If u and v are real numbers, what is the value of u + 2v? (1) 3u + 6v = 15 (2) u^2 - 4v^2 … — GMAT

If $u$ and $v$ are real numbers, what is the value of $u + 2v$ ?

(1) $3u + 6v = 15$
(2) $u^2 - 4v^2 = 0$

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.

Dividing Statement (1) by 3 directly gives

u + 2v = 5

, providing a unique numerical answer. Statement (2) permits multiple values for

u + 2v

because

(u - 2v)(u + 2v) = 0

only guarantees that at least one factor is zero, not necessarily

u + 2v = 0

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

Analyze Statement (1) algebraically.

The equation is

3u + 6v = 15

. Factoring out 3 gives

3(u + 2v) = 15

. Dividing both sides by 3 yields

u + 2v = 5

This determines a unique, definitive numerical value for the target expression

u + 2v

. Therefore, Statement (1) alone is sufficient.

Analyze Statement (2) independently.

The equation

u^2 - 4v^2 = 0

factors as

(u - 2v)(u + 2v) = 0

This statement implies that either

u + 2v = 0

u - 2v = 0

. If

u = 4

and

v = 2

, then

u - 2v = 0

and

u + 2v = 8

. If

u = 0

and

v = 0

, then

u + 2v = 0

. Since

u + 2v

can take multiple values, Statement (2) alone is not sufficient.

Algebraic Expression Simplification and Unique Determination in Data Sufficiency

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