CAT Practice : Percents, Profits

Add x and y to simple topics and then they take a sinister hue. This question is a classic example.

Percentages - Variables

    Q.2: 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?
    1. 10% to 28%
    2. 10% to 25%
    3. 10% to 37%
    4. 10% to 43%

 

  • Correct Answer
    Choice C. 10% to 37%

Detailed Solution

P =
Q =
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)

Correct Answer: 10% to 37%



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