sparkles3144 wrote: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.
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