If k, m and n are integers and km - kn is odd, which of the following

Question

If k, m and n are integers and km - kn is odd, which of the following must be odd?

(A) k
(B) m
(C) n
(D) km
(E) kn

GMATinsight · Answer

km - kn = odd

i.e. k (m-n) = odd

i.e.   k is ODD   and m and n are both even or both odd

Answer: Option A

D3N0 · Answer

Ans: A
Ans: Km-Kn odd : k(m-n) =odd 
for it to odd K has to be odd 100% and m and n can have (m,n) (odd,even) or (even,odd) combination.

Ans: A

BrentGMATPrepNow · Answer

The solutions above show the best/fastest approach. 
However, I thought I'd mention that we can also solve this by  testing numbers

The question asks, "Which of the following  must  be odd?"
So, if we can show that an answer choice can be EVEN, then we can ELIMINATE it.

For example, when k = 3, m = 2 and n = 1, we see that km - kn = (3)(2) - (3)(1) = 6 - 3 = 3, which is ODD (perfect - this satisfies the condition that km - kn is odd)
Now, check the answer choices...
(A) k = 3. This IS odd. So, keep answer choice A
(B) m = 2. This is EVEN. So, ELIMINATE answer choice B
(C) n = 1. This IS odd. So, keep answer choice C
(D) km = (3)(2) = 6. This is EVEN. So, ELIMINATE answer choice C
(E) kn = (3)(1) = 3. This IS odd. So, keep answer choice E

We're left with A, C and E. 
Let's test a NEW set of values. 
The values k = 3, m = 1 and n = 2 also satisfy the condition that km - kn is odd)
Now, check the REMAINING answer choices...
(A) k = 3. This IS odd. So, keep answer choice A
(C) n = 2. This is EVEN. So, ELIMINATE answer choice C
(E) kn = (3)(2) = . This is EVEN. So, ELIMINATE answer choice E

By the process of elimination, we're left with answer choice A

Answer: A

Cheers,
Brent

MikeHelios · Answer

Hi

k(m-n) is odd
this implies that k is odd and between m and n one is odd and the other even.

If k, m and n are integers and km - kn is odd, which of the following

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GMAT Problem Solving (PS) Questions

If k, m and n are integers and km - kn is odd, which of the following

Prep Toolkit

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