p raised to a, q raised to b, r raised to c, s raised to d = x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?
(1) 18 is a factor of ab and cd
(2) 4 is not a factor of ab and cd
Answer is given as B but I think even A is enough to make sure that the factors cannot be distinct and so the answer should be D.
My reasoning is that if 18 is a factor of ab and cd, then either a or b has to be odd. Now, as x is a perfect square, this odd number must be complemented with a odd power in cd. So the numbers cannot be distinct.
Can anyone help me in understanding why the answer is B and not D
(1) 18 is a factor of ab and cd
(2) 4 is not a factor of ab and cd
Answer is given as B but I think even A is enough to make sure that the factors cannot be distinct and so the answer should be D.
My reasoning is that if 18 is a factor of ab and cd, then either a or b has to be odd. Now, as x is a perfect square, this odd number must be complemented with a odd power in cd. So the numbers cannot be distinct.
Can anyone help me in understanding why the answer is B and not D
