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# If r and t are positive integers, is rt even?

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Manager
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If r and t are positive integers, is rt even? [#permalink]

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31 Jan 2010, 14:28
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Difficulty:

15% (low)

Question Stats:

76% (01:34) correct 24% (00:40) wrong based on 132 sessions

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If r and t are positive integers, is rt even?

(1) r + t is odd
(2) r^t is odd
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Jul 2013, 06:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: DS : Odd - even [#permalink]

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31 Jan 2010, 14:53
If r and t are positive integers, is rt even?

(1) r + t is odd. Either r = odd and t = even OR r = even and t = odd. In both cases rt = even. Sufficient.

(2) r^t is odd --> r = odd and t = any. rt either even or odd. Not sufficient.

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Re: DS : Odd - even [#permalink]

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02 Feb 2010, 10:13
It should be A only, same explanation above.
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Manager
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Re: DS : Odd - even [#permalink]

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12 Feb 2010, 15:47
A

1. One of r,t is even -- so sufficient
2. r is odd, no information on t -- insufficient
Manager
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Re: DS : Odd - even [#permalink]

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14 Feb 2010, 23:28
r and t are positive integers, is rt even?
a. r + t is odd
b. r^t is odd

a. if r+t is odd then at least either r or t should be even so if any one of the 2 numbers is even then their product should be even

so choice a is sufficient

b. if r and t both are odd then rt is odd
if r is even and t is odd then rt is even

so choice b is insufficient

so my choice is A
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Re: r and t are positive integers, is rt even? a. r + t is odd [#permalink]

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04 Jul 2013, 06:40
Statement

1 is A+B = odd >> so one has to be even the other odd >> sufficient!

2 $$R^T$$= odd

Take examples

$$3^2$$ = 9 >> $$3*2$$ = 6 Answer is yes

$$3^1$$ = 1 >> $$3*1$$ = 3 Answer is no

Insufficient!
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Re: r and t are positive integers, is rt even? a. r + t is odd   [#permalink] 04 Jul 2013, 06:40
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