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If x^2/9 – 4/y^2 = 12, what is the value of x?

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If x^2/9 – 4/y^2 = 12, what is the value of x? [#permalink] New post 18 Nov 2009, 20:33
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If x^2/9 – 4/y^2 = 12, what is the value of x?

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

(2) x/3 – 2/y = 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2014, 22:59, edited 1 time in total.
Edited the question and added the OA.
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x? [#permalink] New post 18 Nov 2009, 20:47
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



E

the original equation is (x/3 + 2/y) (x/3 – 2/y) = 12 and option 1 and 2 provide values of individual expressions. both are insuff alone and together
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x? [#permalink] New post 18 Nov 2009, 21:19
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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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Re: If x^2/9 – 4/y^2 = 12, what is the value of x? [#permalink] New post 19 Nov 2009, 03:09
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IanStewart wrote:
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.


darn me :x ...it should be D just adding option 1 and 2 gives value of x :oops: :( :cry:
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x? [#permalink] New post 27 Jul 2014, 17:29
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x? [#permalink] New post 26 Aug 2015, 00:55
Dumb question:

Is it enough to say, two equations, two unknowns, both HAVE to be sufficient?
Re: If x^2/9 – 4/y^2 = 12, what is the value of x?   [#permalink] 26 Aug 2015, 00:55
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