If a and b are integers, is a + b + 3 an odd integer? (1)

[BTGmoderatorDC]

If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

OA D

Source: Official Guide

[Brent@GMATPrepNow]

If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

OA D

Source: Official Guide

Target question: Is a + b + 3 an odd integer?

Given: a and b are integers

Statement 1: ab is an odd integer.
Some useful rules:
1. ODD - ODD = EVEN
2. ODD - EVEN = ODD
3. EVEN - ODD = ODD
4. EVEN - EVEN = EVEN
5. (ODD)(ODD) = ODD
6. (ODD)(EVEN) = EVEN
7. (EVEN)(EVEN) = EVEN

Since ab is odd, we can be certain that a and b are both ODD
If a and b are both ODD, then a + b + 3 = (ODD) + (ODD) + 3 = EVEN + 3 = ODD. In other words, a + b + 3 is an odd integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a − b is an even integer
If a - b = even, then EITHER a is odd and b is odd OR a is even and b is even
In ether case, a + b = EVEN
a + b + 3 = EVEN + 3 = ODD.
In other words, a + b + 3 is an odd integer
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

[GMATGuruNY]

If a and b are integers, is a + b + 3 an odd integer?

(1) ab is an odd integer.
(2) a − b is an even integer.

a+b+3 = ODD only if a and b are both odd or both even.
Question stem, rephrased:
Are a and b both odd or both even?

Statement 1:
ab = ODD implies that a and b are both odd.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
a-b = EVEN implies that a and b are either both odd or both even.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is D.