If $5|P(2),2|P(5)$ then which of the followings divides $P(7)$? 
Suppose that $P(x)$ is a polynomial with integer coefficients.If $5|P(2),2|P(5)$ then which of the followings divides $P(7)$?
  a)10
  b)7
  c)3
  d)4
  e)8  

$5|P(2),2|P(5)\Rightarrow5-2|p(5)-p(2)$ but this doesn't help.I don't know any property of polynomials useful here.

Meta-solution
There are no restriction on the degree of your polynomial.
If you take the constant polinomial $P(x)=10$ the conditions required are satisfied.
So the only coherent answer is $a)$
