CAT - Percents

Question: 

 

P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the range of values x can take?

A.  10% to 28%

B.  10% to 25%

C.  10% to 37%

D.  10% to 43% 

Correct Answer: (C)

Explanation:

P = Q

Q = R

R =

P > R

(100 + x) (110 – x) > 100 x 100

11,000 + 110x – 100x – x² > 10000

1000 + 10x – x² > 0

x² – 10x – 1000 < 0

x² – 10x + 25 < 1000 + 25

(x – 5)² < 1025

x – 5 < 32

x < 37

x could range from 10% to 37%

Answer Choice (C)

Difficulty level II