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If (5^21) x (4^11) = 2 x (10^n) what is the value of n? A)

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If (5^21) x (4^11) = 2 x (10^n) what is the value of n? A) [#permalink]

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New post 27 Jul 2008, 13:23
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If (5^21) x (4^11) = 2 x (10^n) what is the value of n?


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

Last edited by ryguy904 on 27 Jul 2008, 13:40, edited 1 time in total.

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Re: Evil Exponents [#permalink]

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New post 27 Jul 2008, 13:28
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ryguy904 wrote:
If (5^21) x (4^11) = 2 x (10^n) what is the value of x?


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



Don't you mean what is the value of n?

21

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Re: Evil Exponents [#permalink]

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New post 27 Jul 2008, 13:42
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gmatnub wrote:
ryguy904 wrote:
If (5^21) x (4^11) = 2 x (10^n) what is the value of x?


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



Don't you mean what is the value of n?

21


Oops! I went back and fixed it.

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Re: Evil Exponents [#permalink]

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New post 27 Jul 2008, 13:42
Still looking for an explanation from someone, please :)

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Re: Evil Exponents [#permalink]

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New post 27 Jul 2008, 14:04
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(5^21) x (4^11) = 2 x (10^n)

(5^21) * (4^11) = (5^21) * 2^1 * (2^21)

2 * (10^n) = 2^1 * (2^n) (5^n)

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Re: Evil Exponents [#permalink]

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New post 27 Jul 2008, 15:25
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5^21 x 4^11
= 5^21 x 2^2^11
= 5^21 x 2^22
= 5^21 x 2^21 x 2
= 10^21 x 2

Therefore n = 21

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Re: Evil Exponents [#permalink]

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New post 28 Jul 2008, 01:12
ryguy904 wrote:
Still looking for an explanation from someone, please :)



Answer is 21.

Approach:

A zero would occur only if there's a presence of the set 2 * 5. Total 21 such sets could be counted in the expression of the question. Thus the answer is 21.

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Re: Evil Exponents [#permalink]

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New post 28 Jul 2008, 09:30
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ryguy904 wrote:
If (5^21) x (4^11) = 2 x (10^n) what is the value of n?


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


(5^21) x (4^11) = 2 x (10^n)
(5^21) x (2^22) = 2 x (2^n) x (5^n)
(5^21) x (2^22) = [2^(n+1)] x (5^n)
n = 21

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Current Student
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Re: Evil Exponents [#permalink]

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New post 28 Jul 2008, 13:28
Thank you all for your feedback and answer detail. This was the first question that I received on a recent gmatprep test. Does this seem like a 500-550 level question? Maybe I am just not very good at backing out exponents. I usually score 46-49 in quant, so it's not like I'm terrible....Nevertheless, thanks for the help!

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Re: Evil Exponents [#permalink]

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New post 28 Jul 2008, 13:34
more like a 400 level question

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Re: Evil Exponents   [#permalink] 28 Jul 2008, 13:34
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If (5^21) x (4^11) = 2 x (10^n) what is the value of n? A)

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