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Manager  Joined: 11 Aug 2009
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If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 51% (01:48) correct 49% (02:16) wrong based on 398 sessions

### HideShow timer Statistics 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

Originally posted by kairoshan on 18 Nov 2009, 21:33.
Last edited by Bunuel on 27 Jul 2014, 23:59, 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]

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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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##### General Discussion
Senior Manager  Joined: 30 Aug 2009
Posts: 261
Location: India
Concentration: General Management
Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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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

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
Senior Manager  Joined: 30 Aug 2009
Posts: 261
Location: India
Concentration: General Management
Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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1
2
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 ...it should be D just adding option 1 and 2 gives value of x   Manager  Joined: 07 Apr 2015
Posts: 162
Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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Dumb question:

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

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noTh1ng wrote:
Dumb question:

Is it enough to say, two equations, two unknowns, both HAVE to be sufficient?

that's exactly what i was thinking. BUT, (2) gives us the same info as what is given. therefore, can we still use the "2 variables, 2 equations = sufficient" rule?

can anyone answer? Bunuel, chetan2u, mikemcgarry, VeritasPrepKarishma, msk0657, Skywalker18, etc.
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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LakerFan24 wrote:
noTh1ng wrote:
Dumb question:

Is it enough to say, two equations, two unknowns, both HAVE to be sufficient?

that's exactly what i was thinking. BUT, (2) gives us the same info as what is given. therefore, can we still use the "2 variables, 2 equations = sufficient" rule?

can anyone answer? Bunuel, chetan2u, mikemcgarry, VeritasPrepKarishma, msk0657, Skywalker18, etc.

Take this with a grain of salt because I by no means have this stuff mastered, but my advice would be to only follow that rule when you're rushed for time or don't see a clear way to prove a solution definitively because the GMAT often presents problems that work around the "2-variables-2-equations-rule", specifically to trick the people using it.
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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kairoshan wrote:
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

This is just another a sub b question - (a +b)(a-b) = a^2-b^2

D
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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After factorizing the expression given, (x/3 + 2/y)(x/3 - 2/y) = 12
If we get the value of any of the 2 brackets given above, the other value can be found very easily.
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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The equation can also be written as (x/-3)^2 - (-2/y)^2 right?
if yes,then the equation would be (-x/3 -2/y)(-x/3 + 2/y)=12
since the denominator of square root of 9 can be -3 or 3.
Am i right?
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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balagevr wrote:
The equation can also be written as (x/-3)^2 - (-2/y)^2 right?
if yes,then the equation would be (-x/3 -2/y)(-x/3 + 2/y)=12
since the denominator of square root of 9 can be -3 or 3.
Am i right?

Yes , you are correct. In either case, the result is the same.
However, we have to design (a+b)(a-b) in such a fashion that we can utilise the information provided in st1 and st2.
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Re: If x^2/9 – 4/y^2 = 12, what is the value of x?  [#permalink]

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kairoshan wrote:
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

$$\frac{x^2}{9} – \frac{4}{y^2} = 12$$
$$(\frac{x}{3}-\frac{2}{y})\frac{(x}{3}+\frac{2}{y}) =12$$

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
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Please provide kudos if you like my post. Re: If x^2/9 – 4/y^2 = 12, what is the value of x?   [#permalink] 10 Jul 2019, 22:35
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