odd integer

[gibran]

If a and b are positive integers 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

Official Answer is D.

[larbgai]

Having a hard time seeing the Official Answer on this one.....

a-b = e

a/b = e
Thus:
a = b * e

Thus a is even.
So:
e - b = e

Therefore, b must be even.

So: a is even, b is even

A: even/2 = even or odd (depending on the number), therefore not always odd

B: even/2 = even or odd

C: even + even = even, then even/2 = even or odd, therefore not always odd

D: e+2 / 2 = even or odd (i.e. a = 8, so 8+2 = 10/2 = 5 OR a=6, 6+2 =8/2 = 4) - we get two conflicting answers.

E: Ditto what we did in D.

I don't get how the Official Answer is what it is. Are you missing a constraint where a>b or something like that......?

[mannu08]

@gibran: Are we missing something here?

[winna.7]

Yes! all of the given choices turn out to be even . SOmething missing for sure!

[krovvidy]

IMO, the question is all right. Remember, this is a MUST-BE-TRUE question of Quant ...

a-b is an even integer => a & b are either both odd or even

But a/b is even => a & b are even and a is a multiple of 4

i.e., (a/2) must be even

i.e., (a/2)+1 must be odd

i.e., (a+2)/2 must be odd ... hence D ...

Consider E; (b+2)/2 can be even when b=2 and odd when b=4 ... NOT TRUE

Same way you can workout for A, B & C also and see why they're NOT TRUE.

[larbgai]

Thanks, krovvidy. I missed that a and b are either both odd or even by using my approach.