If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 03 Dec 2016, 03:59
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.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

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

Hide Tags

Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 43

Kudos [?]: 666 [0], given: 723

Premium Member Reviews Badge
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 04 Jan 2013, 01:21
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (02:05) correct 34% (01:25) wrong based on 100 sessions

HideShow timer Statistics

If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8

(2) x < -2


I have tried this Question and got it wrong first time (Wrong approach). But I don't agree with OA.
[Reveal] Spoiler: OA

_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”


Last edited by Bunuel on 04 Jan 2013, 01:54, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35840
Followers: 6828

Kudos [?]: 89699 [0], given: 10381

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 04 Jan 2013, 01:59
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8. The question becomes: is \(x^2 - x - 6\geq{x^2 - 2x - 8}\)? --> is \(x\geq{-2}\)? We don't know that, hence this statement is insufficient.

(2) x < -2. We know noting about g(x). Not sufficient.

(1)+(2) From (1) the question became: is \(x\geq{-2}\)? and (2) answers this question with a NO. Sufficient.

Answer: C.

Hope it's clear.
_________________

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

Manager
Manager
User avatar
Status: Tougher times ...
Joined: 04 Nov 2012
Posts: 51
Location: India
GMAT 1: 480 Q32 V25
WE: General Management (Manufacturing)
Followers: 2

Kudos [?]: 26 [0], given: 44

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 12 May 2013, 07:02
Bunuel wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8. The question becomes: is \(x^2 - x - 6\geq{x^2 - 2x - 8}\)? --> is \(x\geq{-2}\)? We don't know that, hence this statement is insufficient.

(2) x < -2. We know noting about g(x). Not sufficient.

(1)+(2) From (1) the question became: is \(x\geq{-2}\)? and (2) answers this question with a NO. Sufficient.

Answer: C.

Hope it's clear.


hi banuel,

From statement 1 , how you conclude we hace solve for whether x<= -2 ?
_________________

Kabilan.K
Kudos is a boost to participate actively and contribute more to the forum :)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35840
Followers: 6828

Kudos [?]: 89699 [0], given: 10381

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 12 May 2013, 09:55
kabilank87 wrote:
Bunuel wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8. The question becomes: is \(x^2 - x - 6\geq{x^2 - 2x - 8}\)? --> is \(x\geq{-2}\)? We don't know that, hence this statement is insufficient.

(2) x < -2. We know noting about g(x). Not sufficient.

(1)+(2) From (1) the question became: is \(x\geq{-2}\)? and (2) answers this question with a NO. Sufficient.

Answer: C.

Hope it's clear.


hi banuel,

From statement 1 , how you conclude we hace solve for whether x<= -2 ?


\(x^2 - x - 6\geq{x^2 - 2x - 8}\)
Cancel x^2 on both sides and re-arrange \(- x +2x\geq{ - 8+6}\) -->\(x\geq{-2}\).

Hope it's clear.
_________________

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
MBA Admissions Consultant
User avatar
Joined: 26 Jan 2013
Posts: 182
Schools: Stanford '19
GMAT 1: 770 Q51 V44
Followers: 7

Kudos [?]: 17 [0], given: 3

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 12 May 2013, 10:33
Question: \(f(x) = x^2 - x - 6\). Is \(f(x) >= g(x)\)?

1) \(g(x) = x^2 - 2x - 8\)
2) \(x < - 2\)

Consider statement (1):

For \(f(x)\) to be greater than or equal to \(g(x)\), \(x^2-x-6\) should be greater than or equal to \(x^2-2x-8\). This implies that: \(x^2-x-6>=x^2-2x-8\) (or)
\(x>=-2\).

We don't know for sure that this is true. So this is not sufficient.

Consider statement (2):

\(x < -2\). However, we know nothing about the form of the function \(g(x)\). So this is not sufficient, either.

Consider both together:

If \(g(x)\) is given by the function in option (1), then we require \(x>=-2\) in order for \(f(x)\) to be greater than or equal to \(g(x)\). From (2) we know that \(x < -2\). Therefore, both statements together are sufficient to prove that \(f(x)\) is NOT greater than or equal to \(g(x)\).

The correct answer, therefore, is C.
_________________

Karthik P.
Founder and CEO,
August Academy.

http://www.mbaadmissions.augustacademy.in

Schedule a free consultation with us.

Click here to view GMATclub verified student testimonials.

Click here to view all our student testimonials.


If you like this post - please give us kudos :) Thanks much!

Intern
Intern
avatar
Joined: 12 May 2013
Posts: 1
Followers: 0

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

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 12 May 2013, 22:42
mridulparashar1 wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8

(2) x < -2


I have tried this Question and got it wrong first time (Wrong approach). But I don't agree with OA.

How to answer it??
where are the options??
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35840
Followers: 6828

Kudos [?]: 89699 [0], given: 10381

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 13 May 2013, 02:14
shankg06 wrote:
mridulparashar1 wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8

(2) x < -2


I have tried this Question and got it wrong first time (Wrong approach). But I don't agree with OA.

How to answer it??
where are the options??


This is a data sufficiency question.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope it's clear.
_________________

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

Intern
Intern
User avatar
Joined: 05 Mar 2013
Posts: 45
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Followers: 1

Kudos [?]: 49 [0], given: 14

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 14 May 2013, 01:13
Bunuel wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8. The question becomes: is \(x^2 - x - 6\geq{x^2 - 2x - 8}\)? --> is \(x\geq{-2}\)? We don't know that, hence this statement is insufficient.

