If 5^21 X 4^11 = 2x10^n. What is the value of n? : GMAT Problem Solving (PS)
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# If 5^21 X 4^11 = 2x10^n. What is the value of n?

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If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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02 Sep 2007, 13:44
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If 5^21 X 4^11 = 2x10^n. What is the value of n?

A. 11
B. 21
C. 22
D. 23
E. 32

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-5-21-4-11-2-10-n-what-is-the-value-of-n-98809.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Sep 2014, 15:48, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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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
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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02 Sep 2007, 14:45
wow ok. its just trickery with the exponents to arrange what you're looking for.

Thanks
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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02 Sep 2007, 17:23
5^21 * 2^22 = 10^21 * 2

So n = 21
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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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
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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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
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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20 Sep 2014, 14:53
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n? [#permalink]

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20 Sep 2014, 15:49
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Trying_not_to_suck wrote:
If 5^21 X 4^11 = 2x10^n. What is the value of n?

A. 11
B. 21
C. 22
D. 23
E. 32

When we have exponents on both sides it's good idea to get common base.

We have $$5^{21}*4^{11}=2*10^n$$. Little trick for this question: we can forget about 2's on both sides and concentrate on 5-s --> $$5^{21}*4^{11}=2*2^n*5^n$$ --> powers of 5 on both sides must be equal --> $$n=21$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-5-21-4-11-2-10-n-what-is-the-value-of-n-98809.html
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Re: If 5^21 X 4^11 = 2x10^n. What is the value of n?   [#permalink] 20 Sep 2014, 15:49
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