Problema Solution

When positive integer N is divided by 5, the remainder is 1. When N is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

Answer provided by our tutors

The number N can be represented as

 

N = 5t+1

and

N= 7l+3

=> 5t+1 = 7l+3 => 5t = 7l+2

 

the smallest value of l for this to happen is l=4

=> Smallest N = 7*4+3 = 31

=> k = 35-N = 35-31 = 4