Hi folks,
I am trying to look for as many questions for minimum/maximum problems. I can’t find a subcategory on Greg’s Quant Problems Section. Could someone please guide me on where to find these?
I have found so many questions on ETS’s mock asking at least 1 or 2 questions related to the=is category, and I always mess up on these.
Any support on this would be appreciated, TIA!
I don’t think I can find general minimum/maximization problems easily since they cover many different topics (Algebra, Geometry, Probability, etc), but there are a few flavors of this type of question, so practicing each of these skills can be helpful.
First of all, you may be asked to find the minimum or maximum of a quadratic function f(x) = ax^2+bx+c. You may complete the square on the equation to get the function into vertex form f(x) = a(x-h)^2 + k, so you can easily read off the y-value of the vertex (k) to get the min/max (min if a>0 or max if a<0).
Similarly, if you have an absolute value equation, such as y = |x+1| +4, then you can notice that the |x+1| >= 0. Thus, the minimum occurs when |x+1| = 0, which occurs when x = -1. In that case, y = |x+1| + 4 = 0 + 4 = 4, so the minimum y-value is 4.
Otherwise, you may be asked to find the maximum area covered by a polygon inscribed in a circle. In this case, the area is maximized if the polygon is a regular polygon (same sides and same interior angles).
Another case is to find the maximum or minimum of P(A or B) or P(A and B) given that you know P(A) and P(B). You can check both the complete overlap case and the mutually exclusive cases to find upper and lower bounds. 0 <= P(A and B) <= smaller of P(A) and P(B), where 0 happens if A and B are mutually exclusive and the bound above is complete overlap. Similarly, larger of P(A) and P(B) <= P(A or B) <= P(A) + P(B), where the lower bound is the complete overlap case and the upper bound is the mutually exclusive case.
There are some other cases but hopefully I highlighted some common cases and you can find the associated Quant Flashcard Quizzes under the 1-month/2-month plans for those topics. In addition, feel free to take advantage of the Topics-Based Quizzes under Quizzes → Quant Foundation Quizzes.
I hope that helps!