Q is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in Q?
I. 9
II. 15
III. 27  Select:	A) I only	B) II only	C) I and II only	D) I and III only	E) I, II, and III
Ans: C   Q-&gt;{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3   means x must contain 3^2 and 5^2   so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25   but 27 is not a divisor because it can't divide 9*25 fully.   so Ans : I and II only
<result>C</result>
Q is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in Q?
I. 9
II. 15
III. 27