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If x and y are positive integers...

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jasonmaehara
 Post subject: If x and y are positive integers...
 Post Posted: Mon Apr 04, 2011 8:27 pm 
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Students


Posts: 23
If X and Y are positive integers, is the product XY even?

1) 5x - 4y is even
2) 6x + 7y is even

Answer: D

Could use some help as to why! Thanks
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smohit04
 Post subject: Re: If x and y are positive integers...
 Post Posted: Mon Apr 04, 2011 10:42 pm 
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Course Students


Posts: 28
Rephrasing - we need to find if either X or Y is even..?

(1)- 5x - 4y is even

Since 4y is even (irrespective of y being odd/even), 5x has to be even. Thus x will be even - SUFFICIENT

(2) - 6x + 7y is even

Since 6x is even (irrespective of x being odd/even), 7y has to be even. Thus y will be even - SUFFICIENT
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RonPurewal
 Post subject: Re: If x and y are positive integers...
 Post Posted: Tue Apr 05, 2011 10:18 am 
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ManhattanGMAT Staff


Posts: 7146
smohit04 wrote:
Rephrasing - we need to find if either X or Y is even..?

(1)- 5x - 4y is even

Since 4y is even (irrespective of y being odd/even), 5x has to be even. Thus x will be even - SUFFICIENT

(2) - 6x + 7y is even

Since 6x is even (irrespective of x being odd/even), 7y has to be even. Thus y will be even - SUFFICIENT


excellent.

--

the other way to do these problems, if you get stuck getting through the kind of reasoning given above, is simply to slog through all of the different possibilities for whether x and y are even or odd, and just see which ones work.

here:
(1) 5x - 4y is even

4 possibilities for (x, y):
(odd, odd): 5x - 4y = odd - even = odd; this doesn't work.
(odd, even): 5x - 4y = odd - even = odd; this doesn't work.
(even, odd): 5x - 4y = even - even = even; this works.
(even, even): 5x - 4y = even - even = even; this works.
in both of the cases that work, x is even, so xy is also even.
SUFFICIENT


(2) 6x + 7y is even

4 possibilities for (x, y):
(odd, odd): 6x + 7y = even + odd = odd; this doesn't work.
(odd, even): 6x + 7y = even + even = even; this works.
(even, odd): 6x + 7y = even + odd = odd; this doesn't work.
(even, even): 6x + 7y = even + even = even; this works.
in both of the cases that work, y is even, so xy is also even.
SUFFICIENT
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jasonmaehara
 Post subject: Re: If x and y are positive integers...
 Post Posted: Tue Apr 05, 2011 6:10 pm 
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Students


Posts: 23
Got it, thanks!
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tim
 Post subject: Re: If x and y are positive integers...
 Post Posted: Tue Apr 05, 2011 6:36 pm 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
glad to hear it!

_________________
Tim Sanders
Manhattan GMAT Instructor
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