Solution:
Let the integer solutions of x be m , n.
So m+n = -b
and mn = c.
Since c is prime, one of m or n has to be 1 or -1 and the other has to be the prime number.
If lxl > 2, it means either x > 2 or x < -2.
So we need to know if both m, n > 2 or both m, n < -2.
Consider first (1) alone.
b is odd.
So m+n = - odd number.
Since one of m and n is 1 or -1, the other has to be even, because only even + odd gives odd.
Also it has to be prime.
The only possibility is -2 or 2.
So the only possible values of m, n are 1, -1, -2, 2.
Now l1l = 1< 2, l2l =2 ,l-1l = 1 < 2, l-2l = 2 .
So lml or lnl is not > 2.
Or lxl is not > 2
So (1) alone is sufficient to answer the question.
Next consider (2) alone.
If c is even c has to be 2 because it is given that is a prime.
Or mn is 2.
So one of m or n is 1 and the other is 2 or one of m, n is -1 and the other is -2.
Now l1l < 2, l2l = 2, l-1l = 1 < 2, l-2l = 2.
So lml or lnl is not > 2.
Or lxl is not > 2.
So (2) alone is also sufficient to answer the question.

The correct answer is (D).