If a and b are non-zero real numbers, what is the value of \frac{a}{b}? (1) 5a - 3b = 0 (2… — GMAT

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

(1) $5a - 3b = 0$
(2) $a + b = 8$

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 to determine the value of

\frac{a}{b}

, but statement (2) alone is not sufficient.

Statement (1) can be rearranged algebraically to

5a = 3b

, which directly gives

\frac{a}{b} = \frac{3}{5}

, providing a single definitive value. Statement (2),

a + b = 8

, allows infinitely many pairs of

(a, b)

yielding different ratios for

\frac{a}{b}

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

Rephrase the question stem target

The target is to find a numerical value for the ratio

\frac{a}{b}

Simplifying the target helps determine if an equation directly yields the ratio without needing individual variable values.

Evaluate Statement (1) independently:

5a - 3b = 0

Rearranging gives

5a = 3b

. Dividing both sides by

5b

(since

b \neq 0

) yields

\frac{a}{b} = \frac{3}{5}

This yields a single, unique numerical value for the target expression. Thus, Statement (1) alone is sufficient.

Evaluate Statement (2) independently:

a + b = 8

a = 4

and

b = 4

, then

\frac{a}{b} = 1

. If

a = 2

and

b = 6

, then

\frac{a}{b} = \frac{1}{3}

Multiple values of the ratio

\frac{a}{b}

are possible. Thus, Statement (2) alone is not sufficient.

Determining ratios from homogeneous linear equations in Data Sufficiency

Question