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If x and y are positive integers, is x an even integer?

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alphonsa
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If x and y are positive integers, is x an even integer? [#permalink] New post   Updated on: 18 Aug 2014, 09:35
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If x and y are positive integers, is x an even integer?

(1) x(y + 11) is an even integer.
(2) y^2 - 6y + 5 is an odd integer.

Source: 4gmat
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C

Originally posted by alphonsa on 18 Aug 2014, 08:55.
Last edited by Bunuel on 18 Aug 2014, 09:35, edited 1 time in total.
Edited the question.
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post   18 Aug 2014, 09:05
Expert Reply
STAT1
If y is odd then X can be even or odd
If y is even then xis even
So, NOT SUFFICIENT

STAT2
(y-1)*(y-5)=odd
=> y = even
Doesn't talk about x so NOT SUFFICIENT

STAT1 and STAT2 Together
we know that y is even
=> y+11 is odd
=> x is even

So, SUFFICIENT
Answer will be C

Hope it helps!
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post   18 Aug 2014, 09:41
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If x and y are positive integers, is x an even integer?

(1) x(y + 11) is an even integer --> if y is an odd integer then y + 5 = even and x can be even as well as odd. Not sufficient.

(2) y^2 - 6y + 5 is an odd integer --> y^2 - 6y + 5 = y^2 - even + odd = y^2 + odd = odd --> y^2 = even --> y = even. No info about x. Not sufficient.

(1)+(2) Since from (2) y is even, then y + 11 = odd, thus for x(y + 11) = x*odd to be even, x must be even. Sufficient.

Answer: C.
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post   21 Nov 2016, 05:16
Given info => x,y are integers
w need to find if x is even or not
Statement 1
x(y+11) is even
Here if y is odd=> x can be even or not => not sufficient
Statement 2
y^+odd=odd => y^2 must be even
hence y must be even
But we don't know the even/odd nature of x
hence insufficient

Combing statements 1 and 2
we get y=even
so y+11=> odd
hence to make x(y+11) even ,x must be even
Hence sufficient
Hence C
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post   21 Jun 2020, 22:09
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alphonsa wrote:
If x and y are positive integers, is x an even integer?

(1) x(y + 11) is an even integer.
(2) y^2 - 6y + 5 is an odd integer.


(1) x(y + 11) is an even integer.
Three possibilities..
a) x and y are odd, then y+11 will be even.
b) x is even and y is odd
c) both x and y are even

(2) \(y^2 - 6y + 5\) is an odd integer.
\(y^2 - 6y + 5\)....6y will be even and 5 is odd, so 5-6y will be odd
\(y^2 - 6y + 5=y^2+odd=odd....y^2=odd-odd=even\), so y is even.
But nothing about x

Combined
y is even, so y+11 will be odd..
Now x(y+11)=x*odd=even, so x is even

C
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post   28 Dec 2023, 21:24
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Re: If x and y are positive integers, is x an even integer? [#permalink]
28 Dec 2023, 21:24
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Bunuel
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