If p and r are positive integers such that (p2)/40=r(p2)/40=r, and p=/=r, then which of the following must also be an integer?
I. r/5r/5
II. r/(2x5)r/(2x5)
III. r/(3x5)r/(3x5)	Select.
A) I only  B) II only  C) I and II only  D) I and III only  E) I, II, and III
(p^2)/40 = r;   p^2 = 40r = 2^3*5r.   2^3*5r equals to the square of an integer (p^2), thus r should complete the powers 2^3 and 5 to the even number, thus the least value of r is 2*5 (in this case p^2 = 2^3*5r = 2^4*5^2). So, r/5 and r/(2*5) must be also be integer.   Answer: I and II only.
<result>C</result>
If p and r are positive integers such that (p2)/40=r(p2)/40=r, and p=/=r, then which of the following must also be an integer?
I. r/5r/5
II. r/(2x5)r/(2x5)
III. r/(3x5)r/(3x5)