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