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# 3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2

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

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29 Jun 2017, 02:58
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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

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director 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] ### Show Tags 29 Jun 2017, 03:11 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 Joined: 19 Mar 2014 Posts: 931 Location: India Concentration: Finance, Entrepreneurship GPA: 3.5 Re: 3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2 [#permalink] ### Show Tags 29 Jun 2017, 03:32 $$\frac{3^{-(x+y)}}{3^{-(x-y)}}=?$$ 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 _________________ "Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475 Math Revolution GMAT Instructor 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] ### Show Tags 02 Jul 2017, 18:08 ==> 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: 3^-(x+y)/3^-(x-y)=? 1) x=3 2) y=2   [#permalink] 02 Jul 2017, 18:08
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