Question

Which is the largest three digit number which when divided by 6 leaves a remainder 5 and when divided by 5 leaves a remainder 3?

Answer 1

The rule: Consider when N is divided by x the remainder is a and when divided by y the remainder is b. Write them as below:

x y

a b

N = x*y*k + b*x+a, where k=0,1,2,…..

This can be extended into any number of pairs of divisors and remainders.

x*y*z*k + (c*y+b)*x+a

According to this rule, you get 6*5*k + 3*6+5

30*k+23

Now, this is less than 1000

So, k<32.5

=>k = 32

Therefore, the answer is 983.

Answer 2

Answer: is 9893 buddy hope it helps