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a/b even, a-b even,which is odd ? 1. a/2 2. b/2 3.

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CEO
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a/b even, a-b even,which is odd ? 1. a/2 2. b/2 3. [#permalink]  12 Sep 2003, 03:09
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a/b even, a-b even,which is odd ?

1. a/2
2. b/2
3. a+b/2
4. a
5. b
Senior Manager
Joined: 21 Aug 2003
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Location: Bangalore
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i am getting both a & b as even given that : a/b=even & a-b=even
In that case none of the answers are coming to be odd.
- Vicks
Senior Manager
Joined: 22 May 2003
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Same as Vicky.. I get a,b both EVEN

Thanks

Martin
CEO
Joined: 15 Aug 2003
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Kudos [?]: 702 [0], given: 781

mystery wrote:

i have no idea how you guys are getting 3.

SVP
Joined: 30 Oct 2003
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I think none of them match.
if a = 8 b = 4
8/4 is even 8-4 is even

1. a/2 = 8/2 = even
2. b/2 = 4/2 = even
3. a+b/2 = 8+4/2 = even
4. a is even
5. b is even
Intern
Joined: 05 Jan 2004
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Does not Match [#permalink]  19 Jan 2004, 09:01
According to me none of the answers could match

if a/b = even then we can say a = (2n)b where n is any integer

a-b = even, then we can say that a-b = 2k where k is any integer

then we can say that b = 2k/(2n-1)

and b could be odd or even, if k = 3, n = 2 b = even
and b could be a fraction as well, not even an integer for other values

so there is really no way to say

That is what I think
Director
Joined: 28 Oct 2003
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As everyone has shown, none of them MUST be odd, however, if you set:

A=0
B=6

Then A/B=0 (even) and A-B=-6 (even).

a/2 even
b/2 odd
a+b/2 odd
a even
b even.
SVP
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Stoolfi's obsession with zero plays out.

I will watchout for zero in every problem now onwards.
Intern
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Odd/Even [#permalink]  19 Jan 2004, 17:14
a/b even, a-b even,which is odd ?

1. a/2
2. b/2
3. a+b/2
4. a
5. b

I pick 3!

A and B must be even. (Cause if A is odd and B is even, you will not get an integer.) So, go through the answer choices.

1) Even/2 is even 4/2= 2
2) Even/2 is even again

Which leaves us to C. Remember, when playing odd and even, choosing numbers doesn't always work. If you pick A=10, B=14; then (10+14)/2= 12. And then you're confused.

Look on the number line... 10 . 11 . 12 . 13. 14, the middle number if 12.

But if you choose A=2, B=4.
Look on the number line.. 2 . 3 . 4.. the middle number if 3;
so (2+4)/2 = 3 which is odd.

Remember how to choose numbers in PS and DS will definately help you. Don't choose random numbers, know what you are trying to prove.
Senior Manager
Joined: 11 Nov 2003
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I think this problem should be addressed in more structured way:

a/b = even => a = even (it does not matter whether b is odd or even, a will always be even)

a-b = even => There are only two possibilities:
a= odd & b = odd OR a= even & b = even

Considering both statements, we can conclude that a and b both should be even.

Now pick numbers, but while picking the numbers, also check that it satisfy the original statements given in the question. For example, we can not select a = 10 and b = 14. Because although both of them are even, they do not satisfy the first statment a/b = even.

a = 2, 4, 6, ,8, 10, 12.......
b = 2, 4, 6, 8, 10, 12.......

Now find few possible pairs of a and b. (2,2) is not possible (does not satisfy the given equation)

possible pairs could be (4,2), (8, 2), (8,4), (12,2), (12,6)

Now check each answer choice. Only choice 3 can become ODD and that too NOT ALWAYS. Because if a = 8, b = 4, then a+b/2 = 6(even).

So I think the question should probably be worded as "which of the following COULD BE ODD". If it is "which of the following MUST BE ODD" then I guess none of the choices meet the criteria.

Director
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Hey-- gmatblast and gmatanh--

Did I make a mistake or did you skip my post?

Using these values:

A=0
B=6

Both b/2 and a+b/2 can be made odd.
Intern
Joined: 05 Dec 2003
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Location: LA
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Yikes.. you are right.. what's the correct answer?
Senior Manager
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stoolfi wrote:
Hey-- gmatblast and gmatanh--

Did I make a mistake or did you skip my post?

Using these values:

A=0
B=6

Both b/2 and a+b/2 can be made odd.

Stoofi,

I did not skip your post. I was just trying to address the problem in more procedural way. I understand whet you tried to say in your post. And I think I missed the point you were trying to make (in hurry..). This resulted in long and unnecessary method.

I think that the question is missing additional information.
Intern
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Re: PS : even/odd [#permalink]  24 Jan 2004, 03:39
[quote="praetorian123"]a/b even, a-b even,which is odd ?

1. a/2
2. b/2
3. a+b/2
4. a
5. b[/quote]

I got Answer 3. i assumed a=4 b=2 4/2= 2 (even). 4-2=2 (even-even=even)
Re: PS : even/odd   [#permalink] 24 Jan 2004, 03:39
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