Ed_Palencia wrote:

I understand perfectly why (1) and (2) separately are insufficient, but I'm stuck at analyzing both statements together. Can anyone shed some light?

Hi

Ed_Palencia Statement 1 => implies, n can have two factors eg \((3 * 5)\)

\(or\)

can have only one prime factor, but \(n = 5 * 5\), so that \(n/5\) has one prime factor => insuff

Statement 2 => implies, \(3n^2\)=> two diff prime factors, so \(n\) can be \((3 * 5) or (5 * 5)\)

if \(n = 3 * 5\),

\(3n^2\) => \(3(3 * 5)\) => two prime factors

if \(n = 5 * 5\),

\(3n^2\) => \(3(5 * 5)\) => two prime factors

so if you combine, still n can be \(3 * 5 or 5 * 5\), not sufficient to tell how many prime factors

Answer (E)

Hope that helps !