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Least possible value of n

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Manager
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Least possible value of n [#permalink] New post 11 Jan 2010, 04:24
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100% (02:12) correct 0% (00:00) wrong based on 4 sessions
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
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Tuck Thread Master
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Re: Least possible value of n [#permalink] New post 11 Jan 2010, 05:22
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4,000,000 = 2^2*1,000,000 = 2^2*10^6=2^2*2^6*5^6 = 2^8*5^6

5^n>2^8*5^6

5^{n-6}>256

625=5^4>256

n-6=4

n=10
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Re: Least possible value of n [#permalink] New post 11 Jan 2010, 06:28
You can solve it with the same way you find LCM.

5 | 4,000,000
5 | 800,000
5 | 160,000
5 | 32,000
5 | 6,400
5 | 1,280
5| 256
5 | 56
5 | 11
2

We have 9 5's and 1x2. For 5^n to be bigger than 4,000,000, we therefore need n=10.
Intern
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Re: Least possible value of n [#permalink] New post 14 Feb 2010, 09:51
shalva wrote:
4,000,000 = 2^2*1,000,000 = 2^2*10^6=2^2*2^6*5^6 = 2^8*5^6

5^n>2^8*5^6

5^{n-6}>256

625=5^4>256

n-6=4

n=10


nice approach. What is OA?
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Re: Least possible value of n [#permalink] New post 14 Feb 2010, 11:15
IMO D -10

5^n > 5^6 * 4 * 2^6
5^n > 5^6 * 2^8
5^n > 5^6 * 256
5^n > 5^6 * 5^3 * \frac{256}{125}
5^n > 5^9* \frac{256}{125} since \frac{256}{125}< 5

n = 10
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Re: Least possible value of n   [#permalink] 14 Feb 2010, 11:15
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