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If p, q, and r are non-negative integers and p^q + r is an even number

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If p, q, and r are non-negative integers and p^q + r is an even number  [#permalink]

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New post 21 Nov 2019, 01:17
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

19% (01:36) correct 81% (01:43) wrong based on 37 sessions

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Re: If p, q, and r are non-negative integers and p^q + r is an even number  [#permalink]

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New post 21 Nov 2019, 19:22
Bunuel wrote:
If p, q, and r are non-negative integers and \(p^q + r\) is an even number which of the following must also be even?

A. p + q + r

B. pqr

C. p + r

D. q + r

E. None of these



This is a must question and we have power in the term so we can play around with it and can have various combinations possible so in all likelihood it should be E

p^q+r is even, so if q=0, p could be anything odd or even and r would be odd.
So p+r and p+q+r are out.....2+1 or 2+0+1
All three could be odd, so 3^1+5...
So pqr is out 3*1*5
Finally q could be even and p and r odd.
So 3^2+3, but 2+3 is odd. Hence q+r is odd.

E
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Re: If p, q, and r are non-negative integers and p^q + r is an even number  [#permalink]

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New post 24 Nov 2019, 19:19
Bunuel wrote:
If p, q, and r are non-negative integers and \(p^q + r\) is an even number which of the following must also be even?

A. p + q + r

B. pqr

C. p + r

D. q + r

E. None of these


Let’s test some numbers. If p = q = r = 1, then 1^1 + 1 = 2, which is even. On the other hand, neither p + q + r = 3, nor pqr = 1 is even; thus, we eliminate A and B.

If p = 2, q = 0 and r = 1, then 2^0 + 1 = 2, which is even. On the other hand, neither p + r = 3, nor q + r = 1 is even. Thus, we eliminate C and D as well. E is the only remaining answer choice.

Answer: E
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Re: If p, q, and r are non-negative integers and p^q + r is an even number   [#permalink] 24 Nov 2019, 19:19
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