Quant Quiz

Directions (1-3) : Study the given information carefully and answer the questions that follow

A basket contains 6 black, 4 yellow and 3 white marbles.

1. If three marbles are picked at random, what is the probability that either all are white or all are black?
(1) 21/143         
(2) 10/243       
(3) 21/286         
(4) 31/286         
(5) None of these


2. If two marbles are drawn at random, what is the probability that both are black?
(1) 5/26         
(2) 15/26       
(3) 5/13         
(4) 21/26          
(5) None of these

3. If three marbles are picked at random, what is the probability that at least one is yellow?
(1) 42/143 
(2) 84/143
(3) 21/143  
(4) 35/143 
(5) None of these

Directions (4-5): Study the given information carefully and answer the questions that follow. 

A committee of five members is to be formed out of 4 trainees, 5 professors and 3 research associates. In how many different ways can this be done if-

4. The committee should have at least three of the four trainees?
(1) 90 
(2) 60
(3) 128 
(4) 120  
(5) None of these

5. The committee should have 2 trainees and 3 professors?
(1) 60 
(2) 90
(3) 120 
(4) 30  
(5) None of these

Direction (6-12): Study the following pie-charts carefully and answer the questions given below:
Year-wise Breakup of the number of candidates appeared for an entrance exam and Year-wise Breakup of the number of candidates who cleared the entrance exam.

Total Number of candidates appeared in the entrance exam from 2007-2012 = 256000

Total Number students who cleared the entrance test  from 2007-2012 = 32000

6. What was the ratio of the number of students appeared for the entrance exam in 2012 and the number of students who cleared the exam in 2007 respectively?
(1) 8 : 1
(2) 36 : 5
(3) 72 : 5
(4) 18 : 10
(5) None of these

7. The total number of students appeared in entrance exam from 2008 and 2011 was what percentage of number of students appeared for the entrance exam in 2009?
(1) 120
(2) 150
(3) 125
(4) 80 
(5) None of these

8. Approximately what was the difference between the number of students who cleared the entrance exam in 2009 and number of students who cleared the entrance exam in 2007?
(1) 960
(2) 1920
(3) 3200
(4) 5120
(5) None of these

9. For which year  was the difference in the number of students selected to number of students appeared in entrance exam the maximum?
(1) 2008 
(2) 2007 
(3) 2010
(4) 2009
(5) None of these

10. The total number of students who cleared the exam from all years together is what percent of the total number of students appeared for the exam in all years together?
(1) 17.5%
(2) 15%
(3) 22.5%
(4) 12.5%
(5) None of these

11. The number of candidates who cleared the entrance exam in 2008 is approximately how much percent of the total number of students who appeared for the exam in the same year?
(1) 12
(2) 18
(3) 15
(4) 8
(5) 5

12. Approximately what was the total number of students cleared the entrance exam in 2010 and 2009 together?
(1) 6400
(2) 15200
(3) 115200
(4) 7920
(5) None of these



ANSWERS

Solutions (1-3)

1. (3)

Required probability = (3C3 + 6C3)/13C3 = 21/286

2. (1)

Required probability = 6C2/13C2 = 5/26

3. (5)

Required probability = 1 – Probability that none is yellow

= 1 - 9C3/13C3 = 101/143

Solutions (4-5)

4. (4)

Required number of ways =  4C3 * 8C2 + 4C4 * 8C1 = 120

5. (1)

Required number of ways = 4C2 * 5C3 = 60

Solutions 

6. (3)

Required ratio = 18%of256000/10% of 32000  = 72 : 5

7. (3)

Required percentage = (15 + 10)/20 * 100 = 125%

8. (2)

Required difference = (16 – 10)% of 32000 = 1920

9. (3)

The difference between number of students selected to number of students appeared in entrance exam in 2007

= 12 % of 256000 – 10% of 32000 = 27520

Similarly calculating for all years, the maximum difference will be for 2010.

10. (4)

Required percentage = 32000/256000 * 100 = 12.5%

11. (1)

Required percentage = 14% of 32000/ 15% of 256000 * 100  = 11.67

12. (5)

Required number = (20 + 16)% of 32000 = 11520