jjjinapinch wrote: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
