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

The question asks for the smallest 1-digit number having exactly 4 distinct factors.

Let's find this number by checking 1-digit numbers:

• 1 has 1 factor (1)
• 2 has 2 factors (1, 2)
• 3 has 2 factors (1, 3)
• 4 has 3 factors (1, 2, 4)
• 5 has 2 factors (1, 5)
• 6 has 4 factors (1, 2, 3, 6)
• 7 has 2 factors (1, 7)
• 8 has 4 factors (1, 2, 4, 8)
• 9 has 3 factors (1, 3, 9)

The 1-digit numbers with exactly 4 distinct factors are 6 and 8. The smallest among these is 6.

Therefore, the answer to the question "What is the smallest 1-digit number having exactly 4 distinct factors?" is 6.

We were able to determine this answer (6) by directly analyzing the 1-digit numbers and their factors, without using any information from Statement I or Statement II.

Let's briefly analyze the statements, though not strictly necessary for option D: Statement I: 2 is one of the factors.

• If the number is 6, 2 is a factor.
• If the number is 8, 2 is a factor. This statement alone would not uniquely identify 6 as the smallest, as both 6 and 8 satisfy having 2 as a factor and 4 distinct factors.

Statement II: 3 is one of the factors.

• If the number is 6, 3 is a factor.
• If the number is 8, 3 is NOT a factor. This statement alone would uniquely identify 6 as the answer among the candidates (6 and 8).

However, the core point is that the original question can be solved independently.

Option D states: The Question can be answered even without using any of the Statements. As shown above, we found the answer to be 6 by direct calculation, without needing Statement I or Statement II. Hence, option D is correct.

The final answer is D.