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 3 : The number of distinct integers \(n\) for which \(\log _{\left(\frac{1}{4}\right)}\left(n^2-7 n+11\right)>0\), is

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Video Explanation

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Explanatory Answer

\(\log_{\frac{1}{4}}(n^2-7n+11)>0\)

Since the base is less than 1:
\(n^2-7n+11>0\)
\(n^2-7n+11<\left(\frac{1}{4}\right)^0\)
\(n^2-7n+11<1\)
\(n^2-7n+10<0\)
\((n-2)(n-5)<0\)
\(2
\(n=3,\ n=4\)

For \(n=3\):
\(n^2-7n+11=-1\) ie < 0
this solution not possible.

For \(n=4\):
\(n^2-7n+11=-1\) ie < 0
this solution not possible.

Therefore no solutions.

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The question is " The number of distinct integers \(n\) for which \(\log _{\left(\frac{1}{4}\right)}\left(n^2-7 n+11\right)>0\), is "

Hence, the answer is '0'

Choice 2 is the correct answer.

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