Problem Solving (Part 2: The Problem Solving Process)

In the following article, we’re going to delve into problem-solving best practices for the GMAT exam. You can either read this article or watch the corresponding video on YouTube. To make things easier to digest, we’ve broken the contents of the video up into 2 parts. In this segment, hosted by one of MyGuru's most experienced GMAT tutors, we will explore the ins and outs of the problem solving process. In part 1 of this article, we discussed the frequency and format of problem solving questions and their strategic implications. If you haven’t yet read it, we suggest you go back and make sure you understand that first. 

Simple Quantitative Problem Solving Question Example

For many years, a surfeit of bears terrorized Yamhill neighborhoods. Then, Bill moved in and every week he was able to safely relocate the greater of either ⅓ of the bears or 30 bears until a sustainable population of fewer than 30 bears remained in the town. If Yamhill had 270 bears upon Bill’s arrival, what was the number of bears in the sustainable population at the end of Bill’s relocation efforts?

1. 0
2. 12
3. 15
4. 20
5. 24

As is the case with every GMAT strategy, the first step is to set up your scratchpad. Before you’ve even read the prompt, list your answer choices vertically from A to E, including simple numbers if provided. Next, skip to the end of the problem to identify your sought values and label your choices as such. In this case, the question is asking you to identify the number of beats at the end of the relocation effort. This will save you the valuable time people often spend reading the whole paragraph to get to what the question is asking and then rereading the whole thing a second time. By getting immediately to the heart of the matter, you can then read the paragraph from the beginning and work through the problem with lazer focus, as shown below:

1. 270 bears at the start
2. Relocate Great of ⅓ or 30 bears weekly until < 30 remaining
3. 270−⅓ (270)=180
4. 180−⅓ (180)=120
5. 120−⅓ (120)=80
6. 80-30=50
7. 50-30=20

Evidently, the correct answer is option D.

Complex Quantitative Problem Solving Question Example

If x and y are integers, and 3x + 3x+2=10y, which of the following must be true?

1. x = y
2. y = 1
3. x = 0
4. I only
5. III only
6. I and III only
7. II and III only
8. I, II, and III

As we did with the previous problem, start by setting up your scratch pad, listing your choices vertically from A to E. Again, you next want to skip to the end of the problem to identify your sought values and label your choices as such. Finally, take notes and make necessary calculations as you work through the problem. In this case, start by considering the four possible problem solving tactics you could apply to the problem:

1. Technical math: Attempt this first, but it abandon quickly if it isn’t easily applicable. In this case, you can apply this method since you have access to the algebraic expression.
2. Logical estimation: Attempt this at each step of every problem. Constantly eliminate possible options so you can quickly and confidently guess when necessary. 
3. Plugging in value: Model the circumstance.
4. Plugging in the choices: Backsolve the problem. 

In this case, you can implement a mix of options 2-4 as an alternative to the potentially more time-consuming technical math. Don’t fully calculate unless it’s absolutely necessary and always look for opportunities to use logical estimation. Work the problem using the chosen tactics until you have only one choice left, as shown below:  

1. Note the Roman numeral format
2. Which of the following must be true?
3. 3ˣ+3ʸˣ⁺²=10ʸ (we know that x and y are integers so we won’t use any fractions here)
4. Consider the best approach in the moment: 
1. Technical math
2. Plugging in values and estimation
5. 3ˣ+3ʸˣ⁺²=10ʸ | 3ˣ (10)=10ʸ

• 3ˣ must = 1 and 10ʸ must = 10
• X must = 0 and y must = 1

The correct choice is D.

(If you aren’t comfortable with the technical math, you can instead note that the iii is the most common numeral in our answer options and plug-in x=0. If we discover that x cannot = 0, then we can immediately identify choice A as the correct answer. In this case, we end up with 1+9=10ʸ. This only works if y=1, which brings us back to option D.)

Conclusion

We hope this overview of the problem solving process for simple and complex problem solving questions was helpful. 

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