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If x, y are integers, is x+y an odd number?

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Mar 16, 2018 5:09 am
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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by DavidG@VeritasPrep » Fri Mar 16, 2018 8:13 am
M7MBA wrote:If x, y are integers, is x+y an odd number?

1) y=3x+5.
2) y=2x-3.

The OA is the option A.

How can I get an answer here just using the statement (1)? Experts, I will wait for your answer.
You could also pick numbers. Just make sure to pick both even and odd values for x.

Statement 1: x = 1, y = 8, x + y = 9. That's ODD so we have a YES
x = 2, y = 11. x _ y = 13. Another YES.
We've already tried an even and an odd for x - no matter what we pick, we'll get a YES. Sufficient.

Statement 2: x = 1, y = -1, x + y = 0. Not ODD, so NO
x = 2, y = 1, x + y = 3. That's ODD, so YES, Not sufficient.

The answer is A
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