the r th term of the HP is:

(a) pqr

(b) pq

(c) pqr^{2}

(d) pr — qr

8. A three digit number is greater by 118 than twice the product of its digits. If the hundredths place digit is greater than the units place digit by 2 and the tenths place digit is 8, ﬁnd the number.

(a) 886

(b) 785

(c) 684

(d) 876

9. A boy standing on top of a building, 50 m in height, sees a layer of fog above him at a height of 70 m. He throws a stone into the fog. The stone follows a path given by the equation y=-x^{2}+40x-271 with the base of the building as the X-axis. Find the distance between the points at which the stone enters the fog and the point at which it comes out of the fog?

(a) 4 units

(b) 5 units

(c) 6 units

(d) Cannot be determined

10. ABCD is a square, EFGH is another square. AE = FD = GC = HB = a and AF = DG = CH = BE = b, then the ratio of the perimeters of ABCD to EFGH is

(a) a : b

(b) (a + b) : (a – b)

(c) (a+b): \sqrt{a^{2}+b^{2}}

(d) 2a^{2}:b^{2}

Practice Set | Important Question |

Advance Questions | Previous Papers |

Mock Test | Sample Paper |

Typical Questions | Model Set |

11. A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

(a) 4 kg

(b) 5 kg

(c) 8 kg

(d) 38 kg

12. A laughter club requires each member to tell a joke. At least two members must laugh at each joke. There are six members A, B, C, D, E and F.

C and E cannot laugh at A’s joke. X x

B and C laugh only at D’s or E’s joke.

F and D laugh at each other‘s jokes.

B and D do not laugh at two consecutive jokes.

If A tells a joke, who does not tell the next joke?

(a) B

(b) D

(c) F

(d) Cannot be determined

13. A letter is selected from each of “the words ‘PROBABILITY’ and ‘SUSCEPTIBILITY’. The probability that the same letter is selected is:

(a) \frac{16}{17}

(b) \frac{13}{154}

(c) \frac{4}{22}

(d) None of these

**Directions for questions 14 to 16: Answer the questions on the basis of the information given below.**

Ganga ﬂows down from Gangotri – Devprayag – Rishikesh – Haridwar. Devprayag is 120 km away from Gangotri and Ganga flows at 60 km/hr between the two places. Devprayag is 90 km away from Rishikesh and 150 km away from Haridwar.

Note: The results derived from the initial questions can be used for subsequent one’s.

14. If it takes 2 hours for a log of wood to travel from Devprayag to Rishikesh, how long would a boat take to travel from Rishikesh to Devprayag, if it can travel at a speed of 60 km/hr in still water?

(a) 1.5 hours

(b) 2 hours

(c) 51 minutes

(d) 6 hours

15. What is the time needed to travel from Rishikesh to Gangotri if I travel at 90 km/hr in still water? ‘

(a) 2.5 hours

(b) 6 hours

(c) 3.5 hours

(d) Data insufficient

16. If a steamer reaches Rishikesh at 9.30 pm having left Haridwar at 7.30 pm on the same day, travelling at 60 km/hr, how long would it take for a log of wood to travel from Rishikesh to Haridwar?

(a) 4 hours

(b) 2 hours

(c) 3 hours

(d0 Data insufficient

**Directions for questions 17 to 20 Answer the questions independently of each other.**

17. The four lines ax \pm by\pm c=0 enclose a rhombus whose area is:

(a) \frac{2c^{2}}{ab}

(b) \frac{ab}{2c^{2}}

(c) \frac{c^{2}}{ab}

(d) \frac{ab}{c^{2}}

18. The function with p and q greater than zero has its minimum value when:

(a) x = – p

(b) x=\frac{p}{2}

(c) x = -2p

(d) x=\frac{-p}{2}

19. In a family of five members, the age of the father is more than thrice the age of the youngest member,1the mother is twice the age of the daughter, who is elder to the twin sons. The family’s combined age is 137. Four years from now, the father’s age will be twice the daughter’s age. Three members in the family can vote. If the sons are over 10 years of age and the voting age is 18 years and more, in how many years will the twin sons be able to vote, if all their ages are taken as integers?

(a) 6

(b) 4

(c) 3

(d) 2

20. Vijay takes a loan of Rs.5000 from Ajay at a simple interest of 5% p.a. and agrees to pay it back in 3 years. Ajay gives him 2 options, either to pay the full amount with the interest at the end of the 3 years or pay the amount in 3 equal annual installments. Vijay chooses the option in which he has to pay less interest. What is the total amount that Vijay pays?

(a) RS.5750

(b) RS.5526

(c) RS.5974

(d) None of these