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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.

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

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

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13 Jul 2017, 00:22

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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?

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

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24 Dec 2017, 18:09

If x and y are positive integers, is the product xy even (1) 5x - 4y is even (2) 6x + 7y is even

1. for 5x-4y = Even, x must be even & y may or may not be even. Since x is even, we can conclude xy is even. SUFFICIENT. Even – Even = Even Even – Odd = Odd Odd – Even = Odd Odd – Odd = Odd

2. for 6x + 7y is even, y must be even. Since y is even, we can conclude xy is even. SUFFICIENT. Even + Even = Even Odd + Even = Odd Even + Odd = Odd

gmatclubot

Re: If x and y are positive integers , is the product xy even
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24 Dec 2017, 18:09