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Problem based on remainders 3 (Updated On Tuesday, July 08, 2014)

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
(N-1) = 5 x quotient 1
N =6 x quotient 2 + 3
(N-3) = 6 x quotient 2

(N-1) and (N-3) should be a multiple of 5 and 6 respectively.
Let us focus on the last digit of the number N as (N-1) is divisible by 5 and (N-3) 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


 

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