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 5 : In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

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Video Explanation

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Explanatory Answer

Possible single digits from 1 to 9:
\(1,2,3,4,5,6,7,8,9\)

Removing non-zero digits that are perfect squares (1,4,9):
\(2,3,5,6,7,8\)

Among these, the prime digits are:
\(2,3,5,7\)

The non-prime digits are:
\(6,8\)

Since the number must contain only one prime digit and three distinct digits, we must choose two non-prime digits. Since only two non-prime digits (6 and 8) are available in our pool, both must be used. To minimize the value of \(N\), we choose the smallest available prime digit (2) and arrange all three digits in increasing order to form the smallest 3-digit number:

\(N=268\)

\(268=2^2\times67^1\)

Number of factors
\(=(2+1)(1+1)=3\times2=6\)

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The answer is '6'

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