Question 103
Let $p(x)$ be a polynomial with integer coefficients such that $p(0)=6$. It is known that among the integers $m$ between 1 and 60 exactly 40 are such that $p(m)$ is a multiple of 3; moreover, it is known that among the integers $m$ between 1 and 60 exactly 30 are such that $p(m)$ is a multiple of 4. How many are the integers $m$ between 1 and 60 such that $p(m)$ is a multiple of 6? Note: all the intervals appearing in this problem are to be considered with their endpoints included.
(A) 10
(B) 20
(C) 25
(D) 30
(E) 40
(A) 10
(B) 20
(C) 25
(D) 30
(E) 40