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 20 : The sum of digits of the number \( ( 625 ) ^ { 65 } \times ( 128 ) ^ { 36 } \), is

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Video Explanation

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Explanatory Answer

Convert to powers of 2 and 5

\((625)^65=(5^4)^65=5^{260}\)
\((128)^36=(2^7)^{36}=2^{252}\)

\(N=5^{260}\times2^{252}=5^8\times(5^{252}\times2^{252})\)
\(=5^8\times10^{252}\)

Calculate \(5^8\)
\(5^8=(5^4)^2=625^2=390625\)

So, \(N=390625\times10^{252}=390625000\ldots000\) (followed by 252 zeros).

Calculate the sum of digits
Sum of digits \(=3+9+0+6+2+5=25\)

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The question is " The sum of digits of the number \( ( 625 ) ^ { 65 } \times ( 128 ) ^ { 36 } \), is "

Hence, the answer is '25'

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