GMAT Problem-Solving Questions: Tips To Improve Scores

GMAT problem-solving questions in the quantitative section of the GMAT exam can be very challenging. However, if you prepare adequately and ensure that you use your time efficiently and effectively, you will improve your chances of achieving your desired target score in the GMAT exam. This article uses a few examples to create a quick summary of how best to go about finding solutions to problems in this section of your exam.

Let’s take a look at what you need to equip yourself in the process of preparing for this section of your GMAT exam.

What to Expect in GMAT’s Problem-Solving Section

There are two types of questions you’ll come across in the Quantitative Reasoning section of the GMAT exam: Problem-solving questions and data-sufficiency questions. Problem-solving questions make up at least half of the total number of questions you’ll come across in this section. Usually, the quantitative reasoning section contains 31 questions, which means approximately 15 of them will be problem-solving questions.

You will always have five options and one correct selection. The answer choices can be presented as numeric values, variables, or even ranges, and this is going to inform your strategy for solving these problems.

Strategic Implications of the Presentation

Take note of the format of choices in order to select an approach that is efficient and enables savvy mental calculation. For instance, if your answer choices are in the form of fractions, do your mental calculations as fractions, and if you are looking for a range of values, then don’t take a lot of time solving for a specific value. Usually, you’ll have 62 minutes to answer all 31 quantitative questions, which gives an average of 2 minutes per question. However, you have a maximum of 3 minutes for any question because some questions will take you a bit less than two minutes.

Check your pacing after every 10 quantitative questions, as this will help you to avoid clock-watching for every question.  The initial questions matter more according to the scaling of the exam, and, therefore, try to avoid mistakes here and be more methodical. It’s essential to spend a bit of time in this section. For the first 10 questions, spend about 24 minutes total for a ~2:24 average. You can look up after the first 10 questions and see if you have more or less than 38 minutes left.

For the second 10 questions, spend the recommended 2-minute average. This means you have to increase your speed as you go. After these 10 questions, check again to see if you have more or less than 18 minutes left. For the final 11, we are looking at roughly ~1:40 average per question. While you need these questions to complete the section, they don’t have as much impact on your overall score as the previous ones.

A good rule of thumb is to try to guess earlier on questions that you are not sure how to proceed with within the final 11 rather than trying to shortcut everything.

Simple Quantitative Problem-Solving Process

An Example of a Problem-Solving Question

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

The Problem-Solving Process

1. Set up your scratchpad listing choices vertically from A to E, including simple numbers if provided.

2. Skip to the end of the problem to identify sought values and label your choices as such.

 # Number of Bears at the end of relocation effort =?

3. Read from the beginning taking notes and completing obviously necessary calculations as you go.

• 270 bears at the start
• Relocate Great of ⅓ or 30 bears weekly until < 30 remaining
• \(270-\frac{1}{3}(270)=180\)
• \(180-\frac{1}{3}(180)=120\)
• \(120-\frac{1}{3}(120)=80\)
• \(80-30=50\)
• \(50-30=20\)

So option D is the correct answer.

Complex Quantitative Problem-Solving Question

An Example of a Problem-Solving Question

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

1. uppercase roman numerals
2. x = y
3. y = 1
4. x = 0

1. I only
2. III only
3. I and III only
4. II and III only
5. I, II, and III

The Problem Solving process

1. Set up your scratchpad listing choices vertically from A to E.

2. Skip to the end of the problem to identify sought values and label your choices as such.

3. Read from the beginning taking notes and completing obviously necessary calculations as you go.

4. Stop to consider all Four possible problems solving tactics

• Technical Math- Attempt first but abandon quickly if it becomes either not apparent or simple to you. In this case, it is apparent because you have been given the algebraic expression, but if it is not simple to you, then quickly abandon this approach.
• Logical estimation- Attempt at each step of every problem. Constantly eliminate things as much as you can so that when you are in a position where you have to guess, it is from one of two or three rather than from one of five.
• Plugging in value (modeling)
• Plugging in the choices(backsolving)

We can basically use a hybrid of ii-iv in our attempt to solve this problem.

5. Work the problem using your chosen tactic until only one choice is left.

 Note: Don’t fully calculate if not needed. For example, if you know your answer is greater than 6 and is negative, and  -12 is the only option that satisfies those conditions, then just pick -12. 

Always look for opportunities to use logical estimation.

Solution

1. Note the Roman numeral format
2. Which of the following must be true?
3. \(3x+3x+2=10y\) (we know that x and y are integers, so we won’t use any fractions here)
4. Let us consider the best approach at the moment for us: (a) Use technical math, (b) Plugging in values and Estimation

       5a. \(3x + 3x+2 =10y\)

         \(3x(1 +32) = 10y\)

          \(3x(10) = 10y\)

 This means that: 3x must  = 1, and 10y must = 10.

 x must = 0 (anything to the power of zero = 1) and y must = 1

Option D is the correct answer.

         5b. If we are not familiar with this math, then we can look at the choices A-E and notice that iii is the most commonly occurring numerical. Then we can plug in x = 0. So if we find out that x cannot = 0 then the answer is A, and we are done.

