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 13 If \((x+6 \sqrt{2})^{\frac{1}{2}}-(x-6 \sqrt{2})^{\frac{1}{2}}=2 \sqrt{2}\), then \(x\) equals

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Video Explanation

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Explanatory Answer

\[ \begin{array}{l} \text { Let }(x+6 \sqrt{2})^{1 / 2}=a+b \sqrt{c} \text { and }(x-6 \sqrt{2})^{1 / 2}=a-b \sqrt{c} \text {. } \\ a+b \sqrt{c}-a+b \sqrt{c}=2 \sqrt{2} \\ 2 b \sqrt{c}=2 \sqrt{2} \\ b=1 \text { and } c=2 \\ (a+\sqrt{2})^2=x+6 \sqrt{2} \\ a^2+2+2 a \sqrt{2}=x+6 \sqrt{2} \\ (3+\sqrt{2})^2=11+6 \sqrt{2} \\ (3-\sqrt{2})^2=11-6 \sqrt{2} \end{array} \] Therefore, the value of \(x=11\)

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The question is "If \((x+6 \sqrt{2})^{\frac{1}{2}}-(x-6 \sqrt{2})^{\frac{1}{2}}=2 \sqrt{2}\), then \(x\) equals "

Hence, the answer is '11'

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