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# Odd/Even

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Senior Manager
Joined: 10 Mar 2008
Posts: 331

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03 Oct 2008, 10:54
I cant figure out which one of these will be ODD. Every single option turns out to be even.

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Manager
Joined: 22 Sep 2008
Posts: 117

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03 Oct 2008, 10:58
c ...

Current Student
Joined: 28 Dec 2004
Posts: 3288
Location: New York City
Schools: Wharton'11 HBS'12

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03 Oct 2008, 11:03
i get d..

a+2/2 will be odd..

from the stem we know both a and b are even..

we also know that a=b*even which means a will always b divisible by 4..

so lets pick 8 +2=10/2=5 you cant pick something like 12 since it violates the stem..

basically a=2^n...

2^n +2=2(2^(n-1) +1)/2 then you get 2^(n-1) + 1 ..i.e even+odd=odd...always
Intern
Joined: 29 Sep 2008
Posts: 46

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03 Oct 2008, 11:03
a combination of calculation and intuition and substitution suggests to me it should be D.
Director
Joined: 27 Jun 2008
Posts: 507
WE 1: Investment Banking - 6yrs

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03 Oct 2008, 11:08
I get D

a = 12
b = 6

I get b,c & d odd

a = 8
b = 4

d is odd
Intern
Joined: 29 Sep 2008
Posts: 46

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03 Oct 2008, 11:15
aim2010 wrote:
a combination of calculation and intuition and substitution suggests to me it should be D.

looking at fresinha post i think i have a mathematical proof for D.

it can be inferred that a can be expressed as 4x and b as 2y. just to drive home the "must" point in the question, it is possible that b can also take a form of 4y, but we are taking the worst case scenario, hence a will ALWAYS have a factor of 4, not b.

(a+2)/2=(4x+2)/2=2x+1 --> always odd none of the other options satisfy with such certainty.
SVP
Joined: 29 Aug 2007
Posts: 2425

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03 Oct 2008, 11:28
fresinha12 wrote:
i get d..

a+2/2 will be odd..

from the stem we know both a and b are even..

we also know that a=b*even which means a will always b divisible by 4..

so lets pick 8 +2=10/2=5 you cant pick something like 12 since it violates the stem..

basically a=2^n...

2^n +2=2(2^(n-1) +1)/2 then you get 2^(n-1) + 1 ..i.e even+odd=odd...always

Agree with D but the statement that "basically a=2^n..." is not true cuz "a" has to be a multiple of 4. in that case "a" could be 4 or 8 or 12. If a is 12, then it doesnot fit anywhere on the expression that a = 2^n.... so a = 2^n is not correct.

the strongest reason why (a+2)/2 is odd is that a must be a multiple of 4.
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Current Student
Joined: 28 Dec 2004
Posts: 3288
Location: New York City
Schools: Wharton'11 HBS'12

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05 Oct 2008, 10:51
I dont think you can have any odd prime factors for a..

lets say for argument sake..a=12 and b=4 12-4=8 but 12/4=3 so you see you can have a multiple of 4, but it wont meet the requirement laid out in the stem..therefore i feel..a at the least has to be 2^n ...

GMAT TIGER wrote:
fresinha12 wrote:
i get d..

a+2/2 will be odd..

from the stem we know both a and b are even..

we also know that a=b*even which means a will always b divisible by 4..

so lets pick 8 +2=10/2=5 you cant pick something like 12 since it violates the stem..

basically a=2^n...

2^n +2=2(2^(n-1) +1)/2 then you get 2^(n-1) + 1 ..i.e even+odd=odd...always

Agree with D but the statement that "basically a=2^n..." is not true cuz "a" has to be a multiple of 4. in that case "a" could be 4 or 8 or 12. If a is 12, then it doesnot fit anywhere on the expression that a = 2^n.... so a = 2^n is not correct.

the strongest reason why (a+2)/2 is odd is that a must be a multiple of 4.
VP
Joined: 17 Jun 2008
Posts: 1477

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05 Oct 2008, 12:23
1
My approach is similar witha different flavor.

If a-b is even then both a and b are either odd or both are even.
If a/b is also even then both a and b cannot be odd.

Hence, combining both, a and b are even in such a way that a = (2x)b for x = 0,1,2,3,4......

Hence, a/2 will be xb and since b is even, xb will always be even and hence a/2 will also always be even and a/2 + 1 will always be odd.
SVP
Joined: 29 Aug 2007
Posts: 2425

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21 Oct 2008, 09:42
missed this one earlier.

Yes you can. Lets take a = 24, which is a multiple of 4 and has 3 as odd prime factor, and b = 4. then
a - b = 24-4 = 20
a/b = 24/4 = 6
(a+2)/2 = (24+2)/2 = 13

So it is not necessary for "a" to have its value a power of 2.

fresinha12 wrote:
I dont think you can have any odd prime factors for a..

lets say for argument sake..a=12 and b=4 12-4=8 but 12/4=3 so you see you can have a multiple of 4, but it wont meet the requirement laid out in the stem..therefore i feel..a at the least has to be 2^n ...

GMAT TIGER wrote:
fresinha12 wrote:
i get d..

a+2/2 will be odd..

from the stem we know both a and b are even..

we also know that a=b*even which means a will always b divisible by 4..

so lets pick 8 +2=10/2=5 you cant pick something like 12 since it violates the stem..

basically a=2^n...

2^n +2=2(2^(n-1) +1)/2 then you get 2^(n-1) + 1 ..i.e even+odd=odd...always

Agree with D but the statement that "basically a=2^n..." is not true cuz "a" has to be a multiple of 4. in that case "a" could be 4 or 8 or 12. If a is 12, then it doesnot fit anywhere on the expression that a = 2^n.... so a = 2^n is not correct.

the strongest reason why (a+2)/2 is odd is that a must be a multiple of 4.

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown

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21 Oct 2008, 16:18
scthakur wrote:
My approach is similar witha different flavor.

If a-b is even then both a and b are either odd or both are even.
If a/b is also even then both a and b cannot be odd.

Hence, combining both, a and b are even in such a way that a = (2x)b for x = 0,1,2,3,4......

Hence, a/2 will be xb and since b is even, xb will always be even and hence a/2 will also always be even and a/2 + 1 will always be odd.

I will go with this approach, except that x can't be ZERO, since a and b are positive integers.
VP
Joined: 17 Jun 2008
Posts: 1477

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22 Oct 2008, 01:04
LiveStronger wrote:
scthakur wrote:
My approach is similar witha different flavor.

If a-b is even then both a and b are either odd or both are even.
If a/b is also even then both a and b cannot be odd.

Hence, combining both, a and b are even in such a way that a = (2x)b for x = 0,1,2,3,4......

Hence, a/2 will be xb and since b is even, xb will always be even and hence a/2 will also always be even and a/2 + 1 will always be odd.

I will go with this approach, except that x can't be ZERO, since a and b are positive integers.

Thanks livestronger for pointing this out. I must improve upon reading the questions in full

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Odd/Even   [#permalink] 22 Oct 2008, 01:04
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# Odd/Even

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