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# If m and n are positive integers, is the product mn even

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Math Expert
Joined: 02 Sep 2009
Posts: 52118
If m and n are positive integers, is the product mn even  [#permalink]

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20 Apr 2018, 05:26
00:00

Difficulty:

35% (medium)

Question Stats:

95% (00:47) correct 5% (01:04) wrong based on 33 sessions

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If m and n are positive integers, is the product mn even?

(1) m + 1 is odd.
(2) m + n is odd

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Joined: 30 May 2017
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If m and n are positive integers, is the product mn even  [#permalink]

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20 Apr 2018, 08:27
Bunuel wrote:
If m and n are positive integers, is the product mn even?

(1) m + 1 is odd.
(2) m + n is odd

Statement (1) is sufficient.

m+1 is odd, therefore m is even and product mn is even

Statement (2) is sufficient.

m+n is odd. Therefore either m or n is even and other odd.

odd+even = odd

even+odd = odd

Therefore mn is even.

Hence (D) EACH statement ALONE is sufficient is the answer.
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Joined: 09 Jun 2012
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Re: If m and n are positive integers, is the product mn even  [#permalink]

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20 Apr 2018, 09:34
1
Given - m >0 , n >0

To prove: mn = even
Type- Y/N

For product to be even, one number should be even.

1. m +1 = odd
=> m is even (even+ odd= odd)
Sufficient

2. m+ n = odd
=> either m or n is even
Sufficient

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Re: If m and n are positive integers, is the product mn even &nbs [#permalink] 20 Apr 2018, 09:34
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