5^n > 4,000,000

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Nov 15, 2011 3:41 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

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Source: Beat The GMAT — Problem Solving | Tue Nov 15, 2011 3:41 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Nov 15, 2011 3:47 am

5^n > 4,000,000
5^n > 4*(10^6)
5^n > 4*(5^6)*(2^6)
5^n > 256 * (5^6)
5^3<256<5^4

Min value of n = 10 IMO D

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Nov 15, 2011 3:47 am

sanju09 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

5^n > 4,000,000
5^n > 2Â² * 10^6
5^n > 2Â² * 2^6 * 5^6
5^n > 2^8 * 5^6
5^(n - 6) > 256
Now 5^4 = 625 > 256
So, n - 6 = 4
n = 10

The correct answer is D.

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vipdst1: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Nov 05, 2011 9:22 pm

by vipdst1 » Tue Nov 15, 2011 9:59 pm

Anurag@Gurome wrote:
sanju09 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
5^n > 4,000,000
5^n > 2Â² * 10^6
5^n > 2Â² * 2^6 * 5^6
5^n > 2^8 * 5^6
5^(n - 6) > 256
Now 5^4 = 625 > 256
So, n - 6 = 4
n = 10

The correct answer is D.

Hi, I got lost at:
This line: 5^n > 2^8 * 5^6

Could you explain its following:
5^(n - 6) > 256
Now 5^4 = 625 > 256

Thanks

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Nov 15, 2011 10:41 pm

Though directed to Anurag, I will try to explain it my way

5^n > 4,000,000
5^n > 2Â² * 10^6
5^n > 2Â² * 2^6 * 5^6
5^n > 2^8 * 5^6
5^(n - 6) > 256
125 < 256 < 625.
5^3 < 256 < 5^4
5^3 < 256 < 5^(n - 6)
Since we need the least integer value of n in 5^(n-6), the value of 5^(n-6) should be 5^4 which is the immediate next power of 5.
Now 5^4 = 5^(n-6)
So, n - 6 = 4
n = 10

Hope that helps !

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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