It is currently 17 Oct 2017, 21:19

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

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Inequalities practice

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 08 Jan 2009
Posts: 326

Kudos [?]: 176 [0], given: 5

Inequalities practice [#permalink]

Show Tags

New post 21 Feb 2009, 20:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What are the values of X that satisfy the inequality x+1/x < 2.5?

Ans :
1/2 < x < 2 .

But i felt x can also be any negative value.

Explain please.

Kudos [?]: 176 [0], given: 5

Senior Manager
Senior Manager
avatar
Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 360 [0], given: 15

Schools: Fuqua
Re: Inequalities practice [#permalink]

Show Tags

New post 21 Feb 2009, 20:49
tkarthi4u,

Please go thru this link. Hope you will get some information on how to solve the Quadratic Inequalities.

http://www.purplemath.com/modules/ineqquad.htm

Kudos [?]: 360 [0], given: 15

Intern
Intern
avatar
Joined: 10 Mar 2009
Posts: 3

Kudos [?]: 1 [0], given: 0

Re: Inequalities practice [#permalink]

Show Tags

New post 10 Mar 2009, 10:49
Hey mrsmarthi, i went through the link given for quad. eqns. It was of tremendous help.Thanks !!
I am posting my solution to the problem in this post using that method. Can you ( or anyone else perhaps) review it and tell me if it is indeed, the right way to go.

SOLUTION :
Since x+1/x<2.5,
I consider x+1/x-2.5<0 and further, i break it down to x+1/x-2.5 = y and y<0.

Now I solve the quadratic eqn considering y=0 i.e. x+1/x-2.5=0 and get the solution, (x-2)*(x-.5)=0.
Thus, on the number line, I plot the points .5 and 2 on the x -axis. We now have three regions on the x axis, which are
x>2, .5<x<2 and x<.5.

Now, for the main equation, we need to see y<0 lies in which of the three regions.
x+1/x-2.5 =0 can be written as x^2-2.5x+1=0. We can find the vertex of the parabola using the formula, v=(-b/2a,c-b^2/4a).
Which gives us v below the x -axis between .5 and 2 and .5 and 2 are the x-intercepts of the parabola.

Thus, between .5 and 2, the parabola x+1/x-2.5 or simply y is less than zero. :help2

Kudos [?]: 1 [0], given: 0

SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1545

Kudos [?]: 178 [0], given: 2

Re: Inequalities practice [#permalink]

Show Tags

New post 10 Mar 2009, 17:19
Can I ask a question on this :

x+1/x < 2.5 can be rewritten as 1+1/x < 2.5 --> 1/x <1.5 --> x>2/3

where did i go wrong ?

Kudos [?]: 178 [0], given: 2

Senior Manager
Senior Manager
avatar
Joined: 30 Nov 2008
Posts: 485

Kudos [?]: 360 [0], given: 15

Schools: Fuqua
Re: Inequalities practice [#permalink]

Show Tags

New post 11 Mar 2009, 07:31
One VERY VERY IMP thing to remember in Inequalities -

DO NOT multiple,divide variable on both sides of the Inequality.(The reason being we don't know the sign of x and depending ont he sign, the inequality will change. )

How ever we can add / subtract a variable on both sides of the Inequality.

pmenon wrote:
Can I ask a question on this :

x+1/x < 2.5 can be rewritten as 1+1/x < 2.5 --> 1/x <1.5 --> x>2/3

where did i go wrong ?


Hilighted part is incorrect. It should translate to --> x + 1/x <2.3 ==> (x^2 + 1) / x < 2.5.

Hope you got the mistake.

Kudos [?]: 360 [0], given: 15

Re: Inequalities practice   [#permalink] 11 Mar 2009, 07:31
Display posts from previous: Sort by

Inequalities practice

  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 | Emoji artwork provided by EmojiOne

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®.