An investor purchased a total of N shares split between Stock X and Stock Y. What percenta… — GMAT

An investor purchased a total of $N$ shares split between Stock $X$ and Stock $Y$ . What percentage of the total number of shares purchased were shares of Stock $X$ ?

(1) The number of shares of Stock $X$ purchased was $40\%$ of the number of shares of Stock $Y$ purchased.
(2) The investor purchased $120$ shares of Stock $Y$ .

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.

Answer

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

Statement (1) establishes a direct proportional relationship between the number of shares of Stock X and Stock Y (

X = 0.40Y

). Substituting this into the part-to-whole expression

\frac{X}{X+Y}

yields

\frac{0.40Y}{1.40Y} = \frac{2}{7}

, which provides a unique percentage without requiring the actual number of shares. Statement (2) provides only the absolute quantity of Stock Y (

120

), leaving the quantity of Stock X completely unknown and preventing the calculation of the percentage. Therefore, Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Step-by-Step Solution

Rephrase the target question algebraically.

The target is to find

\frac{X}{X + Y} \times 100\%

Determining the ratio

\frac{X}{Y}

is sufficient to find

\frac{X}{X + Y}

Evaluate Statement (1).

Statement (1) gives

X = 0.40Y

, which means

\frac{X}{Y} = \frac{2}{5}

. Therefore,

\frac{X}{X + Y} = \frac{0.40Y}{1.40Y} = \frac{2}{7}

, giving a unique percentage of

\frac{200}{7}\%

Since a single unique value is obtained, Statement (1) is sufficient.

Evaluate Statement (2).

Statement (2) gives

Y = 120

, but gives no information regarding

X

Without knowing

X

, the total shares

X + Y

and the fraction

\frac{X}{X + Y}

cannot be determined. Thus, Statement (2) is insufficient.

Key Concept

Part-to-whole percentages can be determined solely from part-to-part ratios without knowing absolute quantities.

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic