CAT 2025 Slot 1 QA Q5 Number Systems

Question 5 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 6 Number Systems TITA

Solution

  1. Non-zero digits that are not perfect squares: 2, 3, 5, 6, 7, 8 (1, 4 and 9 are excluded).
  2. Primes among them: 2, 3, 5, 7. Non-primes: only 6 and 8. With exactly one prime digit, the other two digits must be 6 and 8.
  3. The smallest such number is 268, using the smallest prime 2 as the hundreds digit.
  4. \(268 = 2^2 \times 67\), so it has \((2+1)(1+1) = 6\) factors.

More Number Systems questions from CAT

All 40 Number Systems questions asked since 2017.