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

Redeem

Integer

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Thu Jan 12, 2012 7:18 pm
Thanked: 1 times

Integer

by dreamv » Sat Jan 14, 2012 10:11 pm
For how many integers n is 2^n=n^2?

A.None
B.One
C.Two
D.Three
E.More than three

I was able to find only n=2, please help.
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Sat Jan 14, 2012 10:13 pm
think about n=4,2
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Jan 14, 2012 10:15 pm
I posted an explanation here:

https://www.beatthegmat.com/exponents-t80313.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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 » Sat Jan 14, 2012 10:28 pm
dreamv wrote:For how many integers n is 2^n=n^2?
Note that, 2^n is a power of 2 only. Hence, any integer equal to 2^n must be a power of 2 only.

Now, n is an integer. Hence, for n^2 to be a power of 2 only n must be a power of 2. Say, n = 2^m.

Hence, 2^n = 2^(2^m) and n^2 = (2^m)^2 = 2^(2m)
Hence, 2^(2^m) = 2^(2m)
Or, 2^m = 2m

Only possible solutions for m are m = 1 and m = 2.
Hence, n = 2 and n = 4.

The correct answer is C.
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
Post new topic Post Reply
• Page 1 of 1