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 ?
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
- (b) The Question can be answered by using either Statement alone.
- (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- (d) The Question can be answered even without using any of the Statements. ✓ UPSC's answer
Why the answer is (d)
• The question asks for the smallest 1-digit number with exactly 4 distinct factors.
• The factors of 1 are {1}, so it has 1 factor.
• The factors of 2 are {1, 2}, so it has 2 factors.
• The factors of 3 are {1, 3}, so it has 2 factors.
• The factors of 4 are {1, 2, 4}, so it has 3 factors.
• The factors of 6 are {1, 2, 3, 6}, so it has exactly 4 distinct factors.
• Since 6 is the smallest 1-digit number satisfying the condition, the answer can be determined purely by mathematical enumeration without needing Statement I or Statement II.
Why the other options are wrong
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered…
- The question is solvable without any statements, so it is not dependent on one statement alone.
- (b) The Question can be answered by using either Statement alone.
- The question is solvable without any statements, so it is not dependent on either statement alone.
- (c) The Question can be answered by using both the Statements together, but cannot be…
- The question is solvable without any statements, so it does not require both statements together.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.