CAT 2025 Question Paper | Quant Slot 1

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 4 : In the set of consecutive odd numbers \(\{1,3,5, \ldots, 57\}\), there is a number \(k\) such that the sum of all the elements less than \(k\) is equal to the sum of all the elements greater than \(k\). Then, \(k\) equals

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Video Explanation

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Explanatory Answer

\(1,3,5,\ldots,57\)
\(n=\frac{57-1}{2}+1=29\)
Total Sum = \(29^2=841\)

Let \(k=2m-1\).

Sum less than \(k = (m-1)^2\)
Sum more than \(k = 841-m^2-(2m-1)\)

\((m-1)^2=841-m^2-(2m-1)\)
\(2(m-1)^2+2m-1=841\)
\(m^2-m-420=0\)
\((m-21)(m+20)=0\)
\(m=21\)

\(k=2(21)-1=41\)

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The answer is '41'

Choice 1 is the correct answer.

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