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How many integers? Source : Gmat Prep

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by adi_800 » Mon Jul 05, 2010 6:45 am
Hi, is there any easy way to solve this problem or u should pick the numbers n proceed?

For how many integers n is 2^n = n^2?
A. None
B. One
C. Two
D. Three
E. More than three.

[spoiler]OA:C
Source: Gmat Prep[/spoiler]
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by selango » Mon Jul 05, 2010 6:52 am
2^n=n^2

Sub n=2

2^2=2^2

Sub n=4

2^4=4^2

16=16

Only this 2 values satisfy the equation.
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by jeremy8 » Mon Jul 05, 2010 7:34 am
selango wrote:2^n=n^2

Sub n=2

2^2=2^2

Sub n=4

2^4=4^2

16=16

Only this 2 values satisfy the equation.

Can you explain why that is, or is this just a question of plugging numbers?
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by selango » Mon Jul 05, 2010 7:49 am
2^n=n^2

As LHS is 2 multiples,n^2 is multiple of 2.

Now try to plugin numbers,

n=1,2=4

n=2,4=4

n=3,8=9

n=4,16=16

n=5,32=25

n=6,64=36

n=7,128=49

As you can see from n=5 onwards,2^n value increases.

So n=2 and 4
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by jeremy8 » Mon Jul 05, 2010 7:55 am
selango wrote:2^n=n^2

As LHS is 2 multiples,n^2 is multiple of 2.
Of course, how could I not see that....argh.....Thanks for the explanation.
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