If a and b are integers, is a + b + 3

[jjjinapinch]

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.

Official Guide question
Answer: D

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Hi jjjinapinch,

We're told that A and B are integers. We're asked if (A+B+3) is an ODD integer. This is a YES/NO question. This question deals with Number Properties, so you can solve it using those rules and/or by TESTing VALUES.

1) (A)(B) is an ODD integer.

Since both variables are integers, the ONLY way for (A)(B) to be an ODD product is if BOTH A and B are ODD integers.
For example: (3)(5) = 15. Under these circumstances...

Odd + Odd + 3 = ODD and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) (A - B) is an EVEN integer.

Here, there are TWO ways to end in an EVEN integer: If BOTH variables are Odd OR if BOTH are Even...
For example:
(5 - 1) = 4.... Odd + Odd + 3 = ODD and the answer to the question is YES.
(4 - 2) = 2... Even + Even + 3 = ODD and the answer to the question is YES.
Under these conditions, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[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.

Official Guide question
Answer: D

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

Given: a and b are integers

Statement 1: ab is an odd integer.
Some important 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

[Jeff@TargetTestPrep]

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.

Official Guide question
Answer: D

We need to determine whether a + b + 3 is odd or, in other words, whether a + b is even.

Statement One Alone:

ab is an odd integer.

Thus, a and b are both odd, and since odd + odd = even, a + b is even. Statement one alone is sufficient to answer the question.

Statement Two Alone:

a - b is an even integer.

Since a - b is even, a + b is also even. Statement two alone is sufficient.

Answer: D