Question

if M and N are divided by p, then the reminder obtained are 13 & 31 respectively where M, N, P are natural numbers. Further M + N is divided by the same divisor P the remainder is 4, then the divisor P is:​

Answer 1

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Answer 2

• According to question,

               m%p=13

               n%p=31

• Also,

             (m+n)%p=4

• Which means

                m=Q1*p+13

                 n=Q2*p+31

                m+n=Q3*p+4

                 m-13,n-31,m+n-4 are perfectly divisible by p

• As m-13 and n-31 are individually divisible by divisor p

• Hence,their sum will also be divisible by p

• That means

        m+n-13-31=m+n-44 is perfectly divisible by p

• We know m+n-4 is also perfectly divisible by p

             So p=m+n-4-(m+n-44)

                    =m+n-4-m-n+44

                    =40

                  p=40