CSAT Solved Papers/ 2025/Q68

2025 CSAT — Q68

Quant Data sufficiency 2.5 marks Medium

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 Answer

Worked rationale

First answer the question itself, ignoring the statements. Among the $1$ -digit numbers $1$ – $9$ , which have exactly $4$ distinct factors?

$6 = 2 \times 3$ : factors $\{1, 2, 3, 6\}$ — exactly $4$ . ✓
$8 = 2^3$ : factors $\{1, 2, 4, 8\}$ — exactly $4$ . ✓
(No other single digit qualifies: primes have $2$ factors, $4$ and $9$ have $3$ , etc.)

The candidates are $6$ and $8$ ; the smallest is $6$ . This is a fixed mathematical fact — it is already determined by the question alone, with no statement needed.

Statements I ( $2$ is a factor) and II ( $3$ is a factor) are both true of $6$ , but they add nothing: the answer was $6$ before we read them.

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

Why the other options miss

A

thought a statement was needed when the question stands alone: treats the statements as necessary to narrow $\{6, 8\}$ , not seeing that “smallest” already picks $6$ unaided.
B

called a statement “sufficient” when none is even needed: notes each statement is consistent with $6$ and calls each “sufficient,” when in fact neither is needed.
C

combined statements the question never required: the engineered trap — Statement I admits $\{6,8\}$ , Statement II admits $\{6\}$ , so a student “combines” them to land on $6$ and picks (c), never checking whether the question was self-contained from the start.

Specialist insight

The gold DS reflex that this item rewards is answer the question on its own first. A well-posed “smallest such number” question often has a unique answer before any statement is consulted; the statements are then decoys. Here “smallest $1$ -digit number with exactly $4$ factors” is fully determined ( $= 6$ ), so the correct code is the one almost everyone overlooks — (d), “answerable without any statement.” Train yourself to test self-sufficiency before testing the statements: if the question pins a value alone, neither “alone,” “either,” nor “both” can be right. The −1/3 marking pays for catching that the statements were never load-bearing.

The trap, in one line

The question is self-contained: "smallest $1$ -digit number with $4$ factors" is uniquely $6$ before any statement — so the answer is (d), not the "both together" (c) decoy.

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