(2) x < -2. We know noting about g(x). Not sufficient.

(1)+(2) From (1) the question became: is \(x\geq{-2}\)? and (2) answers this question with a NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel.. I understood Your solution but I have a doubt.

\(x^2 -x -6 = (x-3)*(x+2)\)
\(x^2-2x - 8 = (x-4)*(x+2)\)

now the question becomes is \((x-3)*(x+2) >= (x-4)*(x+2)\)

if x is not equal to -2 then it will become is x-3 > x-4 so YES
if x is equal to -2 then both the sides are equal so YES

So isn't A sufficient ??
_________________

"Kudos" will help me a lot!!!!!!Please donate some!!!

Completed
Official Quant Review
OG - Quant


In Progress
Official Verbal Review
OG 13th ed
MGMAT IR
AWA Structure

Yet to do
100 700+ SC questions
MR Verbal
MR Quant


Verbal is a ghost. Cant find head and tail of it.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35840
Followers: 6828

Kudos [?]: 89699 [0], given: 10381

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 15 May 2013, 01:44
SrinathVangala wrote:
Bunuel wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8. The question becomes: is \(x^2 - x - 6\geq{x^2 - 2x - 8}\)? --> is \(x\geq{-2}\)? We don't know that, hence this statement is insufficient.

(2) x < -2. We know noting about g(x). Not sufficient.

(1)+(2) From (1) the question became: is \(x\geq{-2}\)? and (2) answers this question with a NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel.. I understood Your solution but I have a doubt.

\(x^2 -x -6 = (x-3)*(x+2)\)
\(x^2-2x - 8 = (x-4)*(x+2)\)

now the question becomes is \((x-3)*(x+2) >= (x-4)*(x+2)\)

if x is not equal to -2 then it will become is x-3 > x-4 so YES
if x is equal to -2 then both the sides are equal so YES

So isn't A sufficient ??


The red part is not correct.

If x is not equal to -2, then x+2 could be more (for example, if x=0) as well as less than zero (for example if x=-3).

If x+2 is less than zero, then when reducing \((x-3)*(x+2)\geq{ (x-4)*(x+2)}\) by negative x+2 we should flip the sign and we'll get \(x-3\leq{{x-4}\) --> so the answer is NO.

Hope it's clear.
_________________

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

Intern
Intern
User avatar
Joined: 05 Mar 2013
Posts: 45
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Followers: 1

Kudos [?]: 49 [0], given: 14

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 15 May 2013, 02:06
Bunuel wrote:
SrinathVangala wrote:
Bunuel wrote:
If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

(1) g(x) = x^2 - 2x - 8. The question becomes: is \(x^2 - x - 6\geq{x^2 - 2x - 8}\)? --> is \(x\geq{-2}\)? We don't know that, hence this statement is insufficient.

(2) x < -2. We know noting about g(x). Not sufficient.

(1)+(2) From (1) the question became: is \(x\geq{-2}\)? and (2) answers this question with a NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel.. I understood Your solution but I have a doubt.

\(x^2 -x -6 = (x-3)*(x+2)\)
\(x^2-2x - 8 = (x-4)*(x+2)\)

now the question becomes is \((x-3)*(x+2) >= (x-4)*(x+2)\)

if x is not equal to -2 then it will become is x-3 > x-4 so YES
if x is equal to -2 then both the sides are equal so YES

So isn't A sufficient ??


The red part is not correct.

If x is not equal to -2, then x+2 could be more (for example, if x=0) as well as less than zero (for example if x=-3).

If x+2 is less than zero, then when reducing \((x-3)*(x+2)\geq{ (x-4)*(x+2)}\) by negative x+2 we should flip the sign and we'll get \(x-3\leq{{x-4}\) --> so the answer is NO.

Hope it's clear.



Yes!!!!!!! Awesome!!!! I didn't take into account that we cannot cancel negative numbers on the both sides of a inequality without changing the sign.

All I was thinking about was to avoid the condition where x = -2 so that we cancel the terms.

Thanks a lot!!!! Will remember this!!!!
_________________

"Kudos" will help me a lot!!!!!!Please donate some!!!

Completed
Official Quant Review
OG - Quant


In Progress
Official Verbal Review
OG 13th ed
MGMAT IR
AWA Structure

Yet to do
100 700+ SC questions
MR Verbal
MR Quant


Verbal is a ghost. Cant find head and tail of it.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12851
Followers: 559

Kudos [?]: 157 [0], given: 0

Premium Member
Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)? [#permalink]

Show Tags

New post 30 Aug 2016, 16:01
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

Re: If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?   [#permalink] 30 Aug 2016, 16:01
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If x>0, does f(x^2)=f(x)^2? Bunuel 5 07 Mar 2016, 02:25
5 Experts publish their posts in the topic Is f(x) > 0? Bunuel 10 21 Jan 2015, 01:50
7 what is the greatest possible value of the function f(x)? venkateshreddy 5 07 Apr 2014, 02:47
Experts publish their posts in the topic If f(x) = 2^x + 2^-2, and x is an integer gmatbull 3 06 Dec 2012, 04:07
11 Experts publish their posts in the topic What is the minimal value of function f(x)? manalq8 7 25 Nov 2011, 14:24
Display posts from previous: Sort by

If f(x) = x^2 - x - 6, is f(x) ≥ g(x)?

  new topic 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®.