CAT Quantitative Aptitude Questions | CAT Percentage Questions - Variables

The question is from CAT Percentages. CAT exam is known to test application and understanding of ideas. Solve this question to get better at percentages CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. Percentages is an important topic for CAT. Add x and y to simple topics and then they take a sinister hue. This question is a classic example.

Question 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%

Explanatory Answer

Method of solving this CAT Question from Percentages - Variables: Compare P, Q and R.

P = Q ( 1 + \\frac{x}{100}\\))
Q = R ( 1 − \\frac{x - 10}{100}\\))
R = Q / ( 1 − \\frac{x - 10}{100}\\))
P > R
Q ( 1 + \\frac{x}{100}\\)) > Q / ( 1 − \\frac{x-10}{100}\\))
1 + \\frac{x}{100}\\) > 1 / (\\frac{100-x+10}{100}\\))
\\frac{100 + x}{100}\\) > \\frac{100}{110 - x}\\)
(100 + x) (110 – x) > 100 * 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

The question is "what is the range of values x can take?"
x could range from 10% to 37%

Hence, the answer is 10% to 37%.

Choice C is the correct answer.