Showing posts with label formula. Show all posts
Showing posts with label formula. Show all posts

Thursday, August 12, 2010

The Mystery of the Divisor Addition to the Negative Remainder

I have a doubt regarding the formula used for Remainders in GMATClub's Math Book: see Point #6, Eg. #2.

Q. What is the remainder of (20*27) when it is divided by 25?

Note: Rof = remainder of

A. The formula I used is: Rof xy/n = Rof {Rof[(x-n)/n] * Rof[(y-n)/n]} / n

Therefore,  Rof 20*27/25 = Rof {Rof[(20-25)/25] * Rof[(27-25)/25]} / 25
= Rof {Rof[(-5)/25] * Rof[2/25]} / 25
= Rof [(-5 * 2) / 25]
= Rof [(-10) / 25]
= (-10)

But, since the remainder is negative, we add n to it to give us the remainder.
Therefore, Rof 20*27/25 = -10 + n = -10 + 25 = 15.

Why did we add n to the negative remainder?