$p^a\cdot q^b\cdot r^c\cdot s^d=x,$ where $x$ is a perfect square. If $p, q, r,$ and $s$ are prime integers, are

$p^a\cdot q^b\cdot r^c\cdot s^d=x,$ 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: B

Source: Manhattan GMAT

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