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Prime Number

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Prime Number

by Kumar007 » Mon Mar 30, 2009 10:12 am
If K is a positive integer, is K the square of an integer?

(1) K is divisible by 4.
(2) K is divisible by four different prime number.

Why the B is wrong because with B at least we can say that k is not a square of an integer.
[spoiler]Answer is E
[/spoiler]
Can Someone please give me explanation?
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Source: — Data Sufficiency |
Junior | Next Rank: 30 Posts
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by cm47323 » Mon Mar 30, 2009 10:33 am
This one is kinda tricky. It does not say that K has a total of 4 factors, which would make it nonprime. 4 different prime factors can mean something like

K= 2^2 * 3^2 * 5^2 * 7^2
sqrt(K) = 2*3*5*7

As long as all of the powers are even, it's going to be a square. If they aren't all even, it won't be a square. So, it's insufficient and ans is E.
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