|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
55% (01:48) correct
45%
(02:17)
wrong
based on 1074
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\frac{x^2}{9} – \frac{4}{y^2} = 12\), what is the value of x?
(1) \(\frac{x}{3} + \frac{2}{y} = 6\)
(2) \(\frac{x}{3} – \frac{2}{y} = 2\)
(1) \(\frac{x}{3} + \frac{2}{y} = 6\)
(2) \(\frac{x}{3} – \frac{2}{y} = 2\)
18 Nov 2009, 22:19
Kudos
Bookmarks
kairoshan
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.
General Discussion
10 Jul 2019, 22:35
Kudos
Bookmarks
kairoshan
\(\frac{x^2}{9} – \frac{4}{y^2} = 12\)
\((\frac{x}{3}-\frac{2}{y})\frac{(x}{3}+\frac{2}{y}) =12\)
S1:
\(\frac{x}{3} + \frac{2}{y} = 6\)
\(=> \frac{x}{3} - \frac{2}{y} = \frac{12}{6} =2\)
=> x = 12
SUFFICIENT
S2:
\(\frac{x}{3} - \frac{2}{y} = 2\)
\(=> \frac{x}{3} + \frac{2}{y} = \frac{12}{2} =6\)
=> x = 12
SUFFICIENT
IMO D
