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

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If r and t are positive integers, is rt even? [#permalink] New post 31 Jan 2010, 13:28
00:00
A
B
C
D
E

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  15% (low)

Question Stats:

77% (01:46) correct 23% (00:42) wrong based on 56 sessions
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, 05:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: DS : Odd - even [#permalink] New post 31 Jan 2010, 13:53
Expert's post
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.

Answer: A.
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Re: DS : Odd - even [#permalink] New post 02 Feb 2010, 09:13
It should be A only, same explanation above.
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Re: DS : Odd - even [#permalink] New post 12 Feb 2010, 14:47
A

1. One of r,t is even -- so sufficient
2. r is odd, no information on t -- insufficient
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Re: DS : Odd - even [#permalink] New post 14 Feb 2010, 22:28
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] New post 04 Jul 2013, 05:40
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, 05:40
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