# Problem Solving Practise Test - GRE

#### Q.1

In an essay competition the odds against competitors A, B, C and D are 2:1, 3:1, 4:1 and 5:1 respectively. Find the probability that one of them wins the competition.

- A. 11/120
- B. 114/120
- C. 127/150
- D. 2/17
- E. 135/157
- Answer: C

#### Q.2

A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls at random. Find the probability that among the four balls, there is at least one of each colour.

- A. 31/91
- B. 15/91
- C. 48/91
- D. 24/91
- E. 12/91
- Answer: C

#### Q.3

In a town of 3000 people 600 are over 50 years, and 1000 are female. It is known that 30% of the females are over 50 years. What is the probability that a person chosen at random is either a female or over 50 years?

- A. 11:13
- B. 13:17
- C. 2:3
- D. 9:17
- E. 13:9
- Answer: B

#### Q.4

The probability that Amit will qualify in an exam is 0.05. The probability that Amita will qualify is 0.10. The probability that both will qualify is 0.02. Find the percent chances of both failing to qualify.

- A. 50%
- B. 25.5%
- C. 37%
- D. 53%
- E. 87%
- Answer: E

#### Q.5

Find the probability that a leap year will contain 53 Tuesdays.

- A. 3/14
- B. 2/7
- C. 1/12
- D. 1/4
- E. 1/7
- Answer: B

#### Q.6

Find the probability that a leap will contain either 53 Tuesdays or 53 Wednesdays

- A. 1/5
- B. 2/5
- C. 2/3
- D. 3/7
- E. 1/2
- Answer: D

#### Q.7

Find the probability that a leap will contain 53 Tuesdays and 53 Wednesdays.

- A. 3/7
- B. 1/7
- C. 1/3
- D. 2/7
- E. 1/5
- Answer: B

#### Q.8

Four cards are drawn from a pack of cards. Find the probability of drawing one card from each suit.

- A. 4/20825
- B. 2197/20825
- C. 17160/20825
- D. 17160/6497400
- E. 2197/6497400
- Answer: B

#### Q.9

Four persons are chosen at random from a group of 5 men, 3 women and 4 children. Find the probability of selecting 2 men, 2 woman and 2 children.

- A. 1/5
- B. 2/5
- C. 4/11
- D. 5/13
- E. 1/25
- Answer: C

#### Q.10

Find the odds in favour that when a number is chosen randomly from 1 to 200 then it is an even number and not a multiple of 15.

- A. 12:17
- B. 1:10
- C. 5:11
- D. 43:57
- E. 47:53
- Answer: E

#### Q.11

The odds that Amit speaks the truth are 1:2 and the odds that Bunty speaks the truth are 2:3. What is the probability that exactly one of Amit and Bunty is telling the truth?

- A. 3/5
- B. 4/15
- C. 7/15
- D. 4/7
- E. 3/7
- Answer: C

#### Q.12

Meena has to eat only one fruit out of three. The probability that she eats a banana is 3/2 times the probability that she eats an apple. The probability that she eats a guava is half the probability that she eats a banana. What is her probability of having an apple?

- A. 1/4
- B. 4/13
- C. 1/6
- D. 4/7
- E. 11/36
- Answer: B

#### Q.13

Four members are to be chosen from a group of 3 women and 4 children. Find the probability of selecting exactly 3 children.

- A. 3/50
- B. 12/25
- C. 1/5
- D. 12/35
- E. 1/7
- Answer: D

#### Q.14

The probability of picking an apple from a basket is 0.25 and that of picking a rotten fruit is 0.50. The probability of picking a rotten apple is 0.14. Find the probability that neither an apple is picked nor a rotten fruit is picked.

- A. 0.75
- B. 0.39
- C. 0.25
- D. 0.50
- E. 0.61
- Answer: B

#### Q.15

There are five shirts of different colours and five pants of the same five colours. The shirts have to be matched with the pants of same colours. Find the probability that all the five shirts and pants are matched correctly.

- A. 1/3125
- B. 3124/3125
- C. 119/120
- D. 1/120
- E. 1/5
- Answer: D