kairoshan wrote:

If x2/9 – 4/y2 = 12, what is the value of x?

(1) x/3 + 2/y = 6

(2) x/3 – 2/y = 2

The factorization kp1811 gives above is the key to the problem, but the answer is not E. First, as kp1811 points out above, the expression in the stem can be factored; it's a difference of squares:

\frac{x^2}{9} - \frac{4}{y^2} = \left( \frac{x}{3} + \frac{2}{y} \right) \left( \frac{x}{3} - \frac{2}{y} \right) We know this is equal to 12. Now, using statement 1 alone, we can substitute:

\begin{align*}

\left( \frac{x}{3} + \frac{2}{y} \right) \left( \frac{x}{3} - \frac{2}{y} \right) &= 12 \\

(6)\left( \frac{x}{3} - \frac{2}{y} \right) &= 12 \\

\frac{x}{3} - \frac{2}{y} &= 2

\end{align*}That is, using Statement 1 alone, we can derive the equation in Statement 2. Now if we know both of these equations are true:

\begin{align*}

\frac{x}{3} + \frac{2}{y} &= 6 \\

\frac{x}{3} - \frac{2}{y} &= 2

\end{align*}we can just add these equations to find that

\frac{2x}{3} = 8, so

x = 12. So Statement 1 alone is sufficient.

Statement 2 alone is also sufficient; the analysis is identical to the above. So the answer is D.

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