Question

What whole # when divided by 9 leaves a remainder of 6, divided by 8 leaves a remainder of 5, divided by 7 leaves a remainder of 4

Answer 1

let the no be n;
n=9a-3 by condition 1
n=8b-3 by condition 2
n=7a-3 by condition 3
where a,b,c integer.
so n+3 is divisible by 7,8,9; i.e. their l.c.m
therefore n=504k-3; where k is also an integer. for example you can check, n=501,1005,...etc.