Question

If M and N are divided by P, then the remainder 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:
A) 50
B) 44
C) 70
D) 40
E) None of these​

Answer 1

Answer:

D. 40

Step-by-step explanation:

This is the answer above.

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