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# If a*b is an even integer, is b a multiple of 2?

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Joined: 02 Aug 2009
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If a*b is an even integer, is b a multiple of 2?  [#permalink]

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Updated on: 19 Jul 2017, 21:32
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65% (hard)

Question Stats:

32% (01:23) correct 68% (00:50) wrong based on 43 sessions

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If a*b is an even integer, is b a multiple of 2?

(1) a is not a multiple of 2.
(2) b is product of two consecutive integers.

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Originally posted by chetan2u on 19 Jul 2017, 20:07.
Last edited by Bunuel on 19 Jul 2017, 21:32, edited 1 time in total.
Renamed the topic.
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If a*b is an even integer, is b a multiple of 2?  [#permalink]

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19 Jul 2017, 21:33
if a*b is an even integer and

1) a is not multiple of 2 then b must be multiple of 2 for a*b to be an even number Sufficient

2) b is product of two consecutive no. let take b=3*4 or b=11*12 so as you see b is even Sufficient

Answer is D
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Re: If a*b is an even integer, is b a multiple of 2?  [#permalink]

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19 Jul 2017, 22:36
If a*b is an even integer, is b a multiple of 2?

1. a is not a multiple of 2.
If a is not a multiple of 2
Case 1: If a = 1, and b = 2. The expression a*b is an even integer and a is a multiple of 2
Case 2: If a = 2/3 and b = 3. The expression a*b is an even integer and a is not a multiple of 2(Insufficient)

2. b is product of two consecutive integers.
If b is a product of 2 consecutive integers, it has to be even*odd or odd*even
b will be a multiple of 2. (Sufficient) (Option B)
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Re: If a*b is an even integer, is b a multiple of 2?  [#permalink]

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19 Jul 2017, 23:28
A*B = Even Integer
A,B = ?
1) we don’t know if A & B are integers so B could be an even integer, or A could be a fraction and B could be an odd integer. Insufficient.

2) B = n(n+1) where n is an integer => B is even. Sufficient.

B is the answer.

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Re: If a*b is an even integer, is b a multiple of 2?   [#permalink] 19 Jul 2017, 23:28
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# If a*b is an even integer, is b a multiple of 2?

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