If n = 2×3×5×7×11×13×14, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even  Pick:
A) I only
B) II only
C) III only
D) None of the above
E) I and III
Statement I: 600 = (2^3)*(3)*(5^2) this is true.   Statement 2 Since n is divisible by 19 so n+19 is also divisible by 19. So this is NOT true.   Statement 3: (n+4)/2 = n/2 + 2   So, ODD + 2 cannot be even.   So this is true.   Hence option (I and III).
<result>E</result>
If n = 2×3×5×7×11×13×14, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even