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UPSC Prelims 2025 CSAT, question 68

Topic: Data sufficiency

Q68

A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question :

What is the smallest 1-digit number having exactly 4 distinct factors ?

Statement-I : 2 is one of the factors.

Statement-II : 3 is one of the factors.

Which one of the following is correct in respect of the above Question and the Statements ?

  1. (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
  2. (b) The Question can be answered by using either Statement alone.
  3. (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. (d) The Question can be answered even without using any of the Statements.Correct answer

Solution.

Answer: (d) The Question can be answered even without using any of the Statements.

  1. A number has prime factorization p3p^3 or p×qp \times q to have exactly 44 distinct factors; among 1-digit natural numbers (11 to 99), the only numbers with 44 factors are 66 (1,2,3,61, 2, 3, 6) and 88 (1,2,4,81, 2, 4, 8).
  2. The smallest 1-digit number having 44 distinct factors is uniquely 66 from the Question stem alone, so the Question can be answered even without using any of the Statements.