Is the integer n odd? (1) n is a multiple of 4. (2) n > 5 — GMAT

Is the integer $n$ odd?

(1) $n$ is a multiple of 4.
(2) $n > 5$

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Answer
B
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D
EACH statement ALONE is sufficient.
E
Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (1) tells us that

n

is a multiple of 4, which guarantees that

n

is even. This allows us to answer the question 'Is

n

odd?' with a definitive and unambiguous 'No'. In Data Sufficiency Yes/No questions, a consistent 'No' answer means the statement is sufficient. Statement (2) allows

n

to be 6 (even) or 7 (odd), yielding both 'No' and 'Yes' responses, so it is insufficient. Therefore, the statement stating that Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient, is the correct choice.

Step-by-Step Solution

Understand the decision rule for Yes/No Data Sufficiency questions.

A statement is sufficient if it yields a consistent 'Yes' OR a consistent 'No'. It is insufficient only if it yields 'Yes' for some values and 'No' for others.

Data Sufficiency requires determinacy, not necessarily an affirmative response.

Evaluate Statement (1):

n

is a multiple of 4.

Any multiple of 4 can be written as

n = 4k

for some integer

k

, which is divisible by 2 and therefore even. Since

n

is even, the answer to 'Is

n

odd?' is a definitive 'No'.

Since the answer is always 'No', Statement (1) alone is SUFFICIENT.

Evaluate Statement (2):

n > 5

n = 6

n

is even (Answer: No). If

n = 7

n

is odd (Answer: Yes). Since both 'Yes' and 'No' are possible, Statement (2) alone is INSUFFICIENT.

Statement (2) does not fix the parity of

n

Key Concept

In Yes/No Data Sufficiency questions, a statement that conclusively answers 'No' to the question stem is SUFFICIENT.

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