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? 1. Statement I: 2 is one of the factors. 2. Statement II: 3 is one of the factors. Which one of the following is correct in respect of the above Question and the Statements?

Correct Option (4) The question requires identifying the smallest 1-digit number possessing exactly 4 distinct factors. A systematic enumeration of 1-digit numbers (1 through 9) and their corresponding factors reveals the following: - Numbers with 1 factor: 1 ({1}) - Numbers with 2 factors: 2 ({1, 2}), 3 ({1, 3}), 5 ({1, 5}), 7 ({1, 7}) - Numbers with 3 factors: 4 ({1, 2, 4}), 9 ({1, 3, 9}) - Numbers with 4 factors: 6 ({1, 2, 3, 6}), 8 ({1, 2, 4, 8}) From this analysis, the 1-digit numbers with exactly 4 distinct factors are 6 and 8. The smallest among these is 6. Since the answer (6) can be definitively determined through direct analysis of 1-digit numbers, the question can be answered without relying on either Statement I or Statement II. Incorrect Options: The question can be answered by direct analysis, rendering the statements unnecessary. - Option 1: The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone. - Statement I (2 is one of the factors): Both 6 and 8 satisfy this condition. Since both 6 and 8 have exactly 4 distinct factors, Statement I alone is insufficient to uniquely identify the smallest number (6). - Statement II (3 is one of the factors): Among the numbers with exactly 4 distinct factors (6 and 8), only 6 has 3 as a factor. Thus, Statement II alone is sufficient to identify 6. - While Statement II is sufficient, the overarching fact that the question can be answered without any statement makes this option incorrect. - Option 2: The Question can be answered by using either Statement alone. - As established, Statement I is insufficient because it applies to both 6 and 8. Therefore, this option is incorrect. - Option 3: The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. - Statement II alone is sufficient to identify the number as 6. Therefore, it is not accurate to state that neither statement alone is sufficient or that both statements are required. This option is incorrect.

IAS 2025 — CSAT Reasoning

2025mcqmedium

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?

Official previous-year question

Verified 2 Aug 2026.

Options

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
BThe Question can be answered by using either Statement alone.
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
DThe Question can be answered even without using any of the Statements.

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Solution

Correct Option (4)

The question requires identifying the smallest 1-digit number possessing exactly 4 distinct factors. A systematic enumeration of 1-digit numbers (1 through 9) and their corresponding factors reveals the following:

Numbers with 1 factor: 1 ({1})
Numbers with 2 factors: 2 ({1, 2}), 3 ({1, 3}), 5 ({1, 5}), 7 ({1, 7})
Numbers with 3 factors: 4 ({1, 2, 4}), 9 ({1, 3, 9})
Numbers with 4 factors: 6 ({1, 2, 3, 6}), 8 ({1, 2, 4, 8})

From this analysis, the 1-digit numbers with exactly 4 distinct factors are 6 and 8. The smallest among these is 6. Since the answer (6) can be definitively determined through direct analysis of 1-digit numbers, the question can be answered without relying on either Statement I or Statement II.

Incorrect Options:

The question can be answered by direct analysis, rendering the statements unnecessary.

Option 1: The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
- Statement I (2 is one of the factors): Both 6 and 8 satisfy this condition. Since both 6 and 8 have exactly 4 distinct factors, Statement I alone is insufficient to uniquely identify the smallest number (6).
- Statement II (3 is one of the factors): Among the numbers with exactly 4 distinct factors (6 and 8), only 6 has 3 as a factor. Thus, Statement II alone is sufficient to identify 6.
- While Statement II is sufficient, the overarching fact that the question can be answered without any statement makes this option incorrect.
Option 2: The Question can be answered by using either Statement alone.
- As established, Statement I is insufficient because it applies to both 6 and 8. Therefore, this option is incorrect.
Option 3: The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- Statement II alone is sufficient to identify the number as 6. Therefore, it is not accurate to state that neither statement alone is sufficient or that both statements are required. This option is incorrect.

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Correct Option (4)

Numbers with 1 factor: 1 ({1})
Numbers with 2 factors: 2 ({1, 2}), 3 ({1, 3}), 5 ({1, 5}), 7 ({1, 7})
Numbers with 3 factors: 4 ({1, 2, 4}), 9 ({1, 3, 9})
Numbers with 4 factors: 6 ({1, 2, 3, 6}), 8 ({1, 2, 4, 8})

Incorrect Options:

The question can be answered by direct analysis, rendering the statements unnecessary.

Option 1: The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
- Statement I (2 is one of the factors): Both 6 and 8 satisfy this condition. Since both 6 and 8 have exactly 4 distinct factors, Statement I alone is insufficient to uniquely identify the smallest number (6).
- Statement II (3 is one of the factors): Among the numbers with exactly 4 distinct factors (6 and 8), only 6 has 3 as a factor. Thus, Statement II alone is sufficient to identify 6.
- While Statement II is sufficient, the overarching fact that the question can be answered without any statement makes this option incorrect.
Option 2: The Question can be answered by using either Statement alone.
- As established, Statement I is insufficient because it applies to both 6 and 8. Therefore, this option is incorrect.
Option 3: The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- Statement II alone is sufficient to identify the number as 6. Therefore, it is not accurate to state that neither statement alone is sufficient or that both statements are required. This option is incorrect.

IAS 2025 — CSAT Reasoning

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Correct Option (4)

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IAS 2025 — CSAT Reasoning

Options

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Solution

Correct Option (4)

Incorrect Options:

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More IAS Reasoning questions

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