If we plug in x = 0 then, \(3x(1 +32) = 10y\)

Then 10 = 10y is true if \(y = 1\) (Option D)

In this way, we are able to solve the problem using logical reasoning without needing to know the technical math.

Summary

Step 1

Set up the scratchpad listing the choices vertically from A through E. 

• Include simple numbers with the choices if the numbers are provided
• Note the format of choices to inform tactics and calculation

Step 2

Skip to the end of the problem and label choices as sought value(s)

• Note if you are seeking a specific or non-specific value 
• Don’t auto-solve for individual values if you seeking a combined value

Step 3

Read the question from the beginning as you take notes and perform the required calculations 

• If you see a clear path to solving a problem, take it!
• Most “certain but time-consuming” approaches could take you less than three minutes if you start working immediately.

Step 4

Consider all four possible tactics for the most effective and efficient path to solving a problem at the moment. 

• Technical Mathematics 
• Logical Estimation
• Plugging in values (Modelling)
• Plugging in Choices(Backsolving)

Step 5

Work the problem using your chosen tactic until only one option remains 

• Always be asking, “I’m I pressing for a solution?” If the answer is “No”, Estimate, Eliminate, Guess, and move on in less than 20 seconds. 
• Allow a maximum of a single calm reread, recalculate, or tactical reset before you must estimate, eliminate or guess 

Example

If a rectangular parking lot with width 4 feet shorter than its length was extended into a square parking lot and doubled its area in the process, what would have been the original length of the parking lot?

1. 2
2. 4
3. 8
4. 12
5. 16

Steps 1& 2

We list our choices & skip to the end, and label choices according to what we seek.

Original length

1. 2
2. 4
3. 8
4. 12
5. 16

Step 3

With = w

      Length = \(w+4\)

      Original area = \(w(w+4)\) 

      New width = \(w+4\)

      New are = \((w+4)2\)

The area was doubled. Therefore \(w(w+4)=\frac{1}{2}(w+4)2\)

$$w2+4w=\frac{1}{2}(w2+8w+16)$$

$$2w2+8w=w2+8w+16$$

Let’s collect like terms:

$$w2-16=0$$

Factor:

$$(w+4)(w+4)=0$$

$$w = 4\ \text{or}\ -4$$

 Length cannot be negative, so w = 4

Original length = w+4, = 4+4 = 8(choice C)

OR

1. 2
2. 4
3. 8
4. 12
5. 16

If we plug in 8, then

$$\small{\begin{array}{lllll}\text{Original length} & \text{Original width} & \text{Original area} & \text{New width} & \text{New Area} \\ 8 & 4 & 32& 8 & 64=2(32) \\ \end{array}}$$

So option C) is our correct answer through a backsolving approach that might be a lot more straightforward than technical math and saves us quite a bit of time.

Go ahead and do more practice with all the possible tactics, you will get better and find what works for you best.

How Can You Prepare for the GMAT Problem Solving Questions?

GMAT problem-solving questions don’t test advanced mathematical concepts as one might expect. If anything, for most of the questions, you’re required to apply your knowledge of high school math, though this time around, in a more complex and analytical way. That means a little thinking out of the box, and mathematical reasoning should help you solve the problems without much struggle.

That said, here are a few tips that could be of great help in tackling questions in the problem-solving section of your GMAT exams.

Practice doing calculations without a calculator

It’s high time you get used to using scratch paper for calculations and double-checking your work just to make sure there are no errors. You’re not going to use a calculator for GMAT exams. So get used to making basic calculations by hand.

Plugin numbers

It’s essential to plug in real numbers for the variables in the equations so that it’s easy for you to work on the questions without feeling that they’re complex. Along the way, you might find two or more answers that match the numbers you’ve chosen. In such a case, try plugging in new numbers or solving the problem in a different way until you get a correct answer.

Use answer choices to work backward

If you’ve got an idea of where to start, go ahead and plug in an answer to work backward. In that way, you’ll easily eliminate the choices until you arrive at the correct answer. You can start with the middle choice, last, or the first answer in your guesswork. Somehow, you should finally get the correct choice provided you know your way around.

Avoid estimations by all means

When it comes to geometry questions, don’t rely on your eyes in estimating areas, lengths, angle sizes, or any form of measurement. This kind of visual estimation will see you fail in most of the questions, and this will affect your overall score.

Start with what you know

Keep in mind that GMAT exams will only require you to use high school-level math to answer the questions. Therefore, it’s advisable to start small on the questions by using what you know and break the problem into small steps that you can achieve with the little knowledge you have. In that way, you’ll be able to work towards an answer. 

Use high-quality study materials

The best way to prepare for your GMAT exams is by using real problem-solving practice questions from past exams or questions that specifically follow the GMAT format. At AnalystPrep, we provide lots of study resources for all the sections of your GMAT exams. You can get a GMAT study package with thousands of real problem-solving practice questions to help you prepare for your exams adequately. It’s a one-time investment that will see you improve your GMAT scores and consequently hit your targets.

GMAT problem-solving questions aren’t as hard as you can imagine. All you need to do is to practice adequately for the exams and brace yourself for the exams.