Is k greater than 3?

Is \(k>3\)?

(1) \((k-3)(k-2)(k-1)>0\)

The product of 3 numbers is positive if all three are positive (+++) OR two of them are negative and the third one is positive (+--).

Note that: out of 3 numbers \(k-3\) is the least one and \(k-1\) is the biggest one.

\((+)(+)(+)\) is when even the least one is positive so when \(k-3>0\) --> \(k>3\);
\((+)(-)(-)\) is when the biggest one is positive (\(k-1>0\) --> \(k>1\)) and the next one (hence the leas one too) negative (\(k-2<0\) --> \(k<2\)), so when \(1<k<2\);

So \((k-3)(k-2)(k-1)>0\) means that: \(k>3\) or \(1<k<2\) --> \(k\) may or may not be more than 3. Not sufficient.

(2) \(k>1\). Clearly insufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is the range we had in (1) \(k>3\) or \(1<k<2\), so \(k\) may or may not be more than 3. Not sufficient.

Answer: E.