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If x and y are positive integers, is x^2*y^2 even ? (1) x + [#permalink]
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19 Oct 2010, 10:23
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If x and y are positive integers, is x^2*y^2 even ? (1) x + 5 is a prime number (2) y + 1 is a prime number
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Last edited by Bunuel on 20 Oct 2010, 13:47, edited 1 time in total.
Edited the stem.



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Re: Number properties [#permalink]
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19 Oct 2010, 10:36
A for me.
First off, an even number squared will give an even number(2^2 = 4, 4^2 = 16 etc). An odd number squared will give an odd number (3^2 = 9, 5^2 = 25 etc). Also, for the multiplication between two numbers to come out even, at least one of the numbers must be even.
We know all primes except for 2 are odd. Since x and y are positive, the only way for x + 5 to be prime will be if x is even (i.e. if x = 1 then x + 5 = 6 which is not prime. But if x = 2 then x + 5 = 7 which is prime). Therefore, x^2 will also be even and x^2y^2 will also be even regardless of what y is. statement 1 is sufficient.
Using a similar approach for condition 2, we can set y = 1 (y + 1 = 2 which is prime) or y = 2 (y + 2 = 3 which is also prime). So we see with this condition, y can be both even or odd. So statement 2 alone is not sufficient.



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Re: Number properties [#permalink]
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19 Oct 2010, 10:37
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Re: Number properties [#permalink]
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20 Oct 2010, 13:45
A. Kind of trivial but I was staring at x2y2 for 20 seconds. edit it to x^2y^2 for others maybe?
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Re: If x and y are positive integers, is x^2*y^2 even ? (1) x + [#permalink]
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12 Apr 2015, 21:20
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Re: If x and y are positive integers, is x^2*y^2 even ? (1) x + [#permalink]
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08 Jun 2016, 04:53
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Re: If x and y are positive integers, is x^2*y^2 even ? (1) x + [#permalink]
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01 Jan 2017, 13:55
Excellent Question Given info => x,y are positive integers (very important) We need to check if x^2*y^2 is even or not. Now x^2*y^2 will be even when either x or y or both are even Hence we need to find => "If atleast one of x or y is even" Statement 1 Here the least value of x+5 is 6 (as the least value of x is 1) Here we need to remember that all the Prime numbers greater than 2 are odd. Hence x+5 must be odd so x must be even BINGO sufficient
Statement 2
Here y the least value of y+1 is 2
Let us take y = 1 (as y+1=2 which is a prime too) if x is even => then x^2*y^2 will be even if x is odd => then x^2*y^2 will be odd Hence insufficient
Hence A
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Re: If x and y are positive integers, is x^2*y^2 even ? (1) x +
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