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
evens and odds
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Source: Beat The GMAT — Data Sufficiency |
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anuprajan5
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Target question: Is a−b odd?arellalu wrote: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.
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 Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
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Brent@GMATPrepNow
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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
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
Brent Hanneson - Creator of GMATPrepNow.com
