Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
Answer: A
K and M are positive so K+M must be at least 2 (B and D are eliminated).
Now for the tricky part: If one of the remainders is even then the other remainder must be even. If one of the remainders is odd, the other remainder must also be odd.
For example:
If J = 13, K is 1 and M is 1
If J = 9, K is 3 and M is 1
If J = 10, K is 4 and M is 2
The logic here (which we prefer you learn rather than plugging in numbers) follows: The remainder represents how far the number you are dividing is from the last multiple of the number you are dividing by. Since both 4 and 6 are even, their multiples will always be even. Since the rules for subtracting evens and odds are constant, whatever J is (even or odd), the distance it is from an even number will always be correspondingly even or odd.
Now, since either way the sum of K and M must be even (even + even is even; odd plus odd is even), there are no even values other than 0 and so the answer is none (A).
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