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

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Intern
Joined: 30 Aug 2007
Posts: 19
If 5^21 X 4^11 = 2x10^n. What is the value of n?  [#permalink]

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Updated on: 20 Sep 2014, 15:48
1
1
12
00:00

Difficulty:

15% (low)

Question Stats:

80% (00:32) correct 20% (00:57) wrong based on 331 sessions

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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

Originally posted by Trying_not_to_suck on 02 Sep 2007, 13:44.
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.
Director
Joined: 30 Nov 2006
Posts: 573
Location: Kuwait
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
Intern
Joined: 30 Aug 2007
Posts: 19
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
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4858
Location: Singapore
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
Manager
Joined: 03 Sep 2006
Posts: 232
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
Director
Joined: 30 Jun 2007
Posts: 717
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
Math Expert
Joined: 02 Sep 2009
Posts: 50572
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
2
7
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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Joined: 09 Sep 2013
Posts: 8759
Re: If 5^21 X 4^11 = 2x10^n. What is the value of n?  [#permalink]

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30 Oct 2018, 23:29
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: If 5^21 X 4^11 = 2x10^n. What is the value of n? &nbs [#permalink] 30 Oct 2018, 23:29
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