Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Aug 2016, 01:45
GMAT Club Tests

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Which of the following inequalities has a solution set, when graphed

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
avatar
Joined: 01 Aug 2008
Posts: 769
Followers: 4

Kudos [?]: 512 [0], given: 99

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

Show Tags

New post 02 Mar 2009, 20:47
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (02:24) correct 31% (01:05) wrong based on 185 sessions

HideShow timer Statistics

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

A. x^4 >= 1
B. x^3 <= 27
C. x^2 >= 16
D. 2 <= |x| <= 5
E. 2 <= 3x+4 <= 6

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-inequalities-has-a-solution-set-that-127820.html
[Reveal] Spoiler: OA
Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 500

Kudos [?]: 3060 [1] , given: 360

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

Show Tags

New post 03 Mar 2009, 03:34
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
E

1. Any expressions that contains only x in the form of |x|, x^2, x^4, x^2n are insensitive to sign of x (A,C,D in our case). Therefore, zero must satisfy such expressions, otherwise we will have at least one hole near zero and two segments. So, check x=0 for all three options. None of them fits requirement. So, A,C,D are out and B, E remain.

2. in B x=-inf satisfy the expression, so it doesn't represent finite segments.

3. Only E remains. 3x + 4 is a line cut in points x=2, and x=6 --> a finite segment.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Director
avatar
Joined: 01 Aug 2008
Posts: 769
Followers: 4

Kudos [?]: 512 [0], given: 99

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

Show Tags

New post 03 Mar 2009, 09:02
walker,
Amazing explanation. I did follow the same way what you explained about A, C, D but I chose B and didn't realize it can satisfy infinite also ...

now it is clear to me.

(+1) kudos to you walker.

Thank you.

Last edited by ugimba on 03 Mar 2009, 09:11, edited 1 time in total.
Director
Director
avatar
Joined: 01 Aug 2008
Posts: 769
Followers: 4

Kudos [?]: 512 [0], given: 99

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

Show Tags

New post 03 Mar 2009, 09:06
and one more question, I made 9 mistakes in quant when I write gmatprep and still end up making 50. When I retook the exam and made just 3 mistakes only and still made 50. why it happend? it is huge range for 50 then ( from 9 mistakes to 3 mistakes in my observation)? so to get 51, there should be no wrongs at all? have to make 37 out 37 corrects..?
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 500

Kudos [?]: 3060 [0], given: 360

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

Show Tags

New post 03 Mar 2009, 17:19
ugimba wrote:
and one more question, I made 9 mistakes in quant when I write gmatprep and still end up making 50. When I retook the exam and made just 3 mistakes only and still made 50. why it happend? it is huge range for 50 then ( from 9 mistakes to 3 mistakes in my observation)? so to get 51, there should be no wrongs at all? have to make 37 out 37 corrects..?


A few mistakes (I had 4 mistakes in my prep and 51) at the end of the test still give you chance to get 51.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Manager
Manager
User avatar
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Followers: 1

Kudos [?]: 48 [0], given: 2

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

Show Tags

New post 04 Mar 2009, 12:51
walker wrote:
E

1. Any expressions that contains only x in the form of |x|, x^2, x^4, x^2n are insensitive to sign of x (A,C,D in our case). Therefore, zero must satisfy such expressions, otherwise we will have at least one hole near zero and two segments. So, check x=0 for all three options. None of them fits requirement. So, A,C,D are out and B, E remain.

2. in B x=-inf satisfy the expression, so it doesn't represent finite segments.

3. Only E remains. 3x + 4 is a line cut in points x=2, and x=6 --> a finite segment.


Hi Walker, could you please explain two things (sorry if they are too naive):

How do you check if "inf" satisfies an expression?

How did you figure out the cut points for 3x+4 ?

Thanks
_________________

kris

Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 500

Kudos [?]: 3060 [0], given: 360

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

Show Tags

New post 04 Mar 2009, 13:23
krishan wrote:
How do you check if "inf" satisfies an expression?


