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Bunuel
Which of the following numbers is a perfect square?

(A) \(\frac{14!15!}{2}\)

(B) \(\frac{15!16!}{2}\)

(C) \(\frac{16!17!}{2}\)

(D) \(\frac{17!18!}{2}\)

(E) \(\frac{18!19!}{2}\)

In order for a number to be a perfect square, need our factors to be in even quantities.

Looking at answer choice D, we see that we have:

(17!18!)/2 = (17!17!18)/2 = (17!)^2 x 18/2 = (17!)^2 x 3^2

Thus, the quantity in choice D is a perfect square.

Answer: D
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