evens and odds

[arellalu]

If a and b are positive integers, is a−b odd?

(1) a/b is an odd integer.

(2) b/a is an odd integer.

[anuprajan5]

Answer is D

Statement 1 - a/b is an odd integer. This can happen when both a and b are either odd or even.

Eg:
Case 1- a and b odd
a- 21
b - 7
a/b - 3 -odd


Case 2- a and b even
a- 14
b - 2
a/b - 7 - odd

That being said, if we take each case Odd - Odd or Even - Even will always be Even (Eg: 21-7 = 14 or 14-2 = 12)

Therefore we can say that a-b cannot be odd.

Statement 2 basically states the same.

Regards
Anup

[Brent@GMATPrepNow]

If a and b are positive integers, is a−b odd?

(1) a/b is an odd integer.

(2) b/a is an odd integer.

Target question: Is a−b odd?

Let's begin with two facts:
- (odd)(odd) = (odd)
- (odd)(even) = (even)

Solve for the green (odd) to get:
- (odd) = (odd)/(odd)
- (odd) = (even)/(even)

Note: This does not mean that (odd)/(odd) always results in an odd integer, or that (even)/(even) always results in an odd integer. What it means is that, IF a and b are both integers and a/b = an odd integer, then it must be the case that either:
- a and b are both odd
- a and b are both even

Statement 1: a/b is an odd integer
Using the above logic, we have two possible cases to consider:
case a: a and b are both odd, in which case a-b is even (ie, not odd)
case b: a and b are both even, in which case a-b is even (ie, not odd)
In both cases, we have the same definitive answer to our target question.
So, statement 1 is SUFFICIENT

Statement 2: b/a is an odd integer
Applying the same logic that we used for statement 1, we can see that statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

[Brent@GMATPrepNow]

If anyone wants to practice more Data Sufficiency questions involving odd and even integers, here are a few more:

https://www.beatthegmat.com/what-about-0 ... 17014.html
https://www.beatthegmat.com/is-the-integ ... 19182.html
https://www.beatthegmat.com/og-13th-ds-1 ... 22138.html
https://www.beatthegmat.com/even-or-not- ... nt=Chicago

Cheers,
Brent