Good news, test takers! You can pass the GMAT! Most of the questions are not that difficult. The difficulty in the test is in taking a mid-level question, (5x2 = 10) and rephrasing it in a more difficult way. (5 men walk into a bar. The bartender gives each man a beer for each of their hands. How many beers does the bartender distribute all together?) There is one exception to the rule, though: **Absolute value inequalities.**

It’s a little tough, but not impossible to figure out absolute value inequalities!

We’ll start with absolute value expression’s basic definitions, mathematically and conceptually. Then we’ll use that basic understanding to solve equations and inequalities including absolute value expressions. Finally, we’ll deal with a concept-based application of the absolute value inequalities on the GMAT. Let’s go! **Absolute positive** - Everybody knows that |9|=9 and|-9|=9. What’s so special about those slanted lines? How and why does it neutralize a number? Those bars are the measure of the distance of the number within the bars and zero. -9 and 9 are both 9 units away from 0. Picture it!

Let’s look at it those two ways**1)** The number within the bars will definitely turn positive and **2)** The distance from zero to the number is our basis for digging deeper into absolute value.

This concept becomes difficult when a variable, as opposed to a number, is placed within those bars, |u|. Shouldn’t |u| be equal to u? There’s no sign in front of the u, so absolute values says this u should be positive…but this u could actually be negative! **When dealing with absolute values of variables,** know these constants

1) the expression (number or variable) may have a positive sign [+]

2) the expression (number or valuable) may have a negative [-] sign. **The Bottom Line:** Numbers or variables with the absolute value bars can be negative or positive. **Solving absolute values****Step one:** Remove the bars…but before you do that, consider the possibility of a negative or positive scenario. |u| + 6 =10**Scenario 1:** If u is positive, simply drop the absolute value bars and rewrite the equation as u+6=10, u =4

Remember that if u is greater than 0, then u=4

u>0, then u=4**Scenario 2:** If u is negative, removing the absolute value bars negates [-] the expression. The equation is then written (-u)+8=12, u=-4

u<0, u=-4

Now remember the “5 men walking into a bar” comparison. They want to complicate a simple mid-level equation here, so be very careful. |u+1| =8

SOLVE**Scenario 1:**

Remember that

u+1 is positive, u+1=8, so u=7

Don’t forget that if

u>-1, then u=7**Scenario 2:**

(u+1) is negative (this time)

Then –(u+1)=8 and u=-9.

Therefore, u<-1, and u=-9**Did you see in those two examples that there are two solutions to the GMAT inequalities with absolute value equations? **

This is because a variable absolute expression depends on the value (positive or negative.) Each variable has a breaking point, known as the critical point. The critical point is the zeroing point of the values in the absolute value bars.

For |u|, the critical|zeroing point is 0.**All u’s to the right of the 0 on the number line changes the variable: **

|u| to u**All the u’s to the left of the number line changes the variable: |u| to (-u)**

For the expression, |u-2|, 2 is the critical point.

For the expression, |2u+3|, -3, 2 is the critical point.

**The critical point is important**because it tells the numerical range that makes each equation true. GMAT inequalities with absolute values are one of those topics that teachers use to try and trick unsuspecting students. With a little bit of direction and awareness, you’ll be fine. You only need a little bit of knowledge and the fundamentals. You’ll solve these no-so-tricky problems with ease.

**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)