Given that $$v=w^2yz$$
factors of any number N refers to all members that divide N completely without any remainder
No of factors of a number N such that $$N=p^aq^br^c$$
where p, q, rare prime factor of N and a,b and c are positive exponents of p, q and r respectively
no of factors of n $$n=\left(a+1\right)\left(b+1\right)\left(c+1\right)$$
Expressing the given expression terms of N
$$v=w^2yz$$
w, y, z must be a prime factor of v and 2, 1, 1 are the positive exponents of w, y and z respectively.
w, y, and z must be positive and prime numbers.
Statement 1
w, y and z are integers greater than w, y and z could be even or odd or prime even or odd or prime even though they are positive, it cannot be ascertained that they are prime numbers, this statement cannot answer the target question hence statement 1 is NOT SUFFICIENT.
Statement 2 =>w, y and z are distinct prime numbers.
Since prime numbers cannot be negative and w,y and z are distinct prime numbers, the deduced formula can be used to calculate the no of factors because this statement satisfies the conditions deduced from the question stem
Therefore, number of factors $$=\left(2+1\right)\left(1+1\right)\left(1+1\right)=3\cdot2\cdot2=12$$
Statement 2 alone is SUFFICIENT.
$$Answer\ is\ Option\ B$$
