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If A, B, C, and D are integers such that A - C + B is even a

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If A, B, C, and D are integers such that A - C + B is even a

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If A, B, C, and D are integers such that A - C + B is even and D + B - A is odd, which of the following expressions is always odd?

A. A + D
B. B + D
C. C + D
D. A + B
E. A + C

I'm confused how to set up the formulas here. Can any experts help?

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GMAT/MBA Expert

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ardz24 wrote:
If A, B, C, and D are integers such that A - C + B is even and D + B - A is odd, which of the following expressions is always odd?

A. A + D
B. B + D
C. C + D
D. A + B
E. A + C
Given: A - C + B = EVEN and D + B - A = ODD
Add them to get: (A - C + B) + (D + B - A) = EVEN + ODD
Simplify: 2B + D - C = ODD
Since 2B is ALWAYS even, we get: EVEN + D - C = ODD
So: D - C = ODD - EVEN
This means: D - C = ODD
If D - C is ODD, then we know that one of the numbers is EVEN and the other number is ODD
If one of the numbers is EVEN and the other number is ODD, then C + D must also be ODD

Answer: C

Cheers,
Brent

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