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

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Manager
Joined: 10 Oct 2018
Posts: 118
Location: United States
Schools: Sloan (MIT)
GPA: 4
If p and q are integers and p + q + p is odd, which of the following m  [#permalink]

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Updated on: 17 Nov 2018, 06:39
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Difficulty:

25% (medium)

Question Stats:

74% (00:44) correct 26% (00:55) wrong based on 69 sessions

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

(A) p
(B) q
(C) p+q
(D) pq
(E) pq+p

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Originally posted by topper97 on 17 Nov 2018, 04:34.
Last edited by topper97 on 17 Nov 2018, 06:39, edited 1 time in total.
Intern
Joined: 25 Sep 2018
Posts: 3
Re: If p and q are integers and p + q + p is odd, which of the following m  [#permalink]

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17 Nov 2018, 04:48
If P is Odd -> p + p is even
If P is Even -> p + p is even

Therefore, q must be odd that p + q + p is also odd

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Senior Manager
Joined: 04 Jun 2018
Posts: 388
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
Re: If p and q are integers and p + q + p is odd, which of the following m  [#permalink]

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17 Nov 2018, 05:33
Anser is choice B

q must be odd, e.g. follwing patterns;

2+1+2 = 5
1+3+1 = 5
1+2+1 = 4
2+4+2 = 8

Hence all combinations with an even q would yield even results, thus q must be odd.
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Re: If p and q are integers and p + q + p is odd, which of the following m  [#permalink]

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17 Nov 2018, 06:20
topper97 wrote:
If p and q are integers and p + q + p is odd, which of the following must be odd?

(A) p
(B) q
(C) p+q
(D) pq
(E) pq+p

$$p + q + p = ODD$$

Or, $$2p + q = ODD$$

Whatever be the value of $$p$$ , $$2p$$ must be $$Even$$

So, We have $$Even \ + \ q \ = \ ODD$$; Thus, $$q$$ must be ODD, Answer must be (B)
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Manager
Joined: 20 Dec 2018
Posts: 51
Re: If p and q are integers and p + q + p is odd, which of the following m  [#permalink]

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21 Dec 2018, 20:41
p + q + p = 2p + q
2p can’t be odd because it is a multiple of 2. Hence, q is odd.
Re: If p and q are integers and p + q + p is odd, which of the following m &nbs [#permalink] 21 Dec 2018, 20:41
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