If m and n are positive integers, is m an even integer? (1) m + n is an odd integer. (2) n… — GMAT

If $m$ and $n$ are positive integers, is $m$ an even integer?

(1) $m + n$ is an odd integer.
(2) $n = 5$

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Neither statement alone determines the parity of

m

. However, combining Statement (1) (

m+n

is odd) and Statement (2) (

n=5

, an odd integer) proves that

m

must be an even integer. Therefore, both statements together are sufficient.

Analyze Statement (1) independently.

Statement (1) states that

m + n

is odd. For the sum of two integers to be odd, one integer must be even and the other must be odd. If

n

is odd,

m

is even (Yes). If

n

is even,

m

is odd (No). Since the parity of

n

is unknown, Statement (1) alone is NOT sufficient.

Determining sufficiency requires a unique Yes or No answer.

Analyze Statement (2) independently, ignoring Statement (1).

Statement (2) states that

n = 5

. This gives no information about

m

. Thus, Statement (2) alone is NOT sufficient.

Statement 2 must be evaluated strictly without carrying over information from Statement 1.

Combine Statement (1) and Statement (2).

From Statement (2),

n = 5

, which is an odd integer. Substituting

n = 5

into Statement (1),

m + 5

is odd. Since an odd integer added to an even integer yields an odd integer,

m

must be even. This provides a definitive 'Yes' answer.

Combining both statements provides enough information to uniquely answer the question.

Statement Independence and Combination in Data Sufficiency

Question