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

It is currently 27 Aug 2014, 11:45

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How to STOP searching for values to prove a statement

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 25 Nov 2011
Posts: 261
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 38 [0], given: 20

How to STOP searching for values to prove a statement [#permalink] New post 19 Feb 2012, 05:45
When a statement can't hold good for all set of values, it is easy to find such values (at least in some time).
But, when a statement holds good for all values, how do we prove it? It will take whole life finding values to disprove the statement, unless there is a clear pattern.

So, does GMAT include such kind of questions?
_________________

-------------------------
-Aravind Chembeti

Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4844 [1] , given: 163

Re: How to STOP searching for values to prove a statement [#permalink] New post 20 Feb 2012, 20:46
1
This post received
KUDOS
Expert's post
Chembeti wrote:


On the same post, I have put up a method of handling this question.

if-x-is-positive-which-of-the-following-could-be-correct-71070.html#p1041129

You don't plug in numbers blindly here (or anywhere for that matter). If you try 4 numbers and it works for all 4, how do you know it will also work for the other infinite numbers? So you can do it in one of two ways:
1. Use logic. (As shown in my reply)
2. You find the transition points and then try values on either side. e.g. you see that 1/x = 2x whenx = 1/\sqrt{2}. So x = 1/\sqrt{2} is a transition point. The relation would change around it. On one side of 1/\sqrt{2}, 1/x will be greater. On the other side 2x will be greater.

Try a value less than 1/\sqrt{2} and try one more than 1/\sqrt{2} but less than 1 (because 1 is another transition point).

1/\sqrt{2} = \sqrt{2}/2 = 1.414/2 = .7 apprx. You must try 1/2 and 8/10 (or something similar).
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4844 [1] , given: 163

Re: How to STOP searching for values to prove a statement [#permalink] New post 16 Feb 2013, 20:35
1
This post received
KUDOS
Expert's post
Sachin9 wrote:

So , if we have a inequality, change it with '=' , find the transition point and test using values that are on either side of transition point ..
But what analysis can we make out of the change by pluggin in the nos frm either side of the transition point?


You get the relation between the two expressions in various ranges of values.
To give an example:

To compare two terms e.g. x^2 and 2x, we should focus on the points where they are equal. x^2 = 2x holds when x = 2.
When x < 2, x^2 < 2x
When x > 2, x^2 > 2x
We have two ranges here x < 2 and x > 2. We know the relation between the two expressions in the two ranges.

Similarly 1/x = x^2 when x = 1
When x < 1, 1/x > x^2.
When x > 1, 1/x > x^2

Going on, 1/x = 2x when x = 1/\sqrt{2}
When x < 1/\sqrt{2}, 1/x > 2x
When x > 1/\sqrt{2}, 1/x < 2x


So now you have three ranges in which the relation between the three expressions will be different:
x < 1/\sqrt{2}
1/\sqrt{2} < x < 1
x > 1

If x < 1/\sqrt{2},
1/x > 2x, 1/x > x^2 and x^2 < 2x
So x^2 < 2x < 1/x is possible.

If 1/\sqrt{2} < x < 1
1/x < 2x, 1/x > x^2
So x^2 < 1/x < 2x is possible.

If x > 1
1/x < 2x, 1/x > x^2
So x^2 < 1/x < 2x is possible. (Same as above)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

1 KUDOS received
Manager
Manager
User avatar
Joined: 19 Apr 2009
Posts: 170
Location: San Francisco, California
Followers: 46

Kudos [?]: 169 [1] , given: 1

Re: How to STOP searching for values to prove a statement [#permalink] New post 07 Mar 2013, 15:30
1
This post received
KUDOS
Chembeti,

I will make some general comments about your original question:

Yes, GMAT routinely includes problems, especially in data sufficiency, where the sufficiency can be established without having to resort to using numerical examples. On an official GMAT question if a particular statement is sufficient then 100% of the time there is a clean and logical way to demonstrate that without having to use numbers and examples. It is a different story that you may or may not see that method.

So what do we do in that case. The only option is to try several different numbers(example: negative, positives, very large numbers, numbers between -1 and 1, etc.), if you find the outcome to be a consistent Yes or No then your best bet is to select the statement to be insufficient. You could still be wrong because you did not consider a specific example that could establish insufficiency.

The entire purpose of these types of problems is to differentiate between students who can quickly and cleanly do the problem in a short time versus the ones who would waste a lot of time trying different examples and getting bogged down in computations. This is what makes one problem more difficult than another one.

The example you linked to falls in the category of the hardest GMAT problems. The reason is because students who are trying numbers have to be lucky to be testing numbers between 0.7 and 1 to get this problem right. This is what makes this problem a statistically difficult problem. The students who are comfortable with algebraic manipulation of the inequality would get to the answer quickly.

Cheers,
Dabral
_________________

Free Video Explanations: OFFICIAL GUIDE GMAT 13, 12, 11, 10; QUANT REVIEW 2nd, 1st.

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4844 [0], given: 163

Re: How to STOP searching for values to prove a statement [#permalink] New post 20 Feb 2012, 00:36
Expert's post
Chembeti wrote:
When a statement can't hold good for all set of values, it is easy to find such values (at least in some time).
But, when a statement holds good for all values, how do we prove it? It will take whole life finding values to disprove the statement, unless there is a clear pattern.

So, does GMAT include such kind of questions?


