Brent@GMATPrepNow wrote:m, n and k are positive integers. If the product mn is odd, is k odd?
(1) nm + n + k is odd
(2) n² - kn - 6k² is even
Answer:
D
Difficulty level: 600 - 650
Source:
www.gmatprepnow.com
Target question: Is k odd?
Given: The product mn is odd
If the product mn is odd, when we know that
m is ODD and
n is ODD
Statement 1: mn + n + k is odd
In other words: (
ODD)(
ODD) +
ODD + k is odd
Simplify: ODD + ODD + k is odd
Simplify more: EVEN + k is odd
This means
k must be ODD
So, the answer to the target question is
YES, k IS odd
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: n² - kn - 6k² is even
Let's factor the expression to get: (n - 3k)(n - 2k) is even
In other words: (
ODD - 3k)(
ODD - 2k) is even
Notice that 2k must be EVEN, so we can write: (
ODD - 3k)(
ODD - EVEN) is even
ODD - EVEN = ODD, so we can now say: (
ODD - 3k)(ODD) is even
This tells us that (
ODD - 3k) must be EVEN
In order for (
ODD - 3k) to be EVEN, it must be the case that 3k is ODD
If 3k is ODD, then
k must be ODD
So, the answer to the target question is
YES, k IS odd
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
