CAT 2025 Question Paper | Quant Slot 2

CAT Questions

CAT 2025 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 14 : The set of all real values of \( x \) for which \( \left( x ^ { 2 } - | x + 9 | + x \right) > 0 \), is

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Video Explanation

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Explanatory Answer

Case 1 \((x\geq-9)\)
\(|x+9|=x+9\)
\(x^2-(x+9)+x>0\Rightarrow x^2-9>0\Rightarrow(x-3)(x+3)>0\)
For \(x\geq-9\), this holds for \(x\in[-9,-3)\cup(3,\infty)\).

Case 2 \((x\leq-9)\)
\(|x+9|=-(x+9)\)
\(x^2-(-(x+9))+x>0\Rightarrow x^2+2x+9>0\)

Completing the square gives \((x+1)^2+8>0\), which is true for all real \(x\).
For \(x\leq-9\), this holds for \(x\in(-\infty,-9]\).

Combine solution intervals
Solution Set \(=(-\infty,-9]\cup[-9,-3)\cup(3,\infty)=(-\infty,-3)\cup(3,\infty)\)

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The question is " The set of all real values of \( x \) for which \( \left( x ^ { 2 } - | x + 9 | + x \right) > 0 \), is "

Hence, the answer is '\( ( - \infty , - 3 ) \cup ( 3 , \infty ) \)'

Choice 2 is the correct answer.

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