CAT 2021 Question Paper | Quant Slot 1

CAT Previous Year Paper | CAT Quant Questions | Question 1

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 1 : f(x) = \\frac{x^{2}+2 x-15}{x^{2}-7 x-18}) is negative if and only if

  1. -5 < x < -2 or 3 < x < 9
  2. -2 < x < 3 or x > 9
  3. x < -5 or 3 < x < 9
  4. x < -5 or -2 < x < 3

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Explanatory Answer

f(x) = \\frac{x^{2}+2 x-15}{x^{2}-7 x-18})
f(x) = \\frac{(x+5)(x-3)}{(x-9)(x+2)})
-5, -2, 3, 9 are the roots of the function f(x).
Q1 graph - roots
Keeping these roots on the number line and checking for the range where f(x) becomes negative.
For the numbers below -5, f(x) is positive.
For the numbers between -5 and -2, the value f(x) is negative.
For the numbers between -2 and 3, the value of f(x) is positive.
For the numbers between 3 and 9, the value of f(x) is negative.
For the numbers above 9, the value of f(x) is positive.
Hence the range should be -5 < x < -2 and 3 < x < 9.


The question is " f(x) = \\frac{x^{2}+2 x-15}{x^{2}-7 x-18}) is negative if and only if "

Hence, the answer is '-5 < x < -2 or 3 < x < 9'

Choice A is the correct answer.

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