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

Question

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

rulingbear · Answer

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.

pushpitkc · Answer

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

JeffTargetTestPrep · Answer

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.

Answer: D

Paras96 · Answer

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

According to the question, we can infer that q = odd and nothing can be said about p i.e. p can be odd or even

Going by the options

(A) p – q = even/odd - odd = even/odd.  Incorrect

(B) p + 2q = even/odd + even = even/odd.  Incorrect

(C) 3p + q = even/odd + odd = even/odd.  Incorrect

(D) 2p + q^2 = even + odd = odd.  correct hence answer

(E) 3p + 3q = even/odd + odd = even/odd.  Incorrect

bumpbot · Answer

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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