This is how I solved.

First statement clearly W could be equal to either 3 sqrt (2) or -3 sqrt (2), therefore insufficient.

Second statement, w^3 / sqrt (18) is an integer this doesn't really tell us much.

Both statements together, if we factorize w^3 as w*w^2 and replace statement 1 in this equation we will have 18w = sqrt (18) * k, where 'k' is an integer.

Therefore after simplifying we are left with w = k / sqrt (18), where 'k' is an integer. Since 'k' could be any number there is NOT a definite value for 'w' and thus answer is E.

Hope this helps

Cheers

J