There is a nice concept: when x=inf (or x=-inf) there is no need to calculate complex expression.
For example, y=-8x^8 + x^6 +30 x^3 +4x +2000
at x=inf (or a very huge number) we choose only the biggest power and omit all constants.
So, our complex expression becomes a simple one: y = -x^8 and at x=-inf, y=-inf.
And again, think about inf as a huge number, let's say 1000000000000000

krishan wrote:
How did you figure out the cut points for 3x+4 ?

y=3x+4 is a line. Just draw any line and cut it by two y=a and y=b lines (a,b - any numbers), you will get a segment.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Manager
Manager
User avatar
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Followers: 1

Kudos [?]: 48 [0], given: 2

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

Show Tags

New post 04 Mar 2009, 14:00
thanks a lot Walker..
_________________

kris

Manager
Manager
avatar
Joined: 07 Feb 2010
Posts: 159
Followers: 2

Kudos [?]: 445 [0], given: 101

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

Show Tags

New post 02 Nov 2010, 06:38
which of the following inequalities have a solution set that , when a graphed on the number line is a single line segment of finate length

a x^4 >= 1
b x^3 <= 27
c x^2 >= 16
d 2 <= mod(x) <= 15
e 2 <= 3x+4 <= 6
Manager
Manager
avatar
Joined: 06 Aug 2010
Posts: 225
Location: Boston
Followers: 2

Kudos [?]: 159 [0], given: 5

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

Show Tags

New post 02 Nov 2010, 06:45
anilnandyala wrote:
which of the following inequalities have a solution set that , when a graphed on the number line is a single line segment of finate length

a x^4 >= 1
b x^3 <= 27
c x^2 >= 16
d 2 <= mod(x) <= 15
e 2 <= 3x+4 <= 6


E. You can easily eliminate the other four options:

A) This is true for any value of x such that \(x \leq -1\) or \(x \geq 1\) - two line segments of infinite length.
B) This is true for all \(x \leq 3\) - infinite length.
C) Like (A), this is true for all \(x \leq -4\) or \(x \geq 4\).
D) True for \(-15 \leq x \leq -2\) or \(2 \leq x \leq 15\).
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11091
Followers: 511

Kudos [?]: 134 [0], given: 0

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

Show Tags

New post 19 Mar 2016, 14:40
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34449
Followers: 6274

Kudos [?]: 79607 [0], given: 10022

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

Show Tags

New post 20 Mar 2016, 02:12
Expert's post
5
This post was
BOOKMARKED
ugimba wrote:
Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

A. x^4 >= 1
B. x^3 <= 27
C. x^2 >= 16
D. 2 <= |x| <= 5
E. 2 <= 3x+4 <= 6

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-inequalities-has-a-solution-set-that-127820.html


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.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34449
Followers: 6274

Kudos [?]: 79607 [0], given: 10022

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

Show Tags

New post 20 Mar 2016, 02:14
Bunuel wrote:
ugimba wrote:
Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?

A. x^4 >= 1
B. x^3 <= 27
C. x^2 >= 16
D. 2 <= |x| <= 5
E. 2 <= 3x+4 <= 6

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-inequalities-has-a-solution-set-that-127820.html


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.


OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-inequalities-has-a-solution-set-that-127820.html

SIMILAR QUESTION TO PRACTICE: which-of-the-following-inequalities-has-a-solution-set-that-130666.html

_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: Which of the following inequalities has a solution set, when graphed   [#permalink] 20 Mar 2016, 02:14
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic Which of the following inequalities have their solutions represented Nevernevergiveup 2 15 Mar 2016, 00:55
24 Experts publish their posts in the topic Which of the following inequalities has a solution set that rpamecha 8 14 Apr 2012, 06:43
28 Experts publish their posts in the topic Which of the following inequalities has a solution set that dvinoth86 11 19 Feb 2012, 20:57
24 Experts publish their posts in the topic Which of the following inequalities has a solution set, when anilnandyala 11 03 Jan 2011, 07:06
4 Experts publish their posts in the topic Which of the following inequalities has a solution set that, brokerbevo 9 18 Aug 2008, 13:21
Display posts from previous: Sort by

Which of the following inequalities has a solution set, when graphed

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.