M7MBA wrote:If x, y are integers, is x+y an odd number?
1) y=3x+5.
2) y=2x-3.
Parity = the state of being EVEN or ODD.
x+y = ODD only if x and y have different parities (one is even, while the other is odd).
Question stem, rephrased:
Do x and y have different parities?
Statement 1:
Case 1: x = EVEN
In this case, y = 3(EVEN) + 5 = EVEN + ODD = ODD.
Here, x and y have different parities, so the answer to the question stem is YES.
Case 2: x = ODD
In this case, y = 3(ODD) + 5 = ODD + ODD = EVEN.
Here, x and y have different parities, so the answer to the question stem is YES.
Since the answer is YES in both cases, SUFFICIENT.
Statement 2:
Case 1: x = EVEN
In this case, y = 2(EVEN) - 3 = EVEN + ODD = ODD.
Here, x and y have different parities, so the answer to the question stem is YES.
Case 2: x = ODD
In this case, y = 2(ODD) - 3 = EVEN - ODD = ODD.
Here, x and y have the same parity, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
The correct answer is
A.
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