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

Question

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

Bunuel · Answer

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.

Answer: E.

Hope it's cler.

marcovg4 · Answer

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!

Vips0000 · Answer

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.

sri30kanth · Answer

Bunuel,

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

Bunuel · Answer

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.

Abhishek009 · Answer

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

bumpbot · Answer

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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

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