If n is a real number, is n > 5? (1) n^2 + 6n + 9 = 0 (2) n^2 = 36 — GMAT

If $n$ is a real number, is $n > 5$ ?

(1) $n^2 + 6n + 9 = 0$
(2) $n^2 = 36$

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.

Statement (1) yields

n = -3

, which definitively answers 'No' to the question of whether

n > 5

. In GMAT Data Sufficiency Yes/No questions, a single conclusive 'No' answer makes a statement sufficient. Statement (2) gives

n = 6

n = -6

, leading to both 'Yes' and 'No' answers, making it insufficient. Thus, Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Rephrase the question stem target.

The target is a Yes/No question: 'Is

n > 5

?' A statement is sufficient if it allows us to answer either a conclusive 'Yes' for all valid values or a conclusive 'No' for all valid values.

In Data Sufficiency Yes/No questions, both a definitive 'Yes' and a definitive 'No' constitute sufficiency.

Evaluate Statement (1) independently.

n^2 + 6n + 9 = 0 \Rightarrow (n + 3)^2 = 0 \Rightarrow n = -3

. Testing

n = -3

against

n > 5

gives a definitive 'No'. Therefore, Statement (1) ALONE is sufficient.

Since

n = -3

produces a unique answer ('No') to the question stem, Statement (1) is sufficient.

Evaluate Statement (2) independently.

n^2 = 36 \Rightarrow n = 6

n = -6

. If

n = 6

6 > 5

('Yes'). If

n = -6

-6 \ngtr 5

('No'). Since we get both 'Yes' and 'No', Statement (2) ALONE is not sufficient.

Multiple conflicting answers to a Yes/No question mean the statement cannot conclusively answer the question.

Value vs. Yes/No Data Sufficiency Decision Logic

Question