CAT 2024 Question Paper | Quant Slot 2

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 20 All the values of \(x\) satisfying the inequality \(\frac{1}{x+5} \leq \frac{1}{2 x-3}\) are

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Video Explanation

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Explanatory Answer

\[ \begin{array}{l} 1 /(2 x-3)-1 /(x+5) \geq 0 \\ (x+5-2 x+3) /(2 x-3)(x+5) \geq 0 \\ (8-x) / 2(x-(3 / 2))(x+5) \geq 0 \\ (x-8) /(x-(3 / 2))(x+5) \leq 0 \end{array} \] The values of \(x\) satisfying the inequality : \(x<-5\) or \(3 / 2

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The question is "All the values of \(x\) satisfying the inequality \(\frac{1}{x+5} \leq \frac{1}{2 x-3}\) are"

Hence, the answer is '\(x<-5\) or \(\frac{3}{2}

Choice B is the correct answer.

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