integers

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Ramit88: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Fri Nov 26, 2010 8:25 am; Thanked: 3 times

by Ramit88 » Tue Jan 25, 2011 10:17 pm

For how many integers n 2^n = n^2

a none
b one
c two
d three
e more than 3

[spoiler]
ANS C[/spoiler]

acc to me its B i.e one

when n =2,
2^n = n^2
2^2 = 2 ^2

it can not be zero

2^0 = 0^2
1 = not defined

pls point out my mistake

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Source: Beat The GMAT — Problem Solving | Tue Jan 25, 2011 10:17 pm

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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 Jan 25, 2011 10:39 pm

Ramit88 wrote:For how many integers n 2^n = n^2

a none
b one
c two
d three
e more than 3

There two possible values of n satisfying the relation 2^n = n^2

1. n = 2 --> 2^2 = 4 = 2^2
2. n = 4 --> 2^4 = 16 = 4^2

The correct answer is C.

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prachich1987: Legendary Member; Posts: 752; Joined: Sun Sep 12, 2010 2:47 amFollowed by: 10 members; Thanked: 20 times; GMAT Score:700

by prachich1987 » Fri Jan 28, 2011 3:41 am

Anurag@Gurome wrote:
Ramit88 wrote:For how many integers n 2^n = n^2

a none
b one
c two
d three
e more than 3
There two possible values of n satisfying the relation 2^n = n^2
1. n = 2 --> 2^2 = 4 = 2^2
2. n = 4 --> 2^4 = 16 = 4^2
The correct answer is C.

Hi Anurag,

Is there any algebraic approach to this.

Thanks!

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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 » Fri Jan 28, 2011 3:46 am

prachich1987 wrote:Is there any algebraic approach to this.

Yes, there is.
But unless you have a strong graphical sense and good understanding of logarithm, I discourage you to go for that approach. For GMAT purpose, just remember that there is only two such pair and also remember the values.

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Fri Jan 28, 2011 6:29 am

thanks for posting this problem...

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