Most GMAT questions can be solved by using logic. You don't need to try 10 different values. Or, one or two obvious values will help.
Also, if you do need to use numbers numbers, you need to try out numbers smartly say, you know numbers behave differently in the following regions: < -1, -1 < x < 0, 0<x< 1 and x > 1, so you try out one number from each range.
If you need to prove something, there will be a pattern. Obviously, GMAT will not give you a question where the only way is to plug in numbers and where you can never be sure. No standard test prep company will give such a question either. If you have a question in mind, let us know. There definitely will be a catch.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 25 Nov 2011
Posts: 261
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 38 [0], given: 20

Re: How to STOP searching for values to prove a statement [#permalink] New post 20 Feb 2012, 01:46
VeritasPrepKarishma wrote:
Chembeti wrote:
When a statement can't hold good for all set of values, it is easy to find such values (at least in some time).
But, when a statement holds good for all values, how do we prove it? It will take whole life finding values to disprove the statement, unless there is a clear pattern.

So, does GMAT include such kind of questions?


Most GMAT questions can be solved by using logic. You don't need to try 10 different values. Or, one or two obvious values will help.
Also, if you do need to use numbers numbers, you need to try out numbers smartly say, you know numbers behave differently in the following regions: < -1, -1 < x < 0, 0<x< 1 and x > 1, so you try out one number from each range.
If you need to prove something, there will be a pattern. Obviously, GMAT will not give you a question where the only way is to plug in numbers and where you can never be sure. No standard test prep company will give such a question either. If you have a question in mind, let us know. There definitely will be a catch.


Thanks for the reply, Karishma.
My problem is selecting smart numbers. I understand ranges: -1<x<0, 0<x<1 and x>1. But these ranges are really very vast. Problem is selecting particular number. For e.g., for a problem, for the range 0<x<1, I selected 0.1 and 0.2 but it did not work. But after seeing replies in the forum, 0.9 worked. So, there seems to be some logic like numbers close to one side of the range work and numbers close to other end do not work. Have we figured out a smart way for this?
_________________

-------------------------
-Aravind Chembeti

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4844 [0], given: 163

Re: How to STOP searching for values to prove a statement [#permalink] New post 20 Feb 2012, 03:50
Expert's post
Chembeti wrote:
VeritasPrepKarishma wrote:
Chembeti wrote:
When a statement can't hold good for all set of values, it is easy to find such values (at least in some time).
But, when a statement holds good for all values, how do we prove it? It will take whole life finding values to disprove the statement, unless there is a clear pattern.

So, does GMAT include such kind of questions?


Most GMAT questions can be solved by using logic. You don't need to try 10 different values. Or, one or two obvious values will help.
Also, if you do need to use numbers numbers, you need to try out numbers smartly say, you know numbers behave differently in the following regions: < -1, -1 < x < 0, 0<x< 1 and x > 1, so you try out one number from each range.
If you need to prove something, there will be a pattern. Obviously, GMAT will not give you a question where the only way is to plug in numbers and where you can never be sure. No standard test prep company will give such a question either. If you have a question in mind, let us know. There definitely will be a catch.


Thanks for the reply, Karishma.
My problem is selecting smart numbers. I understand ranges: -1<x<0, 0<x<1 and x>1. But these ranges are really very vast. Problem is selecting particular number. For e.g., for a problem, for the range 0<x<1, I selected 0.1 and 0.2 but it did not work. But after seeing replies in the forum, 0.9 worked. So, there seems to be some logic like numbers close to one side of the range work and numbers close to other end do not work. Have we figured out a smart way for this?


You need to give the exact question. There would be clues which should make you think of a particular section of a range.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 25 Nov 2011
Posts: 261
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 38 [0], given: 20

Re: How to STOP searching for values to prove a statement [#permalink] New post 20 Feb 2012, 05:36
Karishma,

this is what I am talking about:
if-x-is-positive-which-of-the-following-could-be-correct-71070.html
_________________

-------------------------
-Aravind Chembeti

Director
Director
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 550
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 28 [0], given: 562

GMAT Tests User
Re: How to STOP searching for values to prove a statement [#permalink] New post 16 Feb 2013, 03:56
VeritasPrepKarishma wrote:
Chembeti wrote:


On the same post, I have put up a method of handling this question.

if-x-is-positive-which-of-the-following-could-be-correct-71070.html#p1041129

You don't plug in numbers blindly here (or anywhere for that matter). If you try 4 numbers and it works for all 4, how do you know it will also work for the other infinite numbers? So you can do it in one of two ways:
1. Use logic. (As shown in my reply)
2. You find the transition points and then try values on either side. e.g. you see that 1/x = 2x whenx = 1/\sqrt{2}. So x = 1/\sqrt{2} is a transition point. The relation would change around it. On one side of 1/\sqrt{2}, 1/x will be greater. On the other side 2x will be greater.

Try a value less than 1/\sqrt{2} and try one more than 1/\sqrt{2} but less than 1 (because 1 is another transition point).

1/\sqrt{2} = \sqrt{2}/2 = 1.414/2 = .7 apprx. You must try 1/2 and 8/10 (or something similar).



So , if we have a inequality, change it with '=' , find the transition point and test using values that are on either side of transition point ..
But what analysis can we make out of the change by pluggin in the nos frm either side of the transition point?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Re: How to STOP searching for values to prove a statement   [#permalink] 16 Feb 2013, 03:56
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic how do i prove my efficiency?? mohan514 2 10 Jan 2012, 06:32
How to attack Boldface statements in CR asmit123 1 03 May 2011, 20:31
1 how to search for posts within a topic? jk12 2 09 Jan 2011, 04:57
how to prove this ? ghentu 1 07 Dec 2009, 18:53
Experts publish their posts in the topic How to search for a question ?? mavesum 2 24 Mar 2009, 10:09
Display posts from previous: Sort by

How to STOP searching for values to prove a statement

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.