If k is a real number, is k > 0? (1) k^2 + 5k + 6 = 0 (2) |k| = 2 — GMAT

If $k$ is a real number, is $k > 0$ ?

(1) $k^2 + 5k + 6 = 0$
(2) $|k| = 2$

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.

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

The correct option states that Statement (1) alone is sufficient while Statement (2) alone is not. Factoring Statement (1) yields

k = -2

k = -3

. Since both values are negative, we can definitively answer 'No' to whether

k > 0

, making Statement (1) sufficient. In contrast, Statement (2) yields

k = 2

k = -2

, giving both 'Yes' and 'No' as possible outcomes, which makes Statement (2) insufficient.

Analyze the question stem to identify the target logic

The target is a Yes/No question: 'Is

k > 0

?' A statement is sufficient if it yields a definitive 'Yes' OR a definitive 'No'.

In Data Sufficiency Yes/No questions, a consistent negative answer is completely sufficient.

Evaluate Statement (1):

k^2 + 5k + 6 = 0

Factoring gives

(k + 2)(k + 3) = 0

, so

k = -2

k = -3

. In either case,

k

is not greater than 0. The answer to 'Is

k > 0

?' is a definitive 'No'.

Since every possible value of

k

yields the answer 'No', Statement (1) is ALONE sufficient.

Evaluate Statement (2):

|k| = 2

Solving gives

k = 2

k = -2

. If

k = 2

, the answer is 'Yes'. If

k = -2

, the answer is 'No'.

Because Statement (2) allows both 'Yes' and 'No' answers, it is NOT sufficient.

Value vs. Yes/No Data Sufficiency Decision Logic

Question