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# If k is a positive integer, is k the square of an integer?

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Intern
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If k is a positive integer, is k the square of an integer? [#permalink]  22 Apr 2006, 11:25
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If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.

(2) k is divisible by exactly 4 different prime numbers.
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Joined: 20 Nov 2004
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Consider e. g. 2*2*3*5*7 = 420.

It's divisible by 4, and it's divisible by exactly
4 different prime numbers (2,3,5,7).

The square root is 2*sqrt(105), which ISN'T an integer.

==

Consider e. g. 4*(2*3*5*7)^2 = 176400.

It's divisible by 4, and it's divisible by exactly
4 different prime numbers (2,3,5,7).

The square root is 420, which IS an integer.

So E.
Intern
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Nothing more to add.. E should be
Senior Manager
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Agree with ccax, but do you a quick solution for this one

Consider e. g. 4*(2*3*5*7)^2 = 176400.

It's divisible by 4, and it's divisible by exactly
4 different prime numbers (2,3,5,7).

The square root is 420, which IS an integer.
?

As on the real test you will spend a lot of time trying to pick up different digits.

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