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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How many integers? Source : Gmat Prep
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selango
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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
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
--Anand--
