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Power of n

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Power of n

by enniguy » Wed Aug 26, 2009 8:25 am
If n is an integer and (5^n) > 4,000,000, what is the least possible value of n ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

I don't know how to solve this kind of questions. Please let me know if any of you know the method.

OA: D
Last edited by enniguy on Wed Aug 26, 2009 4:46 pm, edited 1 time in total.
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by real2008 » Wed Aug 26, 2009 9:46 am
recheck the qn....
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by ramyaravindran » Wed Aug 26, 2009 10:27 am
https://www.beatthegmat.com/least-value-t30974.html
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Thanks

by enniguy » Wed Aug 26, 2009 4:48 pm
Thanks guys
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Re: Power of n

by shahdevine » Wed Aug 26, 2009 5:39 pm
enniguy wrote:If n is an integer and (5^n) > 4,000,000, what is the least possible value of n ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

I don't know how to solve this kind of questions. Please let me know if any of you know the method.

OA: D
manipulate equation:

5^n>4x10^6
5^n>4 x 2^6 x 5^6

right here you know that n has to be greater than 6 because you have the outstanding factors of 4 and 2^6.

next step is to take outstanding factors and manipulate as close to 5^n

so

5^n>4 x 2^3 x 2^3 x 5^6
5^n>4 x 4^3 x 5^6
5^n>4 ^4 x 5^6

4^4=256

so whatever power we put to 5 has to be greater than that. Meaning 5^3 = 125 which is less than 256. So only 5^4 would cover 256. Hence n has to equal 4+6=10

D

you got this man!
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