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# If m=p^x*q^y, where p and q are different positive prime

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If m=p^x*q^y, where p and q are different positive prime [#permalink]  05 Sep 2008, 19:32
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.If m=p^x*q^y, where p and q are different positive prime numbers. Is m a perfect square number?
(1) x*y is an odd number.
(2) x+y is an even number.
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Re: perfect square or not? [#permalink]  05 Sep 2008, 19:45
arjtryarjtry wrote:
.If m=p^x*q^y, where p and q are different positive prime numbers. Is m a perfect square number?
(1) x*y is an odd number.
(2) x+y is an even number.

A

is m = 1 or 4 or 9 or 16 ....?

statement 1: x*y = odd ---> x and y are odd ---> m will not be a perfect square
OR x*y = odd could mean that x = 2, y =3/2, this will not make m a perfect square either
suff

statement 2: x + y = even, x = 1, y = 1 ---> m is not a perfect square
OR x = 2, y = 2 ----> m is a perfect square
insuff
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Re: perfect square or not? [#permalink]  05 Sep 2008, 19:51
arjtryarjtry wrote:
.If m=p^x*q^y, where p and q are different positive prime numbers. Is m a perfect square number?
(1) x*y is an odd number.
(2) x+y is an even number.

(1) x*y = odd means neither x nor y is even hence we cannot get a perfect sq,since p,q are prime we will get all odd powers of p,q and perfect sq requires even power SUFFI m is never a perfect sq.

(2)x+y =even x,y can both be odd or both be even

wen x,y odd then not a perfect sq,when x,y even it can be perfect sq when x=y hence INSUFFI

IMO A
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Re: perfect square or not?   [#permalink] 05 Sep 2008, 19:51
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