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# If 5^2^1 X 4^1^1 = 2 X 10^n what is the value of n?

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Intern
Joined: 09 Jan 2009
Posts: 7
If 5^2^1 X 4^1^1 = 2 X 10^n what is the value of n?  [#permalink]

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09 Jan 2009, 09:40
If $$5^2^1 X 4^1^1 = 2 X 10^n$$ what is the value of n?

o 11
o 21
o 22
o 23
o 32

Hi, has someone a quick way of getting this done?

Answer A is correct (not E as indicated).

many Thx

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Manager
Joined: 04 Jan 2009
Posts: 229
Re: GMAT Prep - Exponent Problem  [#permalink]

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09 Jan 2009, 09:48
I may be wrong; now I get B.

5^21x4^11 = 5^21x2^21x2=2x(5x2)^21
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tusharvk

Intern
Joined: 09 Jan 2009
Posts: 7
Re: GMAT Prep - Exponent Problem  [#permalink]

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09 Jan 2009, 09:57
sorry it is B
Intern
Joined: 09 Jan 2009
Posts: 7
Re: GMAT Prep - Exponent Problem  [#permalink]

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09 Jan 2009, 10:06
thanks so far....but can you expalain your step from
4^11 to 2^21x2 ?

many thanks
Manager
Joined: 04 Jan 2009
Posts: 229
Re: GMAT Prep - Exponent Problem  [#permalink]

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09 Jan 2009, 11:24
Oh I apologize; in my excitement I just jumped off.
5^21x4^11 = 5^21x(2^2)^11 = 5^21x2^22 = 2x2^21x5^21=2x(5x2)^21=2x10^21.

best.
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tusharvk

Senior Manager
Joined: 02 Nov 2008
Posts: 251
Re: GMAT Prep - Exponent Problem  [#permalink]

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09 Jan 2009, 13:46
1
tusharvk wrote:
Oh I apologize; in my excitement I just jumped off.
5^21x4^11 = 5^21x(2^2)^11 = 5^21x2^22 = 2x2^21x5^21=2x(5x2)^21=2x10^21.

best.

2 = 2^1
10^N = 2^N X 5^N

2 X 10^N = 2^(N+1) X 5^N

4^11 = 2^11 X 2^11
SO:
5^21 X 2^22 = 2^(N+1) X 5^N

Drop the bases and the answer is clearly 21.
Manager
Joined: 01 Nov 2008
Posts: 127
Re: GMAT Prep - Exponent Problem  [#permalink]

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15 Jan 2009, 04:49

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: GMAT Prep - Exponent Problem &nbs [#permalink] 15 Jan 2009, 04:49
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# If 5^2^1 X 4^1^1 = 2 X 10^n what is the value of n?

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