If m is a real number, is m an even integer? (1) 2m is an even integer. (2) m + 1 is an od… — GMAT

If $m$ is a real number, is $m$ an even integer?

(1) $2m$ is an even integer.
(2) $m + 1$ is an odd integer.

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

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

Statement (1) allows

m

to be any integer because multiplying any integer by

2

results in an even integer. Therefore,

m

could be

3

(odd) or

4

(even), making Statement (1) insufficient. Statement (2) specifies that

m + 1

is an odd integer. Subtracting

1

from an odd integer always yields an even integer, so

m

must be an even integer. This provides a single, definitive 'Yes' answer, making Statement (2) alone sufficient.

Analyze the target question stem.

We need to determine whether

m

is an even integer, given that

m

is a real number.

Rephrasing the question clarifies that a definitive 'Yes' or definitive 'No' answer is required.

Evaluate Statement (1):

2m

is an even integer.

m = 4

, then

2m = 8

(even integer), and

m

is an even integer (Yes). If

m = 3

, then

2m = 6

(even integer), but

m

is an odd integer (No).

Since Statement (1) yields both 'Yes' and 'No' answers, Statement (1) is NOT sufficient.

Evaluate Statement (2):

m + 1

is an odd integer.

m + 1

is an odd integer, then

m = (m + 1) - 1

. An odd integer minus

1

is always an even integer.

This guarantees that

m

is an even integer, providing a definitive 'Yes'. Thus, Statement (2) ALONE is sufficient.

Parity and Integer Properties in Data Sufficiency

Question