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Odd/Even [#permalink]
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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. == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost 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.
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Re: Odd/Even [#permalink]
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03 Oct 2008, 10:58
c ...
a+b/2 will be right answer



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Re: Odd/Even [#permalink]
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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^(n1) +1)/2 then you get 2^(n1) + 1 ..i.e even+odd=odd...always



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Re: Odd/Even [#permalink]
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03 Oct 2008, 11:03
a combination of calculation and intuition and substitution suggests to me it should be D. Please confirm.



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Re: Odd/Even [#permalink]
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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



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Re: Odd/Even [#permalink]
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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. Please confirm. 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.



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Re: Odd/Even [#permalink]
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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^(n1) +1)/2 then you get 2^(n1) + 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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Re: Odd/Even [#permalink]
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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=4 124=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^(n1) +1)/2 then you get 2^(n1) + 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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Re: Odd/Even [#permalink]
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05 Oct 2008, 12:23
My approach is similar witha different flavor.
If ab 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.



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Re: Odd/Even [#permalink]
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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 = 244 = 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=4 124=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^(n1) +1)/2 then you get 2^(n1) + 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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Re: Odd/Even [#permalink]
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21 Oct 2008, 16:18
scthakur wrote: My approach is similar witha different flavor.
If ab 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.



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Re: Odd/Even [#permalink]
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22 Oct 2008, 01:04
LiveStronger wrote: scthakur wrote: My approach is similar witha different flavor.
If ab 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 repost 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.










