NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 05:02 It is currently 25 Apr 2024, 05:02
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Compound Inequalities problems

User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [0]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Compound Inequalities problems [#permalink] New post   12 May 2014, 07:10
Concept: Compound inequalities
Question: 5! + 3 < a < 5! + 8
a) 3 < a < 8
b) 0 < a < 5
c) 3 < a- 5! < 8



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [0]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Re: Compound Inequalities problems [#permalink] New post   13 May 2014, 03:26
nehasingh1020 wrote:
Concept: Compound inequalities
Question: 5! + 3 < a < 5! + 8
a) 3 < a < 8
b) 0 < a < 5
c) 3 < a- 5! < 8



ANSWER

3 < a-5! < 8


Don’t make the mistake of subtracting 5! From only first and last term and chosing option (a) as answer. Subtract 5! From all 3 terms, so

5! + 3 < a < 5! + 8
Subtracting 5! From all 3 terms

3! < a- 5! < 8

Mantra: For compound inequalities (inequalities with more than one inequality sign) , perform operations on all terms together, not on first and last term alone.
User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [0]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Re: Compound Inequalities problems [#permalink] New post   14 May 2014, 05:07
Concept: Inequality signs
Question: Is ab < 0 if ac > 0 and bc < 0 ?
a) Yes
b) No
c) Can’t be determined
User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [0]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Re: Compound Inequalities problems [#permalink] New post   15 May 2014, 03:56
nehasingh1020 wrote:
Concept: Inequality signs
Question: Is ab < 0 if ac > 0 and bc < 0 ?
a) Yes
b) No
c) Can’t be determined


Answer

Answer: Yes


Since, ac > 0, both a and c are of same sign (both are positive or both are negative). Similarly bc < 0 implies b and c are of opposite signs. Combining both informations, we know now that b and a are of opposite signs. Multiplying these 2 numbers with opposite signs will yield a negative number, so ab < 0

Mantra: If x and y are of opposite signs , xy < 0 ; if x and y are of same signs then xy > 0
User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [1]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Re: Compound Inequalities problems [#permalink] New post   16 May 2014, 06:10
1
Kudos
Concept: Factors
Question: Which of the following are the roots of y^3 – y = 0 ?
a) 1
b) 0
c) -1
avatar
georgenelson
Intern
Intern
Joined: 15 May 2014
Posts: 12
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: Compound Inequalities problems [#permalink] New post   16 May 2014, 06:18
Great I think this will be good experience to practice.
User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [0]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Re: Compound Inequalities problems [#permalink] New post   17 May 2014, 02:04
georgenelson wrote:
Great I think this will be good experience to practice.


Sure George. You can also try out the GMAT diagnostic tool to get more questions: https://goo.gl/LT72yk

All the best!!
User avatar
P
GeneralEducation
VP
VP
Joined: 12 May 2010
Status:Assisting candidates to get admit in to top global business schools
Affiliations: MBA
Posts: 1313
Own Kudos [?]: 204 [0]
Given Kudos: 8
Location: Bangalore
Schools:HEC, Paris
WE 1: 9 Years
Send PM
Re: Compound Inequalities problems [#permalink] New post   17 May 2014, 02:05
nehasingh1020 wrote:
Concept: Factors
Question: Which of the following are the roots of y^3 – y = 0 ?
a) 1
b) 0
c) -1


Answer: All three

y^3 – y = 0
=> y (y^2 – 1) = 0 ( don’t divide both sides by y and conclude y^2 = 1 i.e y = 1, -1 only, this is wrong)
=> y (y-1) (y + 1) = 0
=> y = 0 , 1 , -1



Mantra: Don’t divide a variable on both sides of equation until you are sure that given variable is not equal to 0.
User avatar
rajatjain14
Intern
Intern
Joined: 20 May 2014
Posts: 28
Own Kudos [?]: 71 [0]
Given Kudos: 16
Location: India
Schools: IIMC
GMAT 1: 700 Q51 V32
Send PM
Re: Compound Inequalities problems [#permalink] New post   22 May 2014, 09:22
Thanks Neha for interesting set of questions.
I would like to specify an approach for solving cubic equations.

Approach to solve cubic equations:

1. Go for hit and trial (Eg 0,-1,1,2,etc) to find the first root.
2. Then divide the complete equation by this factor.
3. Solve the remaining equation (possibly a quadratic equation) to find the remaining roots.

Example

\(x^3 - 6x^2 + 11x - 6 = 0\)
Using Hit and trial, we get \(x=1\) as the root.

So, we get, \((x-1) (x^2 -5x + 6) =0\)

Solving \(x^2 -5x + 6 = 0\),

we get 2, 3 as the roots

Answer: \(x\)= 1, 2 and 3



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Compound Inequalities problems [#permalink]
22 May 2014, 09:22
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions