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

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Manager
Joined: 27 Dec 2009
Posts: 140
If r and t are positive integers, is rt even?  [#permalink]

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Updated on: 04 Jul 2013, 05:48
2
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:00) correct 23% (01:15) wrong based on 198 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

Originally posted by msand on 31 Jan 2010, 13:28.
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.
Math Expert
Joined: 02 Sep 2009
Posts: 51230
Re: DS : Odd - even  [#permalink]

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31 Jan 2010, 13:53
1
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, 09:13
It should be A only, same explanation above.
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Manager
Joined: 10 Feb 2010
Posts: 156
Re: DS : Odd - even  [#permalink]

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12 Feb 2010, 14:47
A

1. One of r,t is even -- so sufficient
2. r is odd, no information on t -- insufficient
Manager
Joined: 26 Nov 2009
Posts: 122
Re: DS : Odd - even  [#permalink]

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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
Director
Joined: 29 Nov 2012
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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, 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: If r and t are positive integers, is rt even?  [#permalink]

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18 Aug 2018, 13:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If r and t are positive integers, is rt even? &nbs [#permalink] 18 Aug 2018, 13:20
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