**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 – x^{2}> 10000

1000 + 10x – x^{2}> 0

x^{2} – 10x – 1000 < 0

x^{2} – 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**

### Related posts

- January 16, 2013 CAT – Percentages
This is an interesting question from Percentages. Simple framework, but finding the answer is not that easy
Question
A is x% more than B and is x% of sum of A and B. What is […] Posted in Percentages
- July 30, 2013 CAT – Percentages
Percentages Question
Question:
An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7. These two alloys are mixed in […] Posted in Percentages
- May 23, 2013 CAT Counting: Question with digits
This is an interesting question from Counting. Simple framework, but one needs to be very careful with the enumeration. One can get wrong answers in a number of […] Posted in Combinatorics
- August 6, 2013 CAT – Trigonometry Questions
Question:
3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?
A. 5
B. -5
C. 4
D. 3
Correct Answer: […] Posted in Trigonometry