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

$$\begin{array}{l} \text { Let }(x+6 \sqrt{ } 2)^{1 / 2}=a+b \sqrt{ } c \text { and }(x-6 \sqrt{ } 2)^{1 / 2}=a-b \sqrt{ } c \text {. } \\ a+b \sqrt{ } c-a+b \sqrt{ }=2 \sqrt{ } 2 \\ 2 b \sqrt{ } c=2 \sqrt{ } 2 \\ b=1 \text { and } c=\sqrt{ } 2 \\ (a+\sqrt{ } 2)^2=x+6 \sqrt{ } 2 \\ a^2+2+2 a \sqrt{ } 2=x+6 \sqrt{ } 2 \\ (3+\sqrt{ } 2)^2=11+6 \sqrt{ } 2 \\ (3-\sqrt{ } 2)^2=11-6 \sqrt{ } 2 \end{array}$$ 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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