carcass wrote:

The remainder when m + n is divided by 12 is 8, and the remainder when m - n is divided by 12 is 6. If m > n, then what is the remainder when mn divided by 6?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Kudos for the right solution and explanation

Easiest and best way would be as also shown above:-

take the least possible values of m and n

so \(m+n=8\) And \(m-n=2\)..

Add two equations.. \(m+n+m-n=8+6....2m=14...m=7\)

So n = 1..

\(mn=7*1=7\)...

Thus remainder will be 1 when 7 is divided by 6..

Now a proper understanding..If m+n leaves a remainder of 8 when divided by 12, it will leave a remainder of 8-6=2 when divided by 6..

Similarly m-n leaves a remainder of 6 when divided by 12, it will leave a remainder of 6-6=0 when divided by 6..So m and n leave the same remainder when divided by 6..

But m+n leaves a remainder of 2, so only possiblity is when both m and n leave a remainder of 1 each..

So mn will leave a remainder of 1*1=1

A

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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