Max@Math Revolution wrote:If a and b are positive integers, is ab an even?
1) (a+1)(b) is even
2) (a+1)^b is odd
Target question: Is ab even
Statement 1: (a+1)(b) is even
This statement doesn't
FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 2. Here, (a+1)(b) = (1+1)(2) = 4, and 4 is even. In this case
ab = (1)(2) = 2. So, ab IS even
Case b: a = 1 and b = 1. Here, (a+1)(b) = (1+1)(1) = 2, and 2 is even. In this case
ab = (1)(1) = 1. So, ab is NOT even
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: (a+1)^b is odd
In other words, the product (a+1)(a+1)...(a+1)
[multiplied b times] is ODD
This means that each value (a+1) in the product must be ODD
If a+1 is ODD, then
a is EVEN
If a is EVEN, then
ab = (EVEN)(b) = EVEN
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
