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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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29 Jan 2009, 04:47
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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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02 Aug 2016, 12:22
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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.

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

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29 Jan 2009, 05:25
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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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03 Aug 2016, 09:29
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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

[Reveal] Spoiler:
D

RELATED VIDEO

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

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29 Jan 2009, 06:43
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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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30 Nov 2014, 09:47
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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, 09:44
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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03 Aug 2016, 10:08
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.

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

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12 Jul 2017, 23:22
In my opinion, this type of problem is super easy if you really understand what you're being asked, and then re-frame the question to be more straightforward. It's more about the question than the math.

Given: (x,y) > 0, AND are integers

Original Question: Is xy even?

We know that any number multiplied by an even number is even, so the question is really asking: Do we know if either "X" or "Y" (or both, or neither) is even?

Reframing the question this way is better, in my opinion.

A.) 5x - 4y is even.

For 5x - 4y to be even, both 5x and 4y have to be of the same parity. ("Parity" is the word that describes whether a number is odd or even)
In other words, odd + odd, or even + even, produce even results.

5x - 4y

We know off the bat that "4y" is even, because 4 is even. 4 times anything would be even. So we have ( 5x - EVEN NUMBER = EVEN NUMBER. ) Therefore, we know that "5x" is also even, because 4y (even) and 5x have to be the same parity. (even minus even = even)

In order to make 5x even, "x" has to be even. That's because 5 is odd.

Knowing that "x" is even is enough to answer the question: Do we know if either "X" or "Y" (or both, or neither) is even?

SUFFICIENT.

B.) 6x + 7y is even

Same drill here. For 6x + 7y to be even, both terms have to be the same parity. Since 6 is even, we know that 6x is even. Since 6x is even, we know that 7y is even. Since 7y is even, we know that y is even (since 7 is odd).

Knowing that "y" is even is enough to answer the question: Do we know if either "X" or "Y" (or both, or neither) is even?

SUFFICIENT

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

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15 Nov 2017, 02:48
$$S1: 5x - 4y = even => 5x = even+4y => 5x = even => x = even => xy = even. Suff$$

$$S2: 6x+7y = even => 7y = even - 6x =>7y = even => y = even => xy = even. Suff$$

Both S1 and S2 are individually sufficient. Final answer = D
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Re: If x and y are positive integers , is the product xy even   [#permalink] 15 Nov 2017, 02:48
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