Target Test Prep

Example 1

medium

If y ≠ $\neq$ 0, what is the value of x?

1) yx=4yx−6y $\frac{y}{x} = \frac{4 y}{x} - 6 y$

2) y = 2

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

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Solution:

Question Stem Analysis:

We must determine the value of x.

Statement One Alone:

\Rightarrow y x = 4 y x - 6 y

$\Rightarrow \frac{y}{x} = \frac{4 y}{x} - 6 y$

Most students will see this equation and conclude that it cannot yield a unique value for x because it contains another variable, y. However, if y can be removed from the equation, x will be the only unknown. Indeed, this one equation is sufficient to determine the value of x.

\Rightarrow y x = 4 y x - 6 y

$\Rightarrow \frac{y}{x} = \frac{4 y}{x} - 6 y$

To simplify the equation, we can multiply the entire equation by x:

\Rightarrow x (y x = 4 y x - 6 y) \Rightarrow y x x = 4 y x x - 6 y x \Rightarrow y = 4 y - 6 y x \Rightarrow y = y (4 - 6 x)

$\begin{array}{l} \Rightarrow x (\frac{y}{x} = \frac{4 y}{x} - 6 y) \\ \Rightarrow \frac{y x}{x} = \frac{4 y x}{x} - 6 y x \\ \Rightarrow y = 4 y - 6 y x \\ \Rightarrow y = y (4 - 6 x) \end{array}$

Dividing both sides by y, which we can do since we are given that y ≠ 0, we have:

\Rightarrow y y = y ( 4 - 6 x ) y \Rightarrow 1 = 4 - 6 x \Rightarrow 6 x = 3 \to x = 1 2

$\begin{array}{l} \Rightarrow \frac{y}{y} = \frac{y (4 - 6 x)}{y} \\ \Rightarrow 1 = 4 - 6 x \\ \Rightarrow 6 x = 3 \to x = \frac{1}{2} \end{array}$

Statement one alone is sufficient. (Notice that since y ≠ 0, we can divide both sides of y = 4y – 6yx by y to obtain 1 = 4 – 6x. Had we not known that y ≠ 0, we could not have.)

Eliminate answer choices B, C, and E.

Statement Two Alone:

⇒ $\Rightarrow$ y = 2

With no information given about x, statement two alone is not sufficient.

Correct answer:A

Target Test Prep Sample GMAT Data Sufficienncy Problem

Example 1