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Notice that we don't have much information about the 3 variables a, b and c Since b + c < 0, we know that at least one variable is negative (which means a must be negative), but that's pretty much it. The missing part here is that we don't really know whether c is positive or negative.
Given the absences of solid information about c, we might solve this question by testing values
Case i: a = -3, b = -2, and c = 1 (these values satisfy the given information). We get: Quantity A: ac = (-3)(1) = -3 Quantity B: 0 In this case, Quantity B is greater
Case ii: a = -3, b = -2, and c = -1 (these values satisfy the given information). We get: Quantity A: ac = (-3)(-1) = 3 Quantity B: 0 In this case, Quantity A is greater
if b+c<0, and a<b<c, then we know that A and B MUST be negative numbers and C can be a number ranging all the way from a negative up to a huge positive (just as long as the negative value of B is a larger negative than C is a positive such that their sum would still be less than 0). Quantity A being AC therefore could either be a negative*negative=positive (in which case quantity A>B) or a negative*positive =negative (in which case quantity A<B). Since we don't have a definitive answer, the correct choice is D.