When positive integer n is divided by 7, the remainder is 1. When n is divided by 11, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 77? Options:
A) 2
B) 4
C) 6
D) 8
E) 10
n = 7p + 1 = 11q + 5   n+6 = 7p + 7 = 11q + 11   n+6 is a multiple of 7 and 11, so it is a multiple of 77.   The answer is 6.
<result>C</result>
When positive integer n is divided by 7, the remainder is 1. When n is divided by 11, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 77?