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# If f and g are both positive integers greater than 1

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Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
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If f and g are both positive integers greater than 1 [#permalink]

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25 Jul 2014, 11:00
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Question Stats:

66% (01:59) correct 34% (01:04) wrong based on 105 sessions

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If f and g are both positive integers greater than 1 and $$g^f = g^{(3f-6)}$$, what is the value of fg ?

(1) g^2 = 2g

(2) g=2
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Jul 2014, 11:07, edited 1 time in total.
Edited the question
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Joined: 02 Sep 2009
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Re: If f and g are both positive integers greater than 1 [#permalink]

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25 Jul 2014, 11:13
If f and g are both positive integers greater than 1 and $$g^f = g^{(3f-6)}$$, what is the value of fg ?

$$g^f = g^{(3f-6)}$$ --> $$\frac{g^f}{g^{(3f-6)}}=1$$ --> $$g^{f-3f+6} =1$$ --> $$g^{6-2f}=1$$. Since g>1, then $$6-2f=0$$ --> $$f=3$$. Thus to get the value of fg we need the value of g.

(1) g^2 = 2g --> $$g(g-2)=0$$ --> g=0 (discard as g>1) or g=2 --> fg=3*2=6. Sufficient.

(2) g=2. Sufficient.

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Re: If f and g are both positive integers greater than 1 [#permalink]

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25 Jul 2014, 18:41
Bunuel can you explain the theory by dropping the g because g>1 and setting it equal to zero ?
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Re: If f and g are both positive integers greater than 1 [#permalink]

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26 Jul 2014, 02:05
bankerboy30 wrote:
Bunuel can you explain the theory by dropping the g because g>1 and setting it equal to zero ?

For $$a^n$$ to be 1, either $$a$$ should be 1 or $$n$$ should be 0:

$$a^0=1$$: any nonzero number to the power of 0 is 1.
$$1^n=1$$: the integer powers of one are one.

Check here for more: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

Hope it helps.
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Re: If f and g are both positive integers greater than 1   [#permalink] 26 Jul 2014, 02:05
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