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:

which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?

Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;

C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Re: which of the following inequalities has a solution that [#permalink]

Show Tags

11 Jun 2011, 21:36

It is good question, It was obvious that A,B , C are incorrect as these are exponent of X but I couldn't figure out which one between d & e is better, so attempted D on GMAT Prep test Later, During review of the question I found that X was actually |X| - absolute value , Hence two lines, So correct is E

Re: Which of the following inequalities has a solution set, when [#permalink]

Show Tags

21 Oct 2013, 08:03

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: Which of the following inequalities has a solution set, when [#permalink]

Show Tags

13 Jul 2014, 07:34

Bunuel wrote:

anilnandyala wrote:

which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?

Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range; C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.

Hi Bunuel, for option B, why isn't it a finite range?

which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?

Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range; C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.

Hi Bunuel, for option B, why isn't it a finite range?

Which of the following inequalities has a solution set, when [#permalink]

Show Tags

18 Feb 2015, 04:35

Bunuel wrote:

anilnandyala wrote:

which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?

Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;

C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.

Could someone explain Option A in detail? I understand upon taking 4th root on both sides it becomes: x>= +-1 But, I don't understand how it gets simplified further as its been explained as: x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\)

which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?

Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;

C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.

Could someone explain Option A in detail? I understand upon taking 4th root on both sides it becomes: x>= +-1 But, I don't understand how it gets simplified further as its been explained as: x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\)

x >= +/- 1 does not make any sense.

When taking 4th root from both sides we'll get \(|x| \geq{1}\), which is the same as \(x\leq{-1}\) or \(x\geq{1}\).

Re: Which of the following inequalities has a solution set, when [#permalink]

Show Tags

18 Jun 2016, 13:47

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.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...