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# can someone tell me the shortcut for this silly problem?

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Intern
Joined: 20 Jun 2007
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can someone tell me the shortcut for this silly problem? [#permalink]

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04 Jul 2007, 15:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

can someone tell me the shortcut for this silly problem?

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

thanks

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Intern
Joined: 03 Jul 2007
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04 Jul 2007, 16:11
no shortcut, but may be it helps?

5^11*5^10*4^11=2*10^n
(5*4)^11 * 5^10 =
20^10*20*5^10 =
100^10 * 20 = 2 * 10^n | :2
10^10*10^10 * 10 = 10^n
10^21 = 10^n

cya
Mazar

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Manager
Joined: 11 Mar 2007
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04 Jul 2007, 18:09
I would do it a slightyly different way:

(5^21)*(4^11)=2*10^n
(5^21)*(2^22)=2*10^n
(5^21)*(2)(2^21)=2*10^n
2*(5^21)*(2^21)=2*10^n
2*10^21...

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GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore

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04 Jul 2007, 18:45
1
KUDOS
5^21 * 2^22 = 5^21 * 2^21 * 2 = 10^21 * 2

so n = 21

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Director
Joined: 09 Aug 2006
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Re: (5^21) x (4^11) = (2 x 10^n) [#permalink]

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05 Jul 2007, 00:45
dzelkas wrote:
can someone tell me the shortcut for this silly problem?

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

thanks

(5^21)(2^22)=2*(2*5)^n
(5^21)(2^22)=2*2^n*5^n
(5^21)(2^22)=2^n+1*5*n
Equate either term to solve for n

5^21=5^n => n=21
or
2^22=2^n+1 => n=21

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Senior Manager
Joined: 24 Nov 2006
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Re: (5^21) x (4^11) = (2 x 10^n) [#permalink]

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05 Jul 2007, 21:55
dzelkas wrote:
can someone tell me the shortcut for this silly problem?

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

thanks

From the expression: 5^21 * (2^2)^11 = 5^21 * 2^22

Now, include this fact: 10 = 5*2

(5*2)^21 * 2 = 10^21 * 2

Therefore, n = ???

Yep, 21.

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Senior Manager
Joined: 11 Jun 2006
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05 Jul 2007, 22:24
Shortcut:

Since you know that there is a 5^21 on the left side. You know that for the equation to be equal, there needs to be exactly 21 5's on the right side. The only way to create 21 5's is to have n=21.

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05 Jul 2007, 22:24
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