# GMAT & MBA Admissions Blog

Any good GMAT tutor provides a wide range of problem-solving strategies for the GMAT. While the GMAT is, as a general rule, a test of problem solving and critical thinking ability, here we are talking about the problem-solving question type itself on the quantitative section of the GMAT.

Designed to measure your mathematical ability, the Quantitative Reasoning portion of the GMAT consists of 31 multiple choice questions that must be completed within 62 minutes. The two kinds of problems in this section pertain to data sufficiency and problem solving. In this article, we’ll be covering the strategies necessary to gain mastery of the problem solving questions. More specifically, we’ll cover the following foundational elements:

● How to identify problem solving questions
● Strategic implications of problem solving questions
● Simple and complex problem solving processes

How to Identify Problem Solving Questions

The most useful clues for identifying problem solving questions are frequency and format. More specifically, problem solving questions meet the following criteria:

● Approximately 50% of 31 Quantitative Questions
● Always Five Options and One Correct Selection
● Choices can be Either Numeric Values or Variables

Strategic Implications

Once you’ve identified a problem solving question, you would be well advised to take the following strategic measures:

● Note the format of your answer choices to select an efficient approach & enable savvy mental calculation
● For example, if your answer choices are presented in fractions, you should conduct your calculations in fractions as well. Having to translate between fractions and decimals will cause you to waste time unnecessarily.

● Maintain a 2 minutes per question average. Because questions vary in terms of difficulty, however, you can spend a maximum of 3 minutes on the harder ones.

● Check your pacing after every 10 questions. You should not be timing yourself constantly as that will distract you. By checking at predefined intervals, you can allow yourself to really focus on the work instead of anxiously checking the clock. Keep in mind that due to the way the computer adaptive way the exam is designed, performing well on the first ten questions will give you a competitive edge. For this reason, you should spend a little extra time on those than on the remaining questions. With this in mind, try to adhere to the following schedule:
● First 10 questions - 2:25 Average | +/- 38:00 Left
● Second 10 questions - 2:00 Average | +/- 18:00 Left
● Final 11 questions - 1:40 Average

Simple Quantitative Problem Solving Process

Below is an example of a simple quantitative problem:

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 1/3 of the bears or 30 bears until a sustainable population of fewer than 30 bears remained in 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 bear relocation effort.

A. 0
B. 12
C. 15
D. 20
E. 24

In order to tackle this questions as effectively as possible, adhere to the followings steps:

1. Set up scratch pad listing choices vertically A to E including simple numbers if provided

2. Skip to the end of the problem to identify sought value(s) & label choices as such

● # of bears end of relo effort = ?

1. Read from beginning taking notes & completing obviously necessary calculations as you go

● Greater of 1/3 or 30 bears relocated per week until < 30 remain in town | 270 bears to start
● 270 – 1/3(270) = 180 |
180 – 1/3(180) = 120 |
120 – 1/3(120) = 80 |
80 – 30 = 50 | 50 – 30 = 20

Complex Quantitative Problem Solving Process

Below is an example of a complex quantitative problem:

If x and y are integers, and , which of the following must be true?
I. x = y
II. y = 1
III. x = 0

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

Again—in order to tackle this questions as effectively as possible, adhere to the followings steps:

1. Set up scratch pad w/ choices A to E

3. Read from beginning taking notes & doing necessary calculations as you go

4. STOP! to consider all four possible problem solving tactics:
1. Technical Math | Attempt first but abandon quickly
2. Logical Estimation | Attempt at each step of every problem
3. Plugging in Values (Modeling)
4. Plugging in Choices (Backsolving)

5. Work problem until one choice left
1. Don’t fully calculate if not needed

6. Note roman numeral format

7. Which of the following must be true?

8. 3x+3x+2=10y

9. Consider best approach in the moment
1. Technical math
2. Plugging in values & estimation

10. 3x(1+32) = 10y |3x(10) = 10y
1. 3x must = 1 and 10y must = 10
2. x must = 0 and y must = 1

11. Plug in x = 0 as most frequent numeral
1. 1 + 9 = 10 = 10y | Works if y = 1
2. Plug in x = 1 = y | 3 + 27 cannot be produced solely by a power of 10
3. Eliminate choices with I | select D

Summary of the Problem Solving Process

1. Set up the scratch pad listing choices vertically A through E
● Include simple numbers with choices if provided
● Note format of choices to inform tactics & calculation

2. Skip to end of the problem & label choices as sought value(s)
● Note if seeking a specific or non-specific value
● Don’t autosolve for individual values if seeking a combined value

3. Read from beginning taking notes & doing needed calculations
● If you see a clear path to solving – take It!
● Most “certain but time-consuming” approaches
Take < 3:00 if begun immediately

4. Consider all four possible tactics for most effective & efficient path to solving in the moment
● Technical Mathematics
● Logical Estimation
● Plugging in Values (Modeling)
● Plugging in Choices (Backsolving)

5. Work problem using your chosen tactic until one choice remains
● Always be asking : am I progressing to a solution ?
As soon as “no” estimate, eliminate, guess & move On in < :20
● Allow maximum of one calm reread, recalculate, or tactical reset before you must estimate, eliminate, guess & move on in < :20

If you are looking for more information on how to approach GMAT problem solving questions, consider requesting a 1-1 consultation with an expert GMAT coach.

