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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x, y are integers, is x+y an odd number? tagged by: M7MBA ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If x, y are integers, is x+y an odd number? 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. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply 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 _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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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.

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