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QOTD#11 If p and q are both positive odd integers, which of

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QOTD#11 If p and q are both positive odd integers, which of [#permalink] New post 25 Oct 2016, 13:05
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Question Stats:

80% (00:39) correct 19% (00:04) wrong based on 46 sessions
If p and q are both positive odd integers, which of the following must be odd?
Indicate all possible values.

A. \(pq\)

B. \(2pq\)

C. \(3pq\)

D. \(pq + p^q\)

E. \(p^q + q^p\)

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Question: 8
Page: 287
[Reveal] Spoiler: OA

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Re: QOTD#11 If p and q are both positive odd integers, which of [#permalink] New post 25 Oct 2016, 13:12
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Explanation

As soon as you see variables in the answer choices, set up your scratch paper to Plug In.

Start with easy numbers like p = 3 and q = 5, and eliminate any answer choice that doesn’t yield an odd result.

Choice A is 15, so keep it.

Choice B is 30, so eliminate choice B.

Choice C is 45, so keep it.

Choice D is 258, and Choice E is 368, so you can eliminate both; if you recognize them as the sum of two odd numbers, you don’t have to calculate either of them. It’s a must be problem, so try another set of numbers in choices A and C to be sure; as long as p and q are both positive odd integers, choices A and C will always work.

Hence options A and C are correct.
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Re: QOTD#11 If p and q are both positive odd integers, which of [#permalink] New post 17 Nov 2016, 16:38
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sandy wrote:
If p and q are both positive odd integers, which of the following must be odd?
Indicate all possible values.

A. pq
B. 2pq
C. 3pq
D. pq + p^q
E. p^q + q^p


[Reveal] Spoiler: OA
A,C


Some important rules:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN

4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN


A. pq = (ODD)(ODD) = ODD
B. 2pq = (EVEN)(ODD)(ODD) = EVEN
C. 3pq = (ODD)(ODD)(ODD) = ODD
D. pq + p^q = (ODD)(ODD) + (ODD)^ODD = ODD + ODD = EVEN
E. p^q + q^p = (ODD)^ODD + (ODD)^ODD = ODD + ODD = EVEN

Answers: A and C

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Re: QOTD#11 If p and q are both positive odd integers, which of [#permalink] New post 08 Jun 2020, 07:37
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Re: QOTD#11 If p and q are both positive odd integers, which of   [#permalink] 08 Jun 2020, 07:37
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