GMAT Problem Solving
GMAT Problem Solving—Know What You Need to Know!
GMAT Problem Solving questions—like all questions on the GMAT exam—are difficult and expensive to produce. Psychometricians go through multiple stages of question writing, meaning that a single GMAT question can go through 12 months of iterations, edits, and quality checks before being approved by the Graduate Management Admission Council (GMAC).
For this reason, test takers should avoid using unofficial practice questions at all costs. At best, these unofficial questions will not test the data interpretation and critical reasoning skills that the GMAT prides itself on testing. However, at worst, they can reinforce inefficient and non-strategic methods of approaching the GMAT.
Below, we'll walk you through an official GMAT Problem Solving practice question with a detailed explanation to help you get acclimated to this new GMAT section.
Best Practices for GMAT Problem Solving Questions
In the quantitative section of the GMAT Focus exam, it is helpful to think of problem solving questions in two categories:
- Type 1: These questions are more just math questions and require you to apply your knowledge of basic calculations, conceptual thinking, and practical math approaches to solve a question.
- Type 2: These questions are made difficult by abstract presentation, complex or tricky wording, red herrings, your choice of approach—for these questions just understanding the math will not get you to the correct answer
Type 2 questions have always been the mainstay of the quantitative section on the GMAT, and these questions are what make the test so hard for students.
Chris Kane, Head of Test Prep at Menlo Coaching says even though he expected to see fewer Type 1 questions in the shift to the GMAT Focus, so far this has NOT been the case. Anecdotally, he says that ¼ of the questions fall into Type 1 and ¾ fall into Type 2 in the new exam, the same proportion as in the legacy version of the GMAT.
This is still a small percentage of the GMAT quant questions overall, but you should think of these Type 1 questions as gifts on the GMAT quant section: if you do the proper prep and understand the math, you will get these quant questions correct with little effort. It is also important to note that the standard for solving pure math questions around the globe is very high. If it is mostly just a math question, you really need to get it right to be competitive on the GMAT quant section.
So, when he reviews missed questions with students and sees that they are missing a Type 1 question, he always says: "Know What you Need to Know! and this question would feel easy."
There is no better example of this than the sample GMAT problem covered in this section, a question far too many students miss.
GMAT Problem Solving, Sample Question #1
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Explanation
Detailed Solution
Anytime you have roots in the denominator, an important best practice in algebra should be applied: remove the root by multiplying by one, a process called rationalizing the denominator. As an example, if you have then you would simply multiply by one as follows to simplify the expression and remove the root from the denominator: =
This process is made more difficult in this official question with two mechanisms:
- The denominator does not just contain individual terms with roots but also integers or multiple roots added together. This makes for a more difficult version of rationalizing the denominator in which you must recognize the difference of squares and "multiply by one" using the conjugate of the denominator. Even though this is harder, these are both core best practices that you learned in algebra in high school and you must know these for the GMAT problem solving questions.
- Three terms with roots in the denominator are being added together, so the test-maker entices students to try to find a common denominator or take some other incorrect approach.
Consider the first term of the three being added together in this problem: When you factor the difference of squares ( into its conjugates, you get (x + y)(x – y). With this knowledge (and some reverse-engineering) you can see that if you multiply by one in the form then all the roots will disappear in the denominator (and in this case the entire denominator!) as shown here:
( = = =
The important point with a manipulation like this is that you simply must recognize what to do: good logic or reasoning or problem solving won't help you!
We cover these types of important math skills in detail in our Refresh Modules in the Menlo Coaching GMAT prep course and then you need to practice the skills with questions like this. Once you see what to do on the first term, then just do the same type of manipulation on each fraction individually and add the simplified terms together.
The 2nd term being added together is simplified in the same way as follows: () = =
And the 3rd term: =
With each of the three fractions simplified and the denominators disappearing, you are simply adding together the following three terms:
((( = 1
Correct Answer
The correct answer is thus (E).
Correct Answer: (E)
As you prepare for the exam, pay special attention to any misses on questions like this that just require math knowledge. They are easier to prepare for and it is important that you choose the correct one from the answer choices. With difficult abstract problems involving lots of red herrings or tricky wording, you simply can't win them all, but for these types of questions, you can develop complete mastery.
Caution: Avoid Unofficial GMAT Problem Solving Questions
Utilizing unofficial problem solving questions could potentially be detrimental to your preparation. The sample GMAT problems prepared by third party test prep companies will be unable to replicate the precise level of difficulty seen in the official GMAT problem solving questions leaving you either under-confident or over-confident about your ability to master problem solving questions in the real exam. The unofficial questions can hardly ever mimic the quality and distribution pattern of the two GMAT problem solving question types in the actual GMAT exam.
Practicing with official GMAT problem solving question samples enables you to develop critical thinking and a nuanced approach in determining the right amount of time to spend on each question and also to build strategies required to tackle the two kinds of question types.
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