Given that:- D, N, and P are positive integers D<N and N is not a power of D
Target question => is D a prime number?
Statement 1 => N has exactly four factors and D is a factor of N
This means factors of N = 1, X, Y, N where N must be equal to xy
D is either x or y
If N = 6, then factors of 6 = 1, 2, 3, 6, some possible values of D(2 and 3) are a prime number in this case
If N=8, then factors of 8 = 1, 2, 4. 8, some possible values of D (2 and 4) are not prime numbers in this case.
Since the target question cannot be answered with certainty, statement 1 is NOT SUFFICIENT.
$$Statement\ 2\ =>D=\left(3^P\right)+2$$
If P = 1 then D = 5 and D is a prime number but if P = 5 then D = 245 and D is NOT a prime number
Since the target question could not be answered with certainty, statement 2 is NOT SUFFICIENT
Combining both statements together=>
Since N is not a power of D, N must be a product of two distinct prime numbers to have four factors
A possible case of factors of N = 1, 2, 3, 6 so D is either 1 or a prime number
$$From\ statement\ 2\ =>D=\left(3^P\right)+2$$
When P = 0, D = 3; minimum value of D =3; So D cannot be 1, hence, D is prime
Both statements together ARE SUFFICIENT
Answer = C
