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If 5^21 x 4^11 = 2x10^n what is the value of n 1) 11 2) 21

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Intern
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If 5^21 x 4^11 = 2x10^n what is the value of n 1) 11 2) 21 [#permalink] New post 02 Sep 2007, 13:44
If 5^21 x 4^11 = 2x10^n what is the value of n

1) 11
2) 21
3) 22
4) 23
5) 32

Explanations Please. Im having problems with this question which im guessing is very simple.

Thanks
Director
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GMAT Tests User
 [#permalink] New post 02 Sep 2007, 14:28
If 5^21 x 4^11 = 2x10^n what is the value of n

4^11 = (2^2)^11 = 2^22
10^n = (5x2)^n = 5^n x 2^n

5^21 x 2^22 = 2x 2^n x 5^n = 2^n+1 x 5^n = 2^22 x 5^21

n = 21
Intern
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 [#permalink] New post 02 Sep 2007, 14:45
wow ok. its just trickery with the exponents to arrange what you're looking for.

Thanks
GMAT Club Legend
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 [#permalink] New post 02 Sep 2007, 17:23
5^21 * 2^22 = 10^21 * 2

So n = 21
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GMAT Tests User
 [#permalink] New post 02 Sep 2007, 18:40
This is GMAT Prep Question - my advice, please, indicate GMAT Prep Q in the Subject area, because some people didn't take GMAT Prep yet, and if they will check there score with GMAT Prep later, they wouldn't be happy to see the questions they already know the answer!

5^11 * 4^11 = 2*10^n
5^11 * 5^10 * 4^11 = 2*10^n
20^11 * 5^10 = 2*10^n
20^10 * 5^10 * 20 = 2*10^n
100^10 * 20 = 2*10^n
(10^2)^10 * 20 = 2*10^n
10^20 * 2 * 10 = 2*10^n
10^21 * 2 = 2*10^n
n = 21
Director
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 [#permalink] New post 03 Sep 2007, 00:12
5 ^ 21 * 4 ^ 11 = 2 * 10 ^ n
5 ^ 20 * 4 ^ 10 * 20 = 2 * 10 ^ n
5 ^ 10 * 20 ^ 10 * 10 = 10 ^ n
100 ^ 10 * 10 = 10 ^ n
10 ^ 20 * 10 = 10 ^ n

N = 21
  [#permalink] 03 Sep 2007, 00:12
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If 5^21 x 4^11 = 2x10^n what is the value of n 1) 11 2) 21

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