When positive integer n is divided by 3, the remainder is 1. When n is divided by 5, the remainder is 4. What is the smallest positive integer p, such that (n + p) is a multiple of 11?  Choose the correct choice from the following options
A) 1 B) 2 C) 5 D) 7 E) 20
When positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1   values of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}   Similarly,   When n is divided by 5, the remainder is 5..i.e., n=5y+4   values of n can be one of {4, 9, 14, 19,...}   combining both the sets we get   n={4,19, 52, ...........}   What is the smallest positive integer p, such that (n + p) is a multiple of 11 or 11x   in case of n=4 p=7   so for min value of p, we take min value of n.   7 is the answer.
<result>D</result>
When positive integer n is divided by 3, the remainder is 1. When n is divided by 5, the remainder is 4. What is the smallest positive integer p, such that (n + p) is a multiple of 11?