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: K = 4

Step-by-step explanation: N/5 remainder is 1, N/7 remainder 3.

Let x represent k

Therefore, 5x + 1 = N and 7x + 3 = N

(Where x can be 1, 2, 3, 4,5, 6 ...)

Substitute values of x until you get similar values of N,

Such that

When x is 6,

5 (6) + 1 = 31 and

When x is 4

7 (4) + 3 = 31.

If K + N/35 must be equal to 1 to find the least value, the K = 4 so that 4 + 31/35 = 1.

Therefore K = 4.