CAT 2021 Slot 1 · Quant · Question 2

CAT 2021 Slot 1 previous year question on Inequalities & Modulus, with the answer and a step-by-step solution.

Inequalities & ModulusAlgebraMultiple choiceMedium
f\left( x \right)=\frac{{x}^{2}+2x-15}{{x}^{2}-7x-18} is negative if and only if
  1. A
    x<-5 or -2<x<3
  2. B
    -5<x<-2 or 3<x<9
  3. C
    -2<x<3 or x>9
  4. D
    x<-5 or 3<x<9
Pick an option, then check.
Answer & solution

Answer: Option B

Factorising, f\left( x \right)=\frac{\left( x+5 \right)\left( x-3 \right)}{\left( x-9 \right)\left( x+2 \right)},

so the critical points are x=-5,\,-2,\,3,\,9.

Checking the sign of f\left( x \right) on each interval,

f\left( x \right)<0 for -5<x<-2 and for 3<x<9.

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