The correct option is B String A will break
Initially, the tension in string B and A would be equal to weight of block A and zero respectively. If, we give a quick downward jerk to the bottom string, we exceed the breaking tension in the bottom string in such a short time that, because of the inertia of the block mass, we cannot accelerate it significantly, and the tension in the top string does not increase significantly above the weight of block that it held initially. Therefore, the bottom string breaks, and the block remains hanging from the top string