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

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

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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
[Reveal] Spoiler: OA

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

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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.

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

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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


D. in either case x and y has to be even.

(1) 5x - 4y is even: x has to be even. suff.
(2) 6x + 7y is even: y has to be even. suff.
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Re: If x and y are positive integers , is the product xy even [#permalink]

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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

Answer =
[Reveal] Spoiler:
D


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

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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


agree with D.

1) 5x - 4y is even -> x must be multiple of 2
5*2k-4y = 2*(any number) even
sufficient
2)6x + 7y is even[/
y should multiple of 2

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

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

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Hello from the GMAT Club BumpBot!

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

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New post 03 Aug 2016, 11:08
krishan wrote:
If x and y are positive integers , is the product xy even

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


For xy to be even, either x or y or both must be even.

(1) 5x - 4y is even
E-E=E
O-O=E

Since 4y is even, 5x has to be even. 5 is not even, hence x is even.

xy will be even.

(2) 6x + 7y is even
E+E= E
O+O=E

Since 6x is even, 7y has to be even. And because 7 is not even y has to be even.

xy will be even.

Both statements are sufficient.

D is the answer
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Re: If x and y are positive integers , is the product xy even   [#permalink] 03 Aug 2016, 11:08
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