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:

2 sums with Modulus and Inequality both [#permalink]

Show Tags

27 Oct 2010, 02:55

2

This post was BOOKMARKED

Following are 2 sums having both Inequality and Modulus function. I cannot provide options here, as I picked it from a book giving only the correct answer.

The problem is not in the questions itself, but in the principles that one applies across the 2 problems. I am not able to grasp a common way of solving them both.

Here it goes:

Q.1> Solve for x, if |x-2| <= 2 and |x+3| >= 4.

Q.2> Solve for x, if |x^2 + 3x| + x^2 - 2 >= 0.

I'll confirm and provide the correct answers as soon somebody explains it.

Solving such equations is very convenient and quick using graphs. I have attached a pdf to show how to solve the first one using graphs. If you understand how it is solved, let me know and I will send the solution of the second one using graphs too. If it is not clear, I will give a quick recap of graph theory for mods.

This implies \(|x^2 + 3x| >= 2 - x^2\) We need to find values of x for which this relation holds. We will draw the graph of both the left side and the right side and find the answer by checking the values of x for which the graph of left side has higher values than graph of right side. Check the attachment for solution.

Re: 2 sums with Modulus and Inequality both [#permalink]

Show Tags

27 Oct 2010, 09:25

@ Krushna

Yes, you have got the first one right The answer is : 1<=x<=4

If u can solve the 2nd one too, that will be a great help. I've been pulling my hair because of the 2nd one. I am not in agreement with its answer.

Cheers, R J

P.S: One more thing though, you gave me the answer as 1,2,3,4, though you musn't forget that the numbers have not been stated as integers. Kudos+1 for the approach that is different than the one I have.

Re: 2 sums with Modulus and Inequality both [#permalink]

Show Tags

27 Oct 2010, 23:50

VeritasPrepKarishma wrote:

Given \(|x^2 + 3x| + x^2 - 2 >= 0\)

This implies \(|x^2 + 3x| >= 2 - x^2\) We need to find values of x for which this relation holds. We will draw the graph of both the left side and the right side and find the answer by checking the values of x for which the graph of left side has higher values than graph of right side. Check the attachment for solution.

Attachment:

Q2.pdf

All right!!.. i understand the explanation, though what I am confused about is that in the 1st question you basically take an INTERSECTION of the two ranges of the values of x and get to the answer; however, in the 2nd question you provide the answers as x>= 1/2 OR x <= -2/3.... Basically i had solved it in this manner - Since it is |x^2 +3x| in the given inequality, alternately assume it to be positive or negative

Case - 1: Considering it +ve Therefore, x^2+3x + x^2 - 2 >=0 Solving this we get: x>=1/2 OR x<=-2 -------> A

Case - 2: Considering it -ve Therefore, -x^2 - 3x + x^2 - 2 >=0 Hence, x<=-2/3 -----------> B

Now here the problem I am facing is whether I find the intersection of the ranges or Union of the ranges. Can you please explain this..

Re: 2 sums with Modulus and Inequality both [#permalink]

Show Tags

27 Oct 2010, 23:59

VeritasPrepKarishma wrote:

Solving such equations is very convenient and quick using graphs. I have attached a pdf to show how to solve the first one using graphs. If you understand how it is solved, let me know and I will send the solution of the second one using graphs too. If it is not clear, I will give a quick recap of graph theory for mods.

Attachment:

Graph of Mod Theory.pdf

Also can you provide for a sum where the slope is not equal to 1, just to make it clear.

Note that in this graph, the point of the graph that lies on the x axis will be at x = 4 not x = 8 because mod(2x - 8) = mod(2(x - 4)). Typically, linear mod inequalities can be easily and quickly solved using just the number line but let us keep that for another day! Get comfortable using graphs and later perhaps we can shorten the time taken even further.

Also, these questions are 700 level and you will see them on GMAT only if you are close to 50/51. Even then, you may not see the second question.
_________________

Re: 2 sums with Modulus and Inequality both [#permalink]

Show Tags

27 Jun 2015, 04:25

Hello from the GMAT Club BumpBot!

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.
_________________

Re: 2 sums with Modulus and Inequality both [#permalink]

Show Tags

19 Jul 2017, 04:28

Hello from the GMAT Club BumpBot!

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.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...