Odd/Even Rule

[sparkles3144]

Is A+B+C even or odd?
(A) A - C - B is even
(B) (A-C)/B is odd

Why is the answer E?

Can't it be A?
I did this:

A=6 B=4 C=2
A-C-B=0

And

A=7 B=3 C=2
A-C-B= 2

[GMATGuruNY]

Is A+B+C even?
(A) A - C - B is even
(B) (A-C)/B is odd

Why is the answer E?

Always notice how a DS problem is constrained and how it is NOT constrained.
Here, there is no requirement that A, B and C be integers.

Statement 1: A-C-B is even
Let A-C-B = 0, which is even.
Then:
A = B+C.

Case 1: A = B+C = 1/2
In this case, A+B+C = 1/2 + 1/2 = 1, which is ODD.
Case 2: A = B+C = 1
In this case, A+B+C = 1+1 = 2, which is EVEN.
INSUFFICIENT.

Statement 2: (A-C)/B is odd
Let (A-C)/B = 1.
Then:
A-C = B
A = B+C.

A = B+C is the SAME EQUATION that we derived in statement 1.
Implication:
Both statements are satisfied by Case 1, in which case A+B+C is ODD.
Both statements are satisfied by Case 2, in which case A+B+C is EVEN.
Thus, even when the statements are combined, it cannot be determined whether A+B+C is even or odd.
INSUFFICIENT.

The correct answer is E.

[GMATinsight]

Is A+B+C even or odd?
(A) A - C - B is even
(B) (A-C)/B is odd

Why is the answer E?

CONCEPT : If the sign among Integers are changed from +Ve to -Ve or from -Ve to +Ve then the result doesn't change in terms of it being Even/Odd
i.e. If A+B+C-D+E-F+G = EVEN,
then, A-B+C+D-E+F+G WILL Also be EVEN
then, A-B-C-D-E-F-G WILL Also be EVEN...and so on...

Statement 1) A - C - B is even
This statement would have been sufficient if A, B and C were integers for sure. But since it's not mentioned that A, B and C are integers therefore
INSUFFICIENT

Statement 2) (A-C)/B is odd
This statement doesn't mention about A,B and C being Integers therefore,
INSUFFICIENT

Combining the Two statements
Same problem still persists i.e. Statements don't mention about A,B and C being Integers therefore,
INSUFFICIENT

Answer: Option E