Abhishek009 wrote:
Though GMATGuruNY has sugegsted that this is out of scope of GMAT Problem still would like to attempt it out of curiosity.
m = dq + r
Or, -100 = 30*-3 -10
Hence r = -10
IMO (D)..
Here's how the GMAT test-makers define remainders:
If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 < r < x.
Notice that the remainder must be greater than or equal to zero AND the remainder must be less than the divisor.
So, we get:
0 < remainder < -100.. Hmmm, the number must be greater than or equal to zero AND less than -100
Obviously, there's no such number.
Also notice that negative values take away the conceptual nature of remainders. Typically, we can get remainders when we're trying to divide some quantity into equal amounts. So, for example, if we have 17 balls and we want to divide them equally among 3 children, then we can give each child 5 balls, at which point we have 2 balls
remaining. Thus 2 is the
remainder.
What happens if we have -17 balls and want to divide them equally among 3 children? How does that work? How many balls does each child get?
Well, we could say that each child gets -5 balls, and there are -2 balls remaining. Here, (-5)(3) + (-2) = -17
We could say that each child gets -6 balls, and there is 1 ball remaining. Here, (-6)(3) + 1 = -17
So, what is the true remainder?
Of course, neither of these scenarios make sense. So, as you can see, the entire concept of remainders falls apart with negative values.
Cheers,
Brent
