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 3 If \(m\) and \(n\) are natural numbers such that \(n>1\), and \(m^n=2^{25} \times 3^{40}\), then \(m-n\) equals

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Video Explanation

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Explanatory Answer

\(\begin{aligned} 2^{25} \times 3^{40} & =\left(2^5 \times 3^8\right)^5 \\ & =\left(32^{* 6561}\right)^5 \\ & =(209952)^5=m^n \\ m-n= & 209952-5=209947\end{aligned}\)

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The question is "If \(m\) and \(n\) are natural numbers such that \(n>1\), and \(m^n=2^{25} \times 3^{40}\), then \(m-n\) equals"

Hence, the answer is '209947'

Choice C is the correct answer.

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