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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42 GPA: 3.82
3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2  [#permalink]

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1 00:00

Difficulty:   25% (medium)

Question Stats: 71% (00:52) correct 29% (01:16) wrong based on 55 sessions

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$$3^{-(x+y)}/3^{-(x-y)}=?$$

1) x=3
2) y=2

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Director  V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2  [#permalink]

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1
MathRevolution wrote:
$$3^{-(x+y)}/3^{-(x-y)}=?$$

1) x=3
2) y=2

Simplifying the fraction, we get;

$$\frac{3^{-(x+y)}}{3^{-(x-y)}} = 3^{-(x+y)}*3^{(x-y)}$$

$$3^{(-x - y + x - y)}$$ $$= 3^{ (-2 y) }$$

So we just need the value of $$y$$ to find the value of the fraction $$\frac{3^{-(x+y)}}{3^{-(x-y)}}$$.

1) $$x=3$$

Value of $$x$$ is not needed. Hence I is Not Sufficient.

2) $$y=2$$

$$3^{( -2 y )}$$ = $$3^{( -2 *2 )}$$ = $$3^{ -4}$$ = $$\frac{1}{3^{ 4}}$$ $$= \frac{1}{81}$$ .

Hence II is Sufficient.

Answer (B)...
Retired Moderator P
Joined: 19 Mar 2014
Posts: 931
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Concentration: Finance, Entrepreneurship
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Re: 3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2  [#permalink]

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$$\frac{3^{-(x+y)}}{3^{-(x-y)}}=?$$

Let's simplify the above equation:

= $$\frac{3^{(x-y)}}{3^{(x+y)}}$$

= $$\frac{3^x * 3^-y}{3^x * 3^y}$$

Cancel out $$3^x$$

$$= \frac{3^-y}{3^y}$$

$$= 3^-2y = ?$$

$$= \frac{1}{3^2y} = ?$$

As per above if we know the value of y we should be able to find the answer.

$$1) x=3$$

Clearly not sufficient as we are not aware of the value of x

Hence, (1) =====> is NOT SUFFICIENT

$$2) y=2$$

As we know the value of y now, we can plug this value in the above equation

$$= \frac{1}{3^2y}$$

$$= \frac{1}{3^2*2} = \frac{1}{3^4} = \frac{1}{81}$$

As we are able to determine the value, B is sufficient

Hence, (2) =====> is SUFFICIENT

Hence, Answer is B
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: 3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2  [#permalink]

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==> If you modify the original condition and the question, you get $$\frac{3^{-(x+y)}}{3^{-(x-y)}}=3^{x-y+x-y}=3^{-2y}$$, so you only need to know y.

The answer is B.
Answer: B
_________________ Re: 3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2   [#permalink] 02 Jul 2017, 18:08
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