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?
Thursday, August 12, 2010
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2 comments:
First lets solve this problem differently:
20*27/25
There is a rule that says
R[pq/x] = R[p/x]*R[q/x]
1. R[20/25]*R[27/25]
First divide 27 by 25. Rem=2
2. We are left with:
R[20/25]*R[2/25] = R[20*2/25]
--using inverse of the rule mentioned above
3. Now find R[40/25], your answer is 15.
Look you can also solve this using -ve remainder rule. Let me know if that is wht you need.
I'm aware of the formula you gave. But I used this formula on purpose, to get a negative remainder, and thus bring out my doubt so as to why we add the divisor to the remainder when it is negative.
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