Logical estimation might be the single most important tactic for GMAT problem solving questions in the quantitative reasoning portion of the GMAT. We’ve already written an article that covers GMAT problem solving questions and strategies more generally, so we recommend you take a moment to read that before continuing if you haven’t yet. Moving forward, this article will address the following key topics:

● A general description of quantitative logical estimation and the conditions under which it should be utilized
● An overview of the strategic implications of logical estimation
● An example of logical estimation in the context of arithmetic
● An example of logical estimation in the context of word problems
● A summary of the logical estimation problem solving process

Quantitative Logical Estimation

Simply put, logical estimation refers to the process of continuously eliminating impossible answer choices as you tackle a problem. As any online GMAT tutor will tell you, it is one of the most important strategies to employ on the GMAT. In other words, thinking critically about what must be false in addition to what must be true can make the difference between an average score and a great score. Not only will this strategy save you time, but it will also allow you to maintain laser focus as you work through the problem-solving section of the test. More specifically, this method is especially useful when a question asks you to seek a range or approximation rather than a specific value.

To effectively implement the logical estimation process, one of your fist considerations as you read through a problem should be where the viable answer falls within the following binaries:

● Positive or negative
● Even or odd
● Integer or non-integer
● Factor or non-factor
● High or low

For example, if the question makes it clear that the correct answer must be even, you can immediately discount all answer choices that are odd–thereby increasing the likelihood of selecting the correct answer.

Strategic Implications

In addition to the binary-based elimination strategy mentioned above, you would be well advised to take the following strategic measures:

● Consciously note your choices at the beginning of the problem for estimation considerations
● Stop and select the correct choice if through estimation only one answer remains viable
● Avoid blindly guessing by using logical estimation until you’ve been stuck for 20 seconds without progressing
● Make note of key terms such as “Approximate” or “Closest to,” as they indicate cases in which logical estimation could be your primary problem-solving tactic.

Arithmetic Example

Question:

104 - 94 is closest to:
A. 1
B. 100
C. 1,000
D. 3,500
E. 6,500

Logical Estimation Process:

1. Set up a scratch pad listing choices vertically from A to E

2. Note inexact sought value and label choices as such
● 104 - 94 is closest to ?

3. Read from the beginning, taking notes and noting logical estimation opportunities to avoid unnecessary calculations
● Eliminate A, B, C
● 94 = 92 x 92 = 81 x 81
● Approximate as 80 x 80 = 6,400
● 10,000 – 6,400 = 3,600
● Select Choice D
● Beware of Too Fast Trap Choice E

Word Problem Example

Question:

If set N is comprised solely by each of the prime numbers less than 20, and the sum of the reciprocals of the terms in set N is a, what must be true of a?
A. a < 0
B. a < ½
C. a < 1
D. 1 < a < 2
E. 2 < a

Logical Estimation Process:

1. Set up a scratch pad listing choices vertically from A to E

2. Note inequalities in choices, not a single numeric value and label choices as such
● What must be true of a?

3. Read from the beginning, taking notes and noting logical estimation opportunities to avoid unnecessary calculations
● List Prime Numbers < 20 as 2, 3, 5, 7, 9, 11, 13, 15, 17, 19
● Note Reciprocals as 1 over each of the terms (ie. ½, ⅓, ⅕, etc.)

4. Work through the problem while consciously considering logical estimation as your primary tactic
● Use common fractions to decimal conversions to determine that ½ + ⅓ + ⅕ = 0.5 + 0.333 + 0.2 > 1
● Eliminate choices A, B, and C
● Note only seven terms remain each ≤ ⅐ remaining sum < 1
● Eliminate E and select choice D!

Summary of Logical Estimation Problem Solving Process

1. Set up a scratch pad listing choices vertically from A to E
● Note large numeric differences or ranges in choices

2. Skip to the end of the problem and label choices as sought value(s)
● Note if seeking a non-specific value

3. Read from the beginning, taking notes and doing needed calculations
● Seek time saving opportunities by not fully calculating

4. Work through the problem while using chosen tactic until one choice remains viable
● Eliminate impossible choices as you go to expedite the process!

If you are looking for more advice, consider requesting a 1-1 consultant with an expert GMAT tutor.

Any good GMAT tutor wants his or her student to review GMAT homework as efficiently as possible. Careful review of missed GMAT problems is one of the most critical parts of GMAT test prep. So what are our best tips for students as they review missed problems on GMAT practice tests?

In this portion of our GMAT Review Series, we’ll take a look at a Sentence Correction: Subject/Verb Agreement question from the Official GMAT Guide 2019 - Verbal Diagnostic. Remember to always use the non-underlined portion of the sentence in question as the answer key to match the underlined segment to.