Question

find the number of 3 digit number which when divided by 4 leaves the remainder 3​

Answer 1

Answer:

103, 107, 111, 115 , ..., 999

Answer 2

Answer:

First, notation. We want all the possible cases of x=3(mod4) , where 100≤x≤999 .

∴ , x−3=4m , meaning if we subtract 3 from x , we get a multiple of 4. How many times does this happen?. With some trail and error, we find 103 is the first solution for x , and we keep adding four until we reach 999!

103,107,111,115,…

Hmm, but how can we count the items in that list? Simple! Subtract 103 starting from the first term:

0,4,8,12,...,896

8964=224

224+1 = 225. Done.

hope it will help you