The GMAT focuses on measuring the candidate’s ability to solve quantitative problems and interpret data. The concept of absolute value inequalities have been known to be the most challenging. With the GMAT being a tightly timed examination, it is crucial that candidates dissect the questions quickly and come up with the correct answers. Let us look at the secrets of mastering absolute value inequalities.**An inequality is a comparison between two values or expression where either values or expressions are not equal to one another**. Most of the algebraic manipulations that are used in mathematical expressions can be applied to inequalities; however, there are several exceptions listed below that need to be applied. These points may seem trivial; however, the consequences can be severe, and can mislead candidates to the wrong answers.

1) When an inequality is being multiplied by a negative value, the direction of the sign must be switched.

2) Unlike expressions, inequalities cannot be squared. This means that a > y will not equal to a^2 > y^2.

3) The square root of both sides cannot be taken to obtain an answer. **Inequalities with an absolute value term will typically have two solutions**. In order to simplify solving absolute value inequalities on the GMAT examination, candidates should follow these steps:

1) Isolate the absolute value expression found in the inequality

2) Set the expression so that it equals to both a positive and a negative value and

3) Solve for the inequality.

Let’s take a look an inequality with only one absolute value term.

5 + | 2x + 1 | < 10

Let us follow the shortcuts

1) First, we will isolate the absolute term from the inequality, so that it is only on one side of the expression:

5 – 5 + | 2x + 1 | < 10 – 5

| 2x + 1 | < 5

2) Next, we will need to find both the positive and negative values of the term. It is important for candidates to remember that most of the absolute value inequalities will have two solutions. Those who fail to remember this will often choose the wrong answer. We can set the positive value by keeping the equation as it is; thus,

2x + 1 < 5

3) We can then apply basic algebraic manipulations to solve this question.

2x + 1 – 1 < 5 – 1

2x < 4

x <2 --> 1 (Positive Solution)

By doing this, we will have the first answer required for solving the absolute value inequalities; however, we need not forget that there is a negative solution as well. To set up the negative solution, we make the absolute value inequalities negative; thus,

- ( 2x + 1 ) < 5

- 2x – 1 < 5

- 2x – 1 + 1 < 5 + 1

- 2x < 6

This is where the tricky part happens. Most candidates will forget to flip the inequality sign when they either divide or multiple by a negative number. Since in this case, we are multiplying 6 by a -2, we will need to apply this trick.

X > -3 --> 2 (Negative Solution)

From Statements 1 and 2 we can assume that the value x is greater than -3, and smaller than 2 which can be written as -3 < x < 2.

The most recommended trick for solving multiple inequalities will be to solve each inequality separately and then combine them. **For example, let’s take a look at | x + 1 | > 3 and | x – 2 | < 4 **

To solve each inequality separately, we would look at | x + 1 | > 3 first. Just like before, it is important to get both the positive and the negative solutions.

For the positive solution of | x + 1 | > 3, we would get:

| x + 1 | > 3

x + 1 – 1 > 3 – 1

x > 2

And, for the negative solution of | x + 1 | > 3, we would get:

| x + 1 | > 3

- ( x + 1 ) > 3

- x – 1 > 3

-x – 1 + 1 > 3 + 1

- x > 4

x < -4

For the positive solution of | x – 2 | < 4, we would get:

| x – 2 | < 4

x – 2 + 2 < 4 + 2

x < 6

For the negative solution of | x – 2 | < 4

| x – 2 | < 4

- ( x – 2 ) < 4

- x + 2 < 4

- x + 2 – 2 < 4 – 2

- x < 2

x > -2

As we can see, the solutions for | x + 1 | > 3 and | x – 2 | < 4 are

x > 2, x < -4 , x < 6 and x > -2**The overlapping regions will be 2 < x < 6**

Solving inequalities with absolute value in GMAT is not too difficult once the correct theorems are applied. Candidates interested in performing well on the quantitative section of the GMAT examination should consider taking some time to practice the absolute term inequalities with only one inequality and then with multiple inequalities.

**Top 31 MBA Programs + Analysis of 24 Industries (United States)**We analyze the MBA Curriculum, Class Profile, Total Cost and Post-MBA Salary of

**Top 31 MBA programs in the US.**

+ Industry Trends

+

+ Industry Trends

**Future of**Aerospace, Agriculture, Artificial Intelligence (AI), Automobile, Clean Tech, Education, Energy, Fashion, Financial Services, Insurance, FinTech, Government, Healthcare, Life Sciences, Military, Manufacturing, Maritime, Media/Advertising, Technology, Tourism, Trade, Transportation and Logistics, Virtual Reality (VR), and Augmented Reality (AR).

**Pages: 327**

**Reviews**

"I have not reviewed many books for MBA Admission consulting companies but doing it now to give all applicants a brief idea on what the book covers. The book includes 31 top MBA programs - almost all the top schools you have heard or considering for your MBA application. Each chapter is categorized by US States where there is at least one top MBA program. So you have California and Massachusetts with the most number of MBA programs and several states with one top program (Washington, Minnesota, Washington D.C., Connecticut, Virginia, and Maryland) and other states with two to three MBA programs. The book focuses on four aspects of an MBA program - curriculum, cost, class profile and post-MBA salary. For me, the breakdown of the cost and post-MBA industry was useful to make my decision on selecting the top 5 programs for 2017-18. It is a fascinating read in an industry where consultants overprice for their expertise. I recently bought a 30-page guide for $49. Compared to the obvious observation in that book, the 300+ page, MBA in US - the Ultimate guide is a goldmine of information and analysis." -

**Verified Purchase (21st June 2017)**

"I bought the ultimate guide after a friend recommended it for me. The guide covers a lot of ground on the history of each prominent US states and goes into the reasons why a certain industry emerged from each state. In addition to the analysis of the economy, trends and expected changes in the next 5 years, the book features top MBA programs in each state with an extensive study of its curriculum. Ultimate guide is an essential reference book for MBA Applicants if they want to shortlist MBA programs based on value and cost, and not just ranking. " -

**Verified Purchase (14th June 2017)**

"Should be a required reading before applying for an MBA. School events and MBA Tours are PR events disguised as a Q&A. On the contrary, the book is an unbiased analysis of each Top MBA program in the US supported by a large dataset and historical context on each industry. The guide builds a case for indstries that are likely to emerge as favourite for MBA graduates. Thorough and a valuable book."

**- Verified Purchase (15th June 2017)**

"What I liked: The breadth of the information. Some of my favorite nonfiction books have taken the same approach as the ultimate guide have - cover background information in-depth. In the book, the author uses parallel threads to demonstrate the history of the state and the rise of industries. Will make you think how schools thrive based on the policy set by the state. California's obsession with Technology has revolutionized how we do Business and changed post-MBA trends. Many MBA applicants will be consulting or doing marketing for a Technology company. That is one key finding from the book. The latest development in AI, FinTech, and Automation is an additional context that I found valuable in the book.

Very informative. I would recommend that you read the book at least once in chronological order before using Table of Contents." -

**Verified Purchase (2nd July 2017)**

Download How to Choose the Best MBA in US: The Ultimate Guide

(2018 Entering Class)

Download How to Choose the Best MBA in US: The Ultimate Guide

(2018 Entering Class)