Quant Quiz

1. A certain fraction is equivalent to 2/5 . If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3 . What is the sum of numerator and denominator of the original fraction?
(1) 49  
(2) 35
(3) 28  
(4) 26  
(5) 21


2. The population of city X increased from 650,000 in 2000 to 700,000 in 2010, and it is projected that the population will increase by the same number from 2010 to 2020. Approximately what is the projected percent increase in population from 2010 to 2020 ?
(1) 7.1%  
(2) 7.7%
(3) 8.3%
(4) 14.3%  
(5) 15.3%

3. Of  the science books in a certain supply room, 40 are on botany, 35 are on zoology, 30 are on physics, 40 are on geology, and 55 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 20 of the books removed are on the same science subject?
(1) 81  
(2) 79  
(3) 96  
(4) 85  
(5) 100

4. In how many different ways, letters of the word MANPOWER be arranged such that all vowels are together?
(1) 360  
(2) 4320
(3) 1440
(4) 2160
(5) 40320

5. On a certain test, 3 students each had a score of 90, 9 students each had a score of 80, 4 students each had a score of 70, and 4 students each had a score of 60. What was the average (arithmetic mean) score for the 20 students ?
(1) 70.5  
(2) 75.0  
(3) 75.5
(4) 80.0  
(5) 80.5

Answers
1. (5)
Let the numerator and denominator be 2x and 5x. Now
(2x + 4)/10 = 1/3
X = 3.
Required sum = 2x + 5x = 7x = 21

2. (1)
Required percentage = (750000 - 700000)/700000 * 100 = 7.14%

3. (3)
Number of books to be removed = 19 5 +1  = 96

4. (2)
Number of arrangements = 3! *  6! = 4320

5. (3)
Total score of students = 3 * 90 + 9 * 80 + 4 * 70 + 4 * 60 = 1510
Required average = 1510/20  =  75.5