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If a negative k and p are NOT both even, which of the following must be odd?

A. kp B. 4(k + p) C. k - p D. k + 1 - p E. 2(k + p) - 1

The question should read: If negative integers k and p are NOT both even, which of the following must be odd?

(A) kp --> can be even if either k or p is even. (B) 4(k + p) --> always even. (C) k – p --> can be even as well as odd. For example consider k-p=odd-odd=even and k-p=odd-even=odd. (D) k + 1 – p --> can be even as well as odd. For example consider, k+1-p=odd+odd-odd=odd and k+1-p=odd+odd-even=even. (E) 2(k + p) – 1 --> always odd, because: 2(k+p)-1=2*integer-odd=even-odd=odd.

Re: If negative integers k and p are NOT both even, which of the [#permalink]

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26 Jan 2013, 15:20

Totally!

I had a dilemma yesterday while answering the question, whether the answer was A or E, but a closer look shows that "both NOT even" infer that one of them could be even, and that's the part I had trouble with. I thought that "both NOT even = both ARE odd".

Thanks for the help Bunuel!
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MV "Better to fight for something than live for nothing.” ― George S. Patton Jr

Re: If negative integers k and p are NOT both even, which of the [#permalink]

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28 Jan 2013, 03:41

marcovg4 wrote:

Totally!

I had a dilemma yesterday while answering the question, whether the answer was A or E, but a closer look shows that "both NOT even" infer that one of them could be even, and that's the part I had trouble with. I thought that "both NOT even = both ARE odd".

Thanks for the help Bunuel!

Actually irrespective of whether they are odd or even, choice E gives an odd number. It's 2 times some number -1 or simply even number - 1, hence odd. You don't need to look beyond.
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Re: If negative integers k and p are NOT both even, which of the [#permalink]

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11 Jul 2014, 09:21

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