m, n and k are positive integers. If the product

[Brent@GMATPrepNow]

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

[Brent@GMATPrepNow]

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