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If negative integers k and p are NOT both even, which of the

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

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26 Jan 2013, 15:52
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If negative integers 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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Jan 2013, 16:00, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Odds and Evens PS [#permalink]

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26 Jan 2013, 16:00
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marcovg4 wrote:
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

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.

Hope it's cler.
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Re: If negative integers k and p are NOT both even, which of the [#permalink]

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26 Jan 2013, 16:20
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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Re: If negative integers k and p are NOT both even, which of the [#permalink]

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28 Jan 2013, 04:41
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, 10:21
Hello from the GMAT Club BumpBot!

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

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22 Aug 2014, 09:23
Bunuel,

Does "NOT both even" mean both k and p cant be even simultaneously?
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Re: If negative integers k and p are NOT both even, which of the [#permalink]

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22 Aug 2014, 10:32
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sri30kanth wrote:
Bunuel,

Does "NOT both even" mean both k and p cant be even simultaneously?

k and p are NOT both even, means that k and p can be both odd, or one odd and another even but not both even.
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Re: If negative integers k and p are NOT both even, which of the [#permalink]

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10 Apr 2017, 10:40
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Re: If negative integers k and p are NOT both even, which of the [#permalink]

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10 Apr 2017, 11:01
marcovg4 wrote:
If negative integers 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

There are 2 possibilities -

1. Both k & p are odd

Plug in 2 values k = -1 & p = -3

(A) kp = 3
(B) 4(k + p) = -16
(C) k – p = 2
(D) k + 1 – p = -3
(E) 2(k + p) – 1 = -9

2. Either k or p is odd and the other is even

Plug in 2 values k = -1 & p = -2

(A) kp = 2
(B) 4(k + p) = -12
(C) k – p = 1
(D) k + 1 – p = -2
(E) 2(k + p) – 1 = -7

Thus, the answer must be (E) -7
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Re: If negative integers k and p are NOT both even, which of the   [#permalink] 10 Apr 2017, 11:01
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