odd integer

[osuguy]

Q: if a and b are positive integer such that a-b and a/b are both even integers, which of the following must be an odd integer?
A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (B+2)/2

Please suggest.

[swatee01]

its C.

Consider a=4 and b=2
4-2 =even and 4/2 = even
But, (4+2)/2 is odd.

[TingLi]

I prefer D:
a/2 is even, and a/2 +1 is odd.

[osuguy]

D is the Official Answer. how do you get a/2 even?

[shobby]

a-b=even
=> either both are even or both are odd

a/b=even=2x
=> a and b are both even
'a' must have atleast two 2s as factors.
so a/2 is even and a/2+1 is odd

[e.cartman]

Agree with shobby.
Also you can see that (a+b)/2 wont work by taking a=8, b=4.

[ramzrambo]

Hi Cartman...
It is the ques that is confusing but the answer is simple.
As we know both A and B have to be even.
Now we are not concerned with the option is odd or even but with the option that is always odd.
taking various cases, it can easily be derived that (a+b)/2 can be odd but then it cam be even also.
However, the problem is with options D and E
if we take B=2, we can see that it does not satisfy option E ..as it will be B/2+1 = 1/1+1 = 2 which is even...also we cannot take A as 2 because B cannot be zero as a/b has to be even...and not indefinite..now this was the catch...
hence option D is answer...cheers!!

[ramzrambo]

Also.....u may argue a=8,b=4...u will find that in almost all the cases that satify conditions in ques...say we take a=12, b = 6.....then option D,E both hold but..it is only option D that always holds true...

I tried a lot reaching a formula in terms of a,b but wasn't able to do that...but still you can reach the answer quite comfortably.

[ramzrambo]

the catch i still believe is that A cannot be equal to 2 and for all other options as we cannot take B as zero both being positive integers and a/b being even.for all other cases...option D always comes out to be odd tho option E can be even.

[ramzrambo]

ah well.....any better method!!!????????????????