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# If p and q are integers and 20p + 3q is odd, which of the following

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Joined: 02 Sep 2009
Posts: 44388
If p and q are integers and 20p + 3q is odd, which of the following [#permalink]

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20 Nov 2017, 11:11
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If p and q are integers and 20p + 3q is odd, which of the following must be odd?

(A) p – q

(B) p + 2q

(C) 3p + q

(D) 2p + q^2

(E) 3p + 3q
[Reveal] Spoiler: OA

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If p and q are integers and 20p + 3q is odd, which of the following [#permalink]

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20 Nov 2017, 11:29
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Bunuel wrote:
If p and q are integers and 20p + 3q is odd, which of the following must be odd?

(A) p – q

(B) p + 2q

(C) 3p + q

(D) 2p + q^2

(E) 3p + 3q

$$p$$ could be odd/even and $$q$$ will always be odd as both variables are integers.

The answer could be narrowed down to D as $$2p$$ is always even regardless and $$q^2$$ is odd. $$Odd + Even = Odd$$.

Hence, D.

Last edited by rulingbear on 20 Nov 2017, 12:00, edited 1 time in total.
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If p and q are integers and 20p + 3q is odd, which of the following [#permalink]

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20 Nov 2017, 11:54
Given data: p,q are integers and 20p + 3q is odd.

Whatever the value of p(odd/even), 20p will be even.
Since the resultant sum is odd, q must be odd.

Substituting values

1. p = q = 1 Option A,C and E are even. Both B and D are odd.
2. p=2, q=1 Option B is even. Only Option D remains

Therefore, Option D($$2p + q^2$$) must be the only expression which is ODD for all possibilities of p,q
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Re: If p and q are integers and 20p + 3q is odd, which of the following [#permalink]

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22 Nov 2017, 13:14
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Expert's post
Bunuel wrote:
If p and q are integers and 20p + 3q is odd, which of the following must be odd?

(A) p – q

(B) p + 2q

(C) 3p + q

(D) 2p + q^2

(E) 3p + 3q

There are three rules that are useful for this problem:

even x any integer = even

even + odd = odd

odd x odd = odd

We see that 20p must be even, so we have:

even + 3q = odd

We see that 3q must be odd, so q must be odd.

Therefore we see that answer D must be odd, because 2p is even and q^2 = odd x odd = odd.

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Re: If p and q are integers and 20p + 3q is odd, which of the following   [#permalink] 22 Nov 2017, 13:14
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