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Re: If x and y are positive integers , is the product xy even [#permalink]

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30 Nov 2014, 10:47

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Re: If x and y are positive integers , is the product xy even [#permalink]

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02 Aug 2016, 10:44

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If x and y are positive integers , is the product xy even [#permalink]

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02 Aug 2016, 13:22

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krishan wrote:

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

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

1) \(4y\) will always be even. Then we have \(5x - even = even\). For this to be the case, \(5x\) must be even. Since 5 can't be even, then x must be even. Thus the product \(xy\) will be even. Sufficient.

2) \(6x\) will always be even. Then we have \(even + 7y = even\). Thus \(7y\) is even, and \(y\) is even, and \(xy\) is even. Sufficient.

Re: If x and y are positive integers , is the product xy even [#permalink]

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03 Aug 2016, 10:29

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krishan wrote:

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

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

Target question:Is xy even?

Statement 1: 5x - 4y is even Let's test all 4 cases case a: x is even and y is even: In this case 5x-4y is EVEN case b: x is even and y is odd: In this case 5x-4y is EVEN case c: x is odd and y is even: In this case 5x-4y is ODD case d: x is odd and y is odd: In this case 5x-4y is ODD So, cases a and b are both possible. In both cases the product xy is even So, xy must be even Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Aside: If anyone is interested, we have a video (below) on testing possible cases for these question types

Statement 2: 6x+7y is even Let's test all 4 cases case a: x is even and y is even: In this case 6x+7y is EVEN case b: x is even and y is odd: In this case 6x+7y is ODD case c: x is odd and y is even: In this case 6x+7y is EVEN case d: x is odd and y is odd: In this case 6x+7y is ODD So, cases a and c are both possible. In both cases the product xy is even So, xy must be even Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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