A number N when divided by 5 leaves remainder 1 and when divided by 6 leaves remainder 3. What is the remainder when N is divided by 30? 1. 19 2. 17 3. 15 4. 21 5.25 Answer: Every number can be represented as  Number = divisor x quotient + remainder. N = 5 x quotient 1 + 1 (N1) = 5 x quotient 1 N =6 x quotient 2 + 3 (N3) = 6 x quotient 2 (N1) and (N3) should be a multiple of 5 and 6 respectively. Let us focus on the last digit of the number N as (N1) is divisible by 5 and (N3) should be divisible by 6. Hence the number should be ending with 8.51 satisfies both the conditions. Hence 51 when dividing by 30 gives a remainder of 21. Another method Check each answer option 21 when divided by 5 leaves remainder of1 . 21 when divided by 6 leaves a remainder of 3 
