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.

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

##### This topic has expert replies

- GMATGuruNY
- GMAT Instructor
**Posts:**15533**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1898 members**GMAT Score:**790

Parity = the state of being EVEN or ODD.M7MBA wrote:If x, y are integers, is x+y an odd number?

1) y=3x+5.

2) y=2x-3.

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.

Mitch Hunt

Private Tutor for the GMAT and GRE

[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3

Private Tutor for the GMAT and GRE

[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3

- [email protected]
- Legendary Member
**Posts:**2663**Joined:**14 Jan 2015**Location:**Boston, MA**Thanked**: 1153 times**Followed by:**127 members**GMAT Score:**770

You could also pick numbers. Just make sure to pick both even and odd values for x.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.

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