Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

DEFINITION

The absolute value of a number is the value of a number without regard to its sign.

For example, \(|3| = 3\); \(|-12| = 12\); \(|-1.3|=1.3\)...

Another way to understand absolute value is as the distance from zero. For example, \(|x|\) is the distance between x and 0 on a number line.

From that comes the most important property of an absolute value: since the distance cannot be negative, an absolute value expression is ALWAYS more than or equal to zero.

GRAPH OF y=|x|

As you can see for any value of x, the value of y, which is |x|, is ALWAYS more than or equal to zero.

IMPORTANT PROPERTY

When \(x\leq{0}\), then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\). Notice that in the negative scenario, we don't simply remove the absolute value bars. We remove the absolute value bars and negate the entire expression contained within, thus making it positive again;

When \(x\geq{0}\), then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\).

OTHER IMPORTANT PROPERTIES

1. \(|x|\geq0\)

2. \(\sqrt{x^2}=|x|\)

3. \(|0|=0\)

4. \(|-x|=|x|\)

5. \(|x-y|=|y-x|\). |x - y| represents the distance between x and y, so naturally it equals to |y - x|, which is the distance between y and x.

6. \(|x|+|y|\geq|x+y|\). Note that "=" sign holds for \(xy\geq{0}\) (or simply when \(x\) and \(y\) have the same sign). So, the strict inequality (>) holds when \(xy<0\);

7. \(|x|-|y|\leq{|x-y|}\). Note that "=" sign holds for \(xy>{0}\) (so when \(x\) and \(y\) have the same sign) and \(|x|\geq{|y|}\) (simultaneously).

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Hi, I've some problem with the graph y=|x| [figure in original post]

would someone please explain it ?

Thanks in advance.

Plug values for x and you get the values of y (|x|). For example, if x=-1, then y=|x|=1, if x=2, then y=|x|=2, if x=0, then y=|x|=0, ... As you can see no matter whether x is negative, positive or 0, the value of y (|x|) will come up as positive or 0, but never as negative. Hence the position of the graph above the x-axis, where only positive y's lie.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

DEFINITION

The absolute value of a number is the value of a number without regard to its sign.

For example, \(|3| = 3\); \(|-12| = 12\); \(|-1.3|=1.3\)...

Another way to understand absolute value is as the distance from zero. For example, \(|x|\) is the distance between x and 0 on a number line.

From that comes the most important property of an absolute value: since the distance cannot be negative, an absolute value expression is ALWAYS more than or equal to zero.

GRAPH OF y=|x|

As you can see for any value of x, the value of y, which is |x|, is ALWAYS more than or equal to zero.

IMPORTANT PROPERTY

When \(x\leq{0}\), then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\). Notice that in the negative scenario, we don't simply remove the absolute value bars. We remove the absolute value bars and negate the entire expression contained within, thus making it positive again;

When \(x\geq{0}\), then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\).

OTHER IMPORTANT PROPERTIES

1. \(|x|\geq0\)

2. \(\sqrt{x^2}=|x|\)

3. \(|0|=0\)

4. \(|-x|=|x|\)

5. \(|x-y|=|y-x|\). |x - y| represents the distance between x and y, so naturally it equals to |y - x|, which is the distance between y and x.

6. \(|x|+|y|\geq|x+y|\). Note that "=" sign holds for \(xy\geq{0}\) (or simply when \(x\) and \(y\) have the same sign). So, the strict inequality (>) holds when \(xy<0\);

7. \(|x|-|y|\leq{|x-y|}\). Note that "=" sign holds for \(xy>{0}\) (so when \(x\) and \(y\) have the same sign) and \(|x|\geq{|y|}\) (simultaneously).

This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty.

DEFINITION

The absolute value of a number is the value of a number without regard to its sign.

For example, \(|3| = 3\); \(|-12| = 12\); \(|-1.3|=1.3\)...

Another way to understand absolute value is as the distance from zero. For example, \(|x|\) is the distance between x and 0 on a number line.

From that comes the most important property of an absolute value: since the distance cannot be negative, an absolute value expression is ALWAYS more than or equal to zero.

GRAPH OF y=|x|

As you can see for any value of x, the value of y, which is |x|, is ALWAYS more than or equal to zero.

IMPORTANT PROPERTY

When \(x\leq{0}\), then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\). Notice that in the negative scenario, we don't simply remove the absolute value bars. We remove the absolute value bars and negate the entire expression contained within, thus making it positive again;

When \(x\geq{0}\), then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\).

OTHER IMPORTANT PROPERTIES

1. \(|x|\geq0\)

2. \(\sqrt{x^2}=|x|\)

3. \(|0|=0\)

4. \(|-x|=|x|\)

5. \(|x-y|=|y-x|\). |x - y| represents the distance between x and y, so naturally it equals to |y - x|, which is the distance between y and x.

6. \(|x|+|y|\geq|x+y|\). Note that "=" sign holds for \(xy\geq{0}\) (or simply when \(x\) and \(y\) have the same sign). So, the strict inequality (>) holds when \(xy<0\);

7. \(|x|-|y|\leq{|x-y|}\). Note that "=" sign holds for \(xy>{0}\) (so when \(x\) and \(y\) have the same sign) and \(|x|\geq{|y|}\) (simultaneously).

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...