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If x, y, and z are all positive integers, is x + y + z even?

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Chetangupta
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If x, y, and z are all positive integers, is x + y + z even? [#permalink] New post   22 Oct 2013, 08:07
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If x, y, and z are all positive integers, is x + y + z even?

1) \(\frac{2x}{(y+z)}\) = odd

2) \(\frac{x^2}{4yz}\) is an integer
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Re: If x, y, and z are all positive integers, is x + y + z even? [#permalink] New post   22 Oct 2013, 09:14
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If x, y, and z are all positive integers, is x + y + z even?

(1) \(\frac{2x}{(y+z)}\) = odd --> \(2x=even=(y+z)*odd\) --> \(y+z=even\). But x can be even or odd. Not sufficient.

(2) \(\frac{x^2}{4yz}\) is an integer --> \(x^2=4yz*integer=even\) --> x must be even. We don't know about y and z. Not sufficient.

(1)+(2) \(y+z=even\) and \(x=even\) --> \(x + y + z=even\). Sufficient.

Answer: C.
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Re: If x, y, and z are all positive integers, is x + y + z even? [#permalink] New post   20 Jan 2017, 10:52
Great Question.
From statement 1->
y+z must be even.
x can be even/odd.
Not sufficient.
From statement 2->
x must be even as x^2 is even.
y and z can be even or odd.
Not sufficient.
Combing them -> x is even and y+z is even => x+y+z must be even too.
Hence sufficient.
Hence C.
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Re: Question posted previously in the GMAT Club [#permalink] New post   18 Jul 2022, 06:42
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This question was published before. It’s an amazing question that I would like to post my answer to help students.
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Re: Question posted previously in the GMAT Club [#permalink]
18 Jul 2022, 06:42
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