I was trying to solve a problem which states:
How many two-digit numbers have remainder 1 when divided by 3 and remainder 2 when divided by 4?
and solved it by writing down individual numbers...
Looking at the solution, I was baffled by the explanation :
The lowest common multiple of 3 and 4 is 12. Hence both of the required conditions are satisfied only by numbers that are 2 less than multiples of 12 and also less than 100, ie: 10, 22, 34, 46, 58, 70, 82 and 94.
Why on earth does the number have to be 2 less than multiples of 12? Could someone offer a better explanation please?