Question 4 - Quant Tickbox Quiz #5 (Algebra Column 2)

GRE Quant Problem Solving
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Hi all, my apologies if my post is not in the right spot. However I encountered the following problem in the Quant Tickbox Quiz #5. The correct solution according to GregMat is “Quantity A is bigger” but I’m not convinced. For me we have the following 3 cases:

Case 1: Both equations have positive discriminant which implies 4 real solution.
Case 2: One equation has positive discriminant (2 solutions) and the other one has discriminant 0 (so only 1 solution) which implies 3 real solution.
Case 3: One equation has positive discriminant (2 solutions) but the other one has negative discriminant (0 solutions) therefore total maximum of number of solutions in this case is 2.

However the values of a,b and c (not known to us except that they are not equal to 0) means that we do not know in which case we are. This means that we could either have maximum 4 real solutions or maximum only 2. Therefore I selected "
The relationship cannot be determined from the information given."

Would appreciate any clarification :slight_smile: - thanks!

2

Imagine you have a set of tuples (a, b, c, t), where t is the number of solutions. We want to pick the tuple with the maximum t. In this case, the maximum t is clearly 4.

3

Ok, so a, b and c are not fixed but instead freely chosen? Because my initial understanding was that a,b and c were fixed and in the worst case we would have 2 max solutions.

4

You consider a set of all possible values of a, b, and c and their corresponding t (the tuple we mentioned above). From that set, you pick the tuple(s) with the maximum t.