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Number Systems -Odds & Evens

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Oct 16, 2013 11:08 am
sukhman 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 free video on testing possible cases for these question types: https://www.gmatprepnow.com/module/gmat- ... ies?id=839

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 = D

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by GMATGuruNY » Wed Oct 16, 2013 11:09 am
sukhman wrote:If x and y are positive integers, is the product xy even?
1). 5x-4y is even 2). 6x+7y is even.
Statement 1:
5x = EVEN + 4y = EVEN + EVEN = EVEN.
5x is even only if x is even.
Since x is even, xy is even.
SUFFICIENT.

Statement 2:
7y = EVEN - 6x = EVEN - EVEN = EVEN.
7y is even only if y is even.
Since y is even, xy is even.
SUFFICIENT.

The correct answer is D.
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by sukhman » Wed Oct 16, 2013 11:11 pm
Statement 1 case b: x is even and y is odd: In this case 5x-4y is EVEN


Staement 2 case b: x is even and y is odd: In this case 6x+7y is ODD

There is disrepancy among these two , in statement 1 and 2
what I did was since xy we need it to be even we can take 3 cases
x-even y-odd
x-odd y-even
x-even y-even
Brent please correct me if I am wrong (I know I am :)
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