If \(n = 2\times 3\times 5\times 7\times 11\times 13\times 17,\) then which of the following statements must be true?

[Vincen]

If \(n = 2\times 3\times 5\times 7\times 11\times 13\times 17,\) then which of the following statements must be true?

I. \(n^2\) is divisible by 600.

II. \(n + 19\) is divisible by 19.

III. \(\dfrac{n + 4}2\) is even.

A. I only
B. II only
C. III only
D. I and III
E. None of the above

Answer: E

Source: Magoosh