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If x and y are positive integers, is the product xy even? 1.

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If x and y are positive integers, is the product xy even? 1. [#permalink] New post 04 Apr 2006, 01:49
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If x and y are positive integers, is the product xy even?

1. 5x - 4y is even

2. 6x + 7y is even
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 [#permalink] New post 04 Apr 2006, 02:03
D

E +/- E = even
O +/- E = odd


From eq 1 - (5x - 4y is even)

The second term is even independent of what Y is. So x HAS to be even for 5x - 4y to be even

From eq 2 - (6x + 7y is even)

Similarly, we get y to be even independent of X


so from either 1 or 2, we get either x or y even.

Now oe = eo = ee = even

So xy is even!

hence, D
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 [#permalink] New post 04 Apr 2006, 05:37
xy is even if x is even or y is even or both are even.

1) 5x - 4y = even

4y must be even. So 5x must be even. Since 5 is odd, x must be even. Sufficient.

2) 6x+7y = even

6x must be even. So 7y must be even, thus y must be even. Sufficient.

Ans D
  [#permalink] 04 Apr 2006, 05:37
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If x and y are positive integers, is the product xy even? 1.

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