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If a and b are integers, is a·b even?

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If a and b are integers, is a·b even?  [#permalink]

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New post 21 Aug 2017, 09:12
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (00:32) correct 34% (00:48) wrong based on 82 sessions

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Re: If a and b are integers, is a·b even?  [#permalink]

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New post 21 Aug 2017, 09:18
Given a and B are integers.

Find : ab = even or not

1. a is even. if a is even. anything integer multiplied to even integer gives even integer output . So ab is even . Sufficient.

2. ab^2 is even => either a is even or b^2 even ie b is even or both a and b are even.
So again anything multiplication of even integer with any other integer gives even result. so ab=even.
Sufficient

Answer= D
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If a and b are integers, is a·b even?  [#permalink]

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New post 21 Aug 2017, 09:19
Bunuel wrote:
If a and b are integers, is a·b even?

(1) a is even.

(2) a·b^2 is even.


For \(a.b\) to be even either \(a\) or \(b\) can be even

Statement 1: \(a\) is even, so any number multiplied by even number will be even. hence sufficient

Statement 2: \(a.b^2 = Even\). this implies that either \(a\) or \(b\) is even. Hence sufficient

Option \(D\)
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Re: If a and b are integers, is a·b even?  [#permalink]

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New post 22 Aug 2017, 10:06
Bunuel wrote:
If a and b are integers, is a·b even?

(1) a is even.

(2) a·b^2 is even.


Statement 1 : SUFFICIENT, whatever b is, a*b must be even.

Statement 2 :
- If \(a*b^2 = even\), then either \(a\) or \(b^2\) is even.
- If \(a\) is even, then \(a*b\) must be even.
- If \(b^2\) even, so b must be even and then \(a*b\) must be even.
SUFFICIENT.

D.
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Re: If a and b are integers, is a·b even?  [#permalink]

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New post 23 Aug 2017, 02:43
is a*b=even,
statement 1 : a is even which would make a*b even as any number multiplied by an even number would result in an even number, hence sufficient.
Statement 2 : a*b^2 is even which means either a is even or b^2 is even. if a is even then a*b is also even. if b^2 is even, then b is also even as even*even is even and hence a*b is also even. hence sufficient.
so answer is D where both statements are sufficient.
Re: If a and b are integers, is a·b even? &nbs [#permalink] 23 Aug 2017, 02:43
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