11. Two of the following four facts about a positive integer $N$ are true and two are false.

What is the value of $N$ ?
A 5
B 10
C 11
D 55
E 110
11. A If $N$ were divisible by 55 , then it would also be divisible by 5 and 11 , making three statements true. Hence $N$ is not divisible by 55 . Therefore exactly two of the remaining statements are true. It is not possible for $N$ to be both less than 10 and divisible by 11 , and it is not possible for $N$ to be divisible by both 5 and 11 without also being divisible by 55 . Therefore the two true statements are $N$ is divisible by 5 and $N$ is less than 10 . Hence the value of $N$ is 5 .