If x and y are non-zero real numbers, what is the value of the ratio \frac{x}{y}? (1) x + … — GMAT

If $x$ and $y$ are non-zero real numbers, what is the value of the ratio $\frac{x}{y}$ ?

(1) $x + y = 10$
(2) $3x - 5y = 0$

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.

Evaluating Statement (2) independently of Statement (1) shows that the equation

3x - 5y = 0

can be rearranged to

3x = 5y

. Dividing both sides by

3y

(since

y \neq 0

) yields

\frac{x}{y} = \frac{5}{3}

. This gives a single, unique value for the target ratio without needing any information from Statement (1). Meanwhile, Statement (1) alone (

x + y = 10

) allows infinitely many pairs of non-zero real numbers

(x, y)

, resulting in different values for the ratio

\frac{x}{y}

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

Evaluate Statement (1) independently

Statement (1) gives

x + y = 10

. If

x = 5

and

y = 5

, then

\frac{x}{y} = 1

. If

x = 8

and

y = 2

, then

\frac{x}{y} = 4

Since multiple values are possible for the ratio

\frac{x}{y}

, Statement (1) alone is not sufficient.

Evaluate Statement (2) independently without carrying over information from Statement (1)

Statement (2) gives

3x - 5y = 0 \implies 3x = 5y \implies \frac{x}{y} = \frac{5}{3}

Since

y \neq 0

, dividing both sides by

3y

yields a single, unique value of

\frac{5}{3}

for the ratio

\frac{x}{y}

Conclude Data Sufficiency determination

Statement (2) alone is sufficient, whereas Statement (1) alone is not sufficient.

Statement (2) independently answers the question stem completely.

Evaluating Statement 2 independently of Statement 1 in Data Sufficiency

Question