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Is integer x odd?

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Senior Manager
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Is integer x odd? [#permalink] New post 20 Feb 2007, 18:09
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Hi all,

Could you please explain this for me? I am posting only one part of a DS question.

Is integer x odd?
(1) x/2 is NOT an even integer.


My answer: (1) is sufficient.

Since 2 is an even integer, there are two situations either [even/even = even] as in 12/2 = 6 or [even/even = odd] as in 10/2 = 5.

Back to the answer: x/2 = NOT an even int, which means x/2 = odd integer. In that case x can be 10, 14, 18 or so.....and x is EVEN. So the answer for this first part is confirmed NO which means (1) is sufficient.

Am I right?

Thanks.
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 [#permalink] New post 20 Feb 2007, 19:13
x/2 is NOT an even integer

from this we can conclude that either x/2 is an odd integer or fraction.

so, (1) is insufficient.
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 [#permalink] New post 21 Feb 2007, 01:21
But the question says that X is an integer.

I'm confused too.
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 [#permalink] New post 21 Feb 2007, 03:14
result is not even and x is even, e.g. :

6/2 = 3 -->x/2 yields an odd (not even) integer and x is even.

result is not even and x is odd, e.g. :

5/2 = 2.5 --> x/2 is "not an even integer' and x is odd

therefore we can't know whether x is odd or not from knowing that x/2 is not an even integer.

INSUFFICIENT
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 [#permalink] New post 21 Feb 2007, 06:06
Yes bz9, that's what confusing me.

Is integer x odd?
(1) x/2 is NOT an even integer

OR

Is integer x odd?
(1) x/2 is NOT an even integer (which means NOT an even integer = ODD integer or FRACTION)
Senior Manager
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 [#permalink] New post 21 Feb 2007, 17:10
Last night I thought about this question and found it was a trap question. NOT is included to make it a trap question.

When we think of a number in general way, 3 types of numbers come to our mind: even int, odd int or a fraction. "NOT an even int" means we deduce the first choice of the three types I listed, therefore it can be an odd int or a fraction.

Is anybody agree with me?

Anyways, the correct answer is (1) is NOT SUFFICIENT.
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 [#permalink] New post 21 Feb 2007, 20:04
Yeah, I think Khaos hit it right on the head.

I think I overlooked the part that said X/2 is not an even integer.

PS Summer,
I corrected that sequence question I posted earlier if you want to give it a try.
  [#permalink] 21 Feb 2007, 20:04
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