The positive integers m and n leave remainders of 2 and 3, respectively when divided by 6. m > n. What is the remainder when m - n is divided by 6?
Oo, am I the first one to answer this?
Solving the hard way: I'm going to get all algebraic here, because that's the way I roll.
m=6k + 2, where k is an integer
n= 6j +3, where j is an integer
(This is just the definition of remainder. I believe it intuitively makes sense as well.)
m-n = 6k + 2 - (6j +3)
= 6(k-j) -1
k and j are both integers, so k-j is an integer too. (Also greater than zero, but I don't think this is actually relevant.) Now, we're looking for something in the form 6 * (an integer) + (a number between 0 and 5). -1 doesn't cut it. But, what if you do this:
= 6(k-j) -1 +6 -6
Then you can get
= 6(k-j-1)+5 (note, k-j-1 is an integer since k, j, and 1 are all integers.)
And your remainder is 5.
(This would still hold if we didn't know m>n, because negative numbers have remainders according to the same formula. -7/6 is -2 remainder 5.)
Easy alternative approach: Of course, since "cannot be determined" is not an answer, you can also just substitute numbers with the appropriate remainders for m and n, such as 8 for m and 3 for n.
I hope this helps!
in both operations we have the base number 6, so the subtraction of ratios will give m/6 - n/6 or the remainder operation 2/6-3/6=-1/6. Since remainder is only positive number (for GMAT and GRE testing) we need to subtract from the whole i.e. 6/6=1 unit's number of m the remainder -1/6 we get 6/6-1/6=5/6
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