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?
The answer would be 4 .yellowho wrote: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?
n = 31 k = 4
n + k = 35
n for 5 giving remainder 1 = [6,11,16,21,26,31,36,41,46,51]
n for 7 giving remainder 3 = [10,17,24,31,38,45,52,59,66,73]
Smallest number common between both sets is 31 .
31/5 gives remainder 1 and 31/7 gives remainder 3 .
