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

 It is currently 25 Apr 2015, 08:26

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# |y| > |y+1|

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Manager
Joined: 02 Nov 2008
Posts: 60
Followers: 1

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

|y| > |y+1| [#permalink]  27 Nov 2008, 11:31
Could somebody help me in coming up with solutions of this ineq

IyI > Iy+1I

Please explain as well. Thx
SVP
Joined: 29 Aug 2007
Posts: 2497
Followers: 57

Kudos [?]: 554 [0], given: 19

Re: absolute ineq [#permalink]  27 Nov 2008, 12:08
HG wrote:
Could somebody help me in coming up with solutions of this ineq

IyI > Iy+1I

Please explain as well. Thx

modulas or absolute value always have two possibilities: +ve and -ve.

1. if y is +ve, y > y+1 but this is not possible. a +ve value added to 1 cannot be less than that +ve value.

2: -y > y+1
-y - y > 1
-2y > 1
y < -1/2

so y should be smaller than -1/2.
_________________
VP
Joined: 09 Jan 2007
Posts: 1045
Location: New York, NY
Schools: Chicago Booth Class of 2010
Followers: 10

Kudos [?]: 157 [0], given: 3

Re: absolute ineq [#permalink]  27 Nov 2008, 12:17
HG wrote:
Could somebody help me in coming up with solutions of this ineq

IyI > Iy+1I

Please explain as well. Thx

Call:
f1(x) = | y | and f2(x) = | y+1 |
We are looking for when f1(x) > f2(x), hence, either y>y+1 or -y>y+1. As the first is impossible, from the second you can get that for y<-1/2.

Visually you would have something as bellow. Sorry to change the axis, I'm lazy right now.

Please some skilled moderator change this topic for the GMAT Q Section.
Attachments

Untitled1.png [ 25.38 KiB | Viewed 1075 times ]

_________________

Rhyme´s guide to interviewing
http://www.gmatclub.com/forum/t55030

Kwam's Profile
111-t57360

Manager
Joined: 02 Nov 2008
Posts: 60
Followers: 1

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

Re: absolute ineq [#permalink]  27 Nov 2008, 13:39
GMATIGER

How come you didn't take - ve sign for the other side meaning

- y > - (y+1)
- y > -y -1 = No solution
SVP
Joined: 29 Aug 2007
Posts: 2497
Followers: 57

Kudos [?]: 554 [0], given: 19

Re: absolute ineq [#permalink]  27 Nov 2008, 18:07
HG wrote:
GMATIGER

How come you didn't take - ve sign for the other side meaning

- y > - (y+1)
- y > -y -1 = No solution

If you multiply both sides by -ve, then it would be same as the +ve y. so change only one side.

Alternatively: If y is negative, square both sides:
y^2 > y^2 + 2y +1
y < -1/2
_________________
SVP
Joined: 17 Jun 2008
Posts: 1573
Followers: 12

Kudos [?]: 202 [0], given: 0

Re: absolute ineq [#permalink]  28 Nov 2008, 03:34
Looking at the inequality itself suggests that y < 0.

Now, if y < 0, the left side will be -y.

For right side, if -1<y<0, then, -y > y+1
or, 2y < -1 or, y < -1/2
Hence, in this case, solution is -1 < y < -1/2

Case2: if, y < -1, then, -y > -(y +1)
or, y < y + 1 and this is true for any value of y (whether y is positive or negative).
Hence, the solution in this case is, y < -1.

Combining 1 and 2, y < -1/2
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
Followers: 2

Kudos [?]: 75 [1] , given: 40

Re: absolute ineq [#permalink]  28 Nov 2008, 06:29
1
This post received
KUDOS
HG wrote:
Could somebody help me in coming up with solutions of this ineq

IyI > Iy+1I

Please explain as well. Thx

http://www.youtube.com/watch?v=D-evkyl2Wj8
Because IyI > Iy+1I >0 so
IyI^2>Iy+1I^2
=> y^2>y^2+2y+1
=> 0>2y+1
=> y<-1/2

http://www.youtube.com/watch?v=HC2nl-d5tDY
Re: absolute ineq   [#permalink] 28 Nov 2008, 06:29
Similar topics Replies Last post
Similar
Topics:
2 Inequality |y|>|y+1| 4 10 Sep 2013, 22:22
1 If y≠0 and y≠-1, is x/y > x/(y+1)? 8 24 Feb 2011, 12:50
1 Is X>Y? 1. x=y+2 2. x/2=y-1 8 09 Aug 2008, 19:10
Is X>Y ? 1. X=Y+2 2. X/2 = Y-1 2 03 Feb 2008, 11:34
Is x-y+1>x+y-1 1- x>0 2- y<0 3 08 Nov 2005, 14:50
Display posts from previous: Sort by

# |y| > |y+1|

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.