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IPMAT Indore 2025 · Question 34 of 90 · Quantitative Ability (MCQ)

IPMAT Indore 2025 — Question 34

The set of all values of $x$ satisfying the inequality $lo g_{(x + 1/ x)} [lo g_{2} (\frac{x - 1}{x + 2})] > 0$ is

ANull set
B $(2, 5)$
C $(5, \infty)$
D $(- 5, - 2)$

Reveal answer

Correct answer

A.Null set

Reveal solution

For $x + 1/ x > 0$ , need $x > 0$ . For the inner $lo g_{2} [(x - 1) / (x + 2)] > 1$ , need $(x - 1) / (x + 2) > 2$ , which leads to $(x + 5) (x + 2) < 0$ , i.e., $- 5 < x < - 2$ . The two conditions contradict, so the solution set is empty.

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