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  "How to Solve It" applied to GMAT Quantitative Questions

Posted by michael on Tue 30 Sep 08 at 9:47pm

Often students believe that the quantitative section of the GMAT exam is a math test. After teaching quite a few students with mathematical backgrounds, including a PhD in Electrical Engineering and an MS in Chemical Engineering, I have realized that there is more to this section than math. Math is just the medium through which creative problem solving skills are tested. Below I outline a few well known problem solving techniques listed in George Pόyla’s book “How to Solve It.”
Draw a picture.
I suggest students draw pictures for several types of GMAT questions including, set questions, absolute value questions, combination questions, and weighted average questions. This technique can often lead to intuitive approaches to questions. For example, a student can draw a seesaw and understands that placing the fulcrum in the right place to balance the seesaw will find a weighted average. Using this approach the student can solve many weighted average questions faster than a student who attempts to solve a weighted average problem algebraically.
Variation of the Problem.
A typical problem solving technique is solving a similar easier problem to establish a rule that can be applied to a more challenging problem. I often use this approach to teach students to remember to add one to inclusive sets. Most students intuitively know that there are exactly 10 integers between 1 and 10, inclusive. After establishing this fact, I ask them to find an equation to find the number of integers between 1 and 10, inclusive. Most students reason 10 minus 1. When I remind them that this results in 9 and not 10, they understand immediately that subtracting alone is not enough. So I ask them how they could make the 9 a 10.
Working Backward.
As a strategy for plugging in answer choices, this is seldom a wise decision (please see “GMAT ‘Tricks’ Part One: Backsolving”). However, working backward can still be useful in GMAT questions. Analyzing the units of an answer choice can often lead to the simplification of ratio problems and equations in word problems. For example, if an answer must be a rate, students can determine that rates must be expressed as a distance divided by a time from the unit miles per hour.
Decomposing and Recombining.
The strategy is to break questions down into smaller parts and then analyze the smaller parts to infer something about the whole. This strategy suggests that prime factorization may be a useful method for analyzing certain GMAT questions. Hopefully, all of us have enough experience with prime factorization to see that decomposing and recombining is a useful strategy.
I believe the problem solving aspect of the exam is what makes the GMAT an interesting exam. It is not testing how well a student can regurgitate an equation. It is testing how well a student can apply mathematics to solve problems. Possibly, this is exactly what mathematics will be used for in an MBA program.



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