When positive integer n is divided by 5, the remainder is 2. When n is divided by 11, the remainder is 8. What is the smallest positive integer k such that k+n is a multiple of 55?  Choose the correct choice from the following: A) 2 B) 3 C) 6 D) 7 E) 10
n = 5p + 2 = 11q + 8   n+3 = 5p + 5 = 11q + 11   n+3 is a multiple of 5 and 11, so it is a multiple of 55.   The answer is 3.
<result>B</result>
When positive integer n is divided by 5, the remainder is 2. When n is divided by 11, the remainder is 8. What is the smallest positive integer k such that k+n is a multiple of 55?