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QOTD#11 If p and q are both positive odd integers, which of
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25 Oct 2016, 13:05

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Question Stats:

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

Indicate all possible values.

A. \(pq\)

B. \(2pq\)

C. \(3pq\)

D. \(pq + p^q\)

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

Drill 2

Question: 8

Page: 287

Question: 8

Page: 287

Re: QOTD#11 If p and q are both positive odd integers, which of
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25 Oct 2016, 13:12

Expert Reply

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.

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
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17 Nov 2016, 16:38

1

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

Indicate all possible values.

A. pq

B. 2pq

C. 3pq

D. pq + p^q

E. p^q + q^p

Show: :: 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
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08 Jun 2020, 07:37

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Re: QOTD#11 If p and q are both positive odd integers, which of
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30 Jul 2024, 11:52

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Re: QOTD#11 If p and q are both positive odd integers, which of [#permalink]

30 Jul 2024, 11:52
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