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
m, n and k are positive integers. If the product
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Target question: Is k odd?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
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