If n is a positive integer, is n divisible by 2?

(1) \(7n - 8\) is divisible by \(20\)

\(7n-8=20a\) or \(7n=20a+8=4(5a+2)\)\(\)

\(n=\frac{4(5a+2)}{7}\)

Since \(n\) is an integer and \(4\)\(\) is not multiple of \(7\), \((5a+2)\) must be a multiple of \(7\) and so \(n\) must be a multiple of \(4\)

So \(n\) is even and divisible by \(2\)

1 is sufficient

(2) \(3n^2 + 2n + 5\) is a prime number

Minimum value of \((3n^2 + 2n + 5)\) is \(10\) so \((3n^2 + 2n + 5)\) must be a prime number greater than \(10\) and so \((3n^2 + 2n + 5)\) must be odd

If \(n\) is odd, \((3n^2 + 2n + 5) = odd+even+odd = even\) ---------- Not possible since we know that \((3n^2 + 2n + 5)\) is odd

So \(n\) is not odd which means \(n\) is even and divisible by \(2\)

2 is sufficient

Answer is (D)