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# If m is an integer, is m odd?

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Joined: 03 Apr 2013
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If m is an integer, is m odd?  [#permalink]

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Updated on: 03 May 2016, 22:24
2
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:26) correct 48% (01:43) wrong based on 112 sessions

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If m is an integer, is m odd?

(1) m/2 is not an even integer.

(2) m – 3 is not an even integer.

My doubt is regarding the interpretation of the statements, as (1) says " m
2 is not an even integer.", does this mean that m can be anything other than a positive integer? i.e. non-positive integer, positive or negative fraction?

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Originally posted by ShashankDave on 03 May 2016, 22:18.
Last edited by Bunuel on 03 May 2016, 22:24, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If m is an integer, is m odd?  [#permalink]

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03 May 2016, 22:27
2
ShashankDave wrote:
If m is an integer, is m odd?

(1) m/2 is not an even integer.

(2) m – 3 is not an even integer.

My doubt is regarding the interpretation of the statements, as (1) says " m
2 is not an even integer.", does this mean that m can be anything other than a positive integer? i.e. non-positive integer, positive or negative fraction?

If m is an integer, is m odd?

(1) m/2 is not an even integer --> $$\frac{m}{2}\neq{even}$$ could occur when $$m$$ is odd as well as when $$m$$ is even (10 and 5 for example) --> $$\frac{m}{2}=\frac{10}{2}=5\neq{even}$$ and $$\frac{m}{2}=\frac{5}{2}=2.5\neq{even}$$. Not sufficient.

(2) m-3 is not an even integer --> $$m-odd=odd$$ --> $$m=odd+odd=even$$. Sufficient.

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If m is an integer, is m odd?  [#permalink]

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11 Jul 2018, 22:47
- In 1st case

m/2 is not an even integer , so if m is divisible by 2 then m has to be even.

How can we test by substituting m=5 ?

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Re: If m is an integer, is m odd?  [#permalink]

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11 Jul 2018, 22:50
prags1989 wrote:
- In 1st case

m/2 is not an even integer , so if m is divisible by 2 then m has to be even.

How can we test by substituting m=5 ?

m/2 is not an even integer does not mean that m/2 is necessarily an odd integer, it can be non-integer too.
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Re: If m is an integer, is m odd? &nbs [#permalink] 11 Jul 2018, 22:50
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