BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

5^n > 4,000,000

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

5^n > 4,000,000

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
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

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
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
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 > 2² * 10^6
5^n > 2² * 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.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
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 > 2² * 10^6
5^n > 2² * 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
Top
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

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 > 2² * 10^6
5^n > 2² * 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
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
Post new topic Post Reply
• Page 1 of 1