Question on numbers

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srn: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Thu Feb 05, 2009 7:35 pm; Thanked: 2 times

by srn » Sun Apr 05, 2009 6:23 am

If x and y are positive integers, is the product xy even?

a. 5x-4y is even.
b.6x+7y is even.

ans -d

Please explain how you came to the conclusion.

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 05, 2009 6:23 am

moutar: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Wed Mar 25, 2009 12:13 pm; Thanked: 10 times

by moutar » Sun Apr 05, 2009 7:51 am

5x - 4y is even implies that 5x is even (4y is even and even - even equals even). If 5x is even, x is even and therefore xy is even. SUFFICIENT

6x+7y is even implies that 7y is even (6x is even and even+even=even). If 7y is even, then y is even and therefore xy is even. SUFFICIENT

Therefore D. Each statement alone is sufficient.

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cubicle_bound_misfit: Master | Next Rank: 500 Posts; Posts: 246; Joined: Mon May 19, 2008 7:34 am; Location: Texaco Gas Station; Thanked: 7 times

by cubicle_bound_misfit » Sun Apr 05, 2009 5:33 pm

more algebra wise,

5x -4y =2k

5x = 4y+2k .... even

hence x is even hence xy is even...

same approach for stmt 2.

Cubicle Bound Misfit

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