CAT Quantitative Aptitude Questions | CAT Percentage Questions - Variables

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CAT Quantitative Aptitude
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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.