What is the value of the real number k? (1) 4k - 8 = 12 (2) k^2 = 25 — GMAT

What is the value of the real number $k$ ?

(1) $4k - 8 = 12$
(2) $k^2 = 25$

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.

Solving Statement (1) gives

4k = 20

, which simplifies to

k = 5

. Because this is a single, unique value, Statement (1) alone is sufficient. Statement (2) gives

k^2 = 25

, which has two valid solutions (

k = 5

k = -5

). Without additional constraints, Statement (2) alone is not sufficient to determine a single value for

k

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

Evaluate Statement (1) independently

4k - 8 = 12 \implies 4k = 20 \implies k = 5

Solving the linear equation gives a single, unique value for

k

. Thus, Statement (1) alone is sufficient.

Evaluate Statement (2) independently

k^2 = 25 \implies k = 5

k = -5

Taking the square root yields two distinct possible values for

k

. Because

k

cannot be uniquely determined, Statement (2) alone is not sufficient.

Select the Data Sufficiency decision key

Statement (1) is sufficient, but Statement (2) is not.

This corresponds to the standard option where Statement (1) alone is sufficient.

Linear vs. Quadratic Degree Sufficiency in Data Sufficiency

Question