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

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Math Expert
Joined: 02 Sep 2009
Posts: 60778
If m=p^x*q^y, where p and q are different positive prime numbers. Is m  [#permalink]

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06 Dec 2019, 03:34
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45% (medium)

Question Stats:

61% (01:25) correct 39% (01:25) wrong based on 40 sessions

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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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Joined: 27 Oct 2019
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Re: If m=p^x*q^y, where p and q are different positive prime numbers. Is m  [#permalink]

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06 Dec 2019, 03:54
1)m is not a perfect square.A perfect square will have even number of distinct factors. So the product will always be even or zero if x and y are zero.
2)m may or may not be a perfect square. X and y can take any even value( negative even numbers or zero or positive even numbers) then m is a perfect square but if x and y take 1 and 3 as values, then here the sum is even but m is not a perfect square.
Bunuel I have my exam in the next 4 days. Can you message me the answer for this question??

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Re: If m=p^x*q^y, where p and q are different positive prime numbers. Is m  [#permalink]

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07 Dec 2019, 04:03
1
for a perfect square the factors of the no will always be odd
so #1 given x*y is odd no. means factors of m will be even so its not perfect square no
#2
x+y is an even no
x & y can be odd so yes and x&y are even so no
IMO A sufficient

Bunuel 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.
Re: If m=p^x*q^y, where p and q are different positive prime numbers. Is m   [#permalink] 07 Dec 2019, 04:03
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