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# r=3^(n+2), then in terms of r, 9^n=

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Senior Manager
Joined: 08 Nov 2010
Posts: 336
r=3^(n+2), then in terms of r, 9^n=  [#permalink]

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19 Feb 2011, 07:47
1
8
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:14) correct 36% (01:29) wrong based on 199 sessions

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r=3^(n+2), then in terms of r, 9^n=

A. r^2/81
B. r^2/9
C. r^2
D. r/3
E. r

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Math Expert
Joined: 02 Sep 2009
Posts: 52122

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19 Feb 2011, 07:54
3
1
144144 wrote:
Hey guys,

r=3^(n+2) , then in terms of r, 9^n=

a - r^2/81
b - r^2/9
c - r^2
d - r/3
e - r

$$r=3^{(n+2)}$$ --> $$r=3^{n}*3^2$$ --> $$3^n=\frac{r}{9}$$ --> square both sides: $$(3^n)^2=3^{2n}=9^n=\frac{r^2}{81}$$.

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19 Feb 2011, 08:00
wow, u made it much simpler than me... thanks. +1
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8783
Location: Pune, India
Re: r=3^(n+2), then in terms of r, 9^n=  [#permalink]

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14 May 2015, 22:20
2
2
144144 wrote:
r=3^(n+2), then in terms of r, 9^n=

A. r^2/81
B. r^2/9
C. r^2
D. r/3
E. r

Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 3^2 = 9
and you need the value of 9^n which is 9^0 = 1

So when you put r = 9 in the options, you should get 1. Only option (A) satisfies.

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Re: r=3^(n+2), then in terms of r, 9^n=  [#permalink]

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12 Jan 2019, 07:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: r=3^(n+2), then in terms of r, 9^n= &nbs [#permalink] 12 Jan 2019, 07:24
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