It is currently 19 Feb 2018, 21:28

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Inequality Question.

Author Message
Intern
Joined: 05 Apr 2011
Posts: 10

Show Tags

10 Apr 2011, 19:53
2
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

50% (03:04) correct 50% (04:13) wrong based on 2 sessions

HideShow timer Statistics

Find the range of values for which:

x+1/|2-x|+x+1/x-5<=0
[Reveal] Spoiler: OA
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 863

Show Tags

10 Apr 2011, 20:23
Can you pls post all the options. After a lengthy algebra I got the range 3.5<=x<5

Posted from my mobile device
Intern
Joined: 05 Apr 2011
Posts: 10

Show Tags

10 Apr 2011, 20:40
QA (negative infinity,-1]U[7/2,5)
Retired Moderator
Joined: 02 Sep 2010
Posts: 792
Location: London

Show Tags

10 Apr 2011, 22:55
1
KUDOS
$$(x+1)*(\frac{1}{|2-x|}+\frac{1}{x-5}) <= 0$$

For this to be true, either the first term is positive and the second negative or vice versa

Case 1 : x+1 >=0 ... x>=-1

$$\frac{1}{|2-x|}+\frac{1}{x-5} <= 0$$
$$\frac{1}{|2-x|}<=\frac{1}{5-x}$$

Note that since |2-x| is always positive, to have 1/(5-x) greater than 1/(|2-x|), it also has to be always positive. which means x<5.

If 2-x>=0 OR x<=2, then this implies 5-x<=2-x , which is impossible

So 2-x<=0 OR x>=0, in which case we get :
5-x<=-(2-x) OR x>=7/2

So we get the range [7/2,5)

Case 2 : x+1 <=0 OR x<=-1

Hence $$\frac{1}{|2-x|}>=\frac{1}{5-x}$$
Since |2-x| is always positive all we need to ensure is that 5-x is a smaller number than |2-x|

5-x >= |2-x|

If 2-x >=0 , i.e, x<=2
then all values of x satisfy
5-x >= 2-x OR 5>=2

If 2-x <0 , its impossible since we already know x<=-1

Hence all numbers in range satisfy (-infinity, -1]

(-infinity,-1] U [7/2,5)
_________________
TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1589
Location: United States (IN)
Concentration: Strategy, Technology

Show Tags

11 Apr 2011, 00:32
Hi shrouded1

Could you please explain this bit :

If 2-x>=0 OR x<=2, then this implies 5-x<=2-x

Regards,
Subhash
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Retired Moderator
Joined: 02 Sep 2010
Posts: 792
Location: London

Show Tags

11 Apr 2011, 13:05
I am trying to solve an inequality in which one of the sides is an absolute value. In such a case, you have to assume two cases, first that the expression inside the absolute value is positive and then that it is negative. So this is simply the first of those two cases.

After taking the case, we remove the absolute value and try to solve the inequality (which in this case, is converted from an 1/Expression form to an Expression form easily since we know both sides are now positive)
_________________
Intern
Joined: 01 Apr 2010
Posts: 4

Show Tags

15 Apr 2011, 01:21
If 2-x>=0 OR x<=2, then this implies 5-x<=2-x

Thanks
Intern
Joined: 05 Apr 2011
Posts: 10

Show Tags

17 Apr 2011, 19:03
Thank you so much, Shrouded 1.

However could anyone tell me whether there are any shortcuts for this inequality?

It takes me too long to solve it. I would like to know how is it possible to solve this inequality within 2 minutes.

Steve.
Intern
Joined: 05 Apr 2011
Posts: 10

Show Tags

15 May 2011, 17:01
Also,

I would like to know what types of inequalities are there on the test.

Thank you,
Steven.
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1260

Show Tags

15 May 2011, 23:16
good question indeed.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Intern
Joined: 05 Apr 2011
Posts: 10

Show Tags

17 May 2011, 17:06
Thank you,
Amit.

Would anyone be able to elaborate on it?

Thank you so much,
Steve.
Re: Inequality Question.   [#permalink] 17 May 2011, 17:06
Display posts from previous: Sort by