GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Jan 2019, 21:02

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 in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Why is this simple inequality not giving stable answers?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
User avatar
B
Joined: 06 Sep 2018
Posts: 37
GMAT 1: 760 Q50 V44
GMAT 2: 740 Q48 V44
Reviews Badge
Why is this simple inequality not giving stable answers?  [#permalink]

Show Tags

New post 27 Sep 2018, 02:10
Hi all! Thanks for your help in advance. This basic question is driving me crazy! Imagine that I have two inequalities,let's call them A and B.

A is (2 < x)
B is (y + 3< x).

My understanding is that if I merge these two inequalities, I am going to get a new inequality C that will yield valid solutions for itself and also the previous two inequalities. My understanding is that to merge A and B, I can only add them up when the signs face the same direction. I did that and got a new inequality C which is

C is (y + 5 < 2x).

Now, if x is 2.5 (which is greater than 2 hence meets inequality A), then substituting 2.5 for x on C gives me y<0 HOWEVER substituting in B gives me y<-0.5. Why? Shouldn't both give me the same?

Thanks a lot.
Director
Director
avatar
V
Joined: 30 Jan 2016
Posts: 883
Location: United States (MA)
Reviews Badge
Why is this simple inequality not giving stable answers?  [#permalink]

Show Tags

New post 27 Sep 2018, 08:56
1
Hi gmat800live,

this is an interesting problem. I might be wrong, but common sense tells me that y should be less than -1 (solved it graphically). Maybe Bunuel could shed some light on this problem? :)
Attachments

xy.jpg
xy.jpg [ 28.7 KiB | Viewed 201 times ]


_________________

Non progredi est regredi

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13331
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Why is this simple inequality not giving stable answers?  [#permalink]

Show Tags

New post 27 Sep 2018, 09:24
1
Hi gmat800live,

In simple terms, the reason why the 'solution' to the two inequalities changes is because you are NOT adding the same value to each side of larger inequality.

Here's a simple example:

0 < X

IF we add 1 to BOTH sides, we have...

(0+1) < (X+1)
1 < X + 1

The solution set for the two inequalities is the SAME because those 2 inequalities are the SAME (once you simplify them).

In your example, you are NOT adding the same value to both sides. You're adding '2' to the 'left side' and 'X' to the 'right side', so you are fundamentally changing the inequality (it's DIFFERENT from the one you started with) - thus, the solution sets will be different.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 669
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Why is this simple inequality not giving stable answers?  [#permalink]

Show Tags

New post 27 Sep 2018, 10:06
1
gmat800live wrote:
Hi all! Thanks for your help in advance. This basic question is driving me crazy! Imagine that I have two inequalities,let's call them A and B.

A is (2 < x)
B is (y + 3< x).

My understanding is that if I merge these two inequalities, I am going to get a new inequality C that will yield valid solutions for itself and also the previous two inequalities. My understanding is that to merge A and B, I can only add them up when the signs face the same direction. I did that and got a new inequality C which is

C is (y + 5 < 2x).

Now, if x is 2.5 (which is greater than 2 hence meets inequality A), then substituting 2.5 for x on C gives me y<0 HOWEVER substituting in B gives me y<-0.5. Why? Shouldn't both give me the same?

Thanks a lot.


If you add together two inequalities that are both true, and the signs are pointing the same way, you'll get a third inequality that's also true.

For example, if x < 10, and y < 3, you can be completely certain that x + y < 13.

The problem you're running into is that it doesn't go the other way. If x + y < 13, that doesn't mean that x < 10 and y < 3. (You can see this by testing numbers, just like you did - x could be 11 and y could be 1, in which case the first of those inequalities is false!)

This is what you're doing in your example, because you're starting with the 'new' inequality you got after doing the addition, and then trying to apply the results you get from it to the 'old' inequalities you added together. That doesn't necessarily work.

In short:

- Adding two correct inequalities together will give you a new, correct inequality
- However, 'splitting up' one correct inequality won't always give you two correct inequalities
_________________

Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!

Intern
Intern
User avatar
B
Joined: 06 Sep 2018
Posts: 37
GMAT 1: 760 Q50 V44
GMAT 2: 740 Q48 V44
Reviews Badge
Why is this simple inequality not giving stable answers?  [#permalink]

Show Tags

New post 28 Sep 2018, 00:34
Thank you so much Akela, EMPOWERgmatRichC and ccooley for looking into this! This has opened some sort of pandora's box :D! I realize that my understanding of some basic concepts is not strong as I thought but I am extremely happy I finally got it! Makes total sense what you guys have said and it has made me think a lot! Final summary is that when I say:

A: 2 < x
B: y + 3 < x

And I add them up to get C: y + 5 < 2x. Then the statement that is true is:

    If you give me values of x and y that satisfy A AND B, I can assure you, that they will also meet C

That's it :). There will then be values that meet for instance C and B, but not A etc! But those shouldn't distract us from the true valid statement above. Gosh... it took me time to get here, but glad it happened. Thanks guys and thank @willteiss for being part of this small discovery :D!
Moderator
avatar
V
Joined: 21 Jun 2014
Posts: 1114
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
GMAT ToolKit User Premium Member
Re: Why is this simple inequality not giving stable answers?  [#permalink]

Show Tags

New post 28 Sep 2018, 01:53
    If you give me values of x and y that satisfy A AND B, I can assure you, that they will also meet C

Yes, this is the right conclusion you drawn. And you will see it used in making of so many DS questions.

When timer is running we tend to forget CHECKING the value of a variable, by putting it into the original inequalities, whether it is VALID.
_________________

---------------------------------------------------------------
Target - 720-740
Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

GMAT Club Bot
Re: Why is this simple inequality not giving stable answers? &nbs [#permalink] 28 Sep 2018, 01:53
Display posts from previous: Sort by

Why is this simple inequality not giving stable answers?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderator: HKD1710



Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.