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

It is currently 21 Oct 2014, 10:52

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

questions including [x]

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 05 Apr 2012
Posts: 5
Followers: 0

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

questions including [x] [#permalink] New post 11 Aug 2012, 06:56
does anyone know what [x] means?

eg: If [x] denotes the greatest integer less than or equal to x, is [x] = 0

I'm having trouble understanding what If [x] denotes the greatest integer less than or equal to x means
Expert Post
Manhattan GMAT Instructor
User avatar
Joined: 05 Jun 2012
Posts: 73
Location: United States
Schools: UCSD (Rady) - Class of 2011
GMAT 1: 760 Q49 V44
GPA: 3.7
WE: Education (Education)
Followers: 194

Kudos [?]: 90 [0], given: 3

Re: questions including [x] [#permalink] New post 11 Aug 2012, 07:56
Expert's post
Well it looks to me like [x] denotes the greatest integer less than or equal to x. :)

("denotes" = "is")

It's a function that the GMAT made up.
_________________

Ryan Jacobs | Manhattan GMAT Instructor | San Francisco

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | View Instructor Profile

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [1] , given: 43

Re: questions including [x] [#permalink] New post 11 Aug 2012, 08:27
1
This post received
KUDOS
rjacobsMGMAT wrote:
Well it looks to me like [x] denotes the greatest integer less than or equal to x. :)

("denotes" = "is")

It's a function that the GMAT made up.


It's not a function made up by GMAT :o)
Carl Friedrich Gauss introduced the square bracket notation [x] for the floor function, which indeed, associates to every x the greatest integer less than or equal to x. Much later, in computer science, Iverson introduced different notations for the floor \lfloor{x}\rfloor (and ceiling \lceil{x}\rceil) function. In mathematics both notations are used.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.


Last edited by EvaJager on 11 Aug 2012, 13:10, edited 2 times in total.
2 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [2] , given: 43

Re: questions including [x] [#permalink] New post 11 Aug 2012, 08:41
2
This post received
KUDOS
Pillah wrote:
does anyone know what [x] means?

eg: If [x] denotes the greatest integer less than or equal to x, is [x] = 0

I'm having trouble understanding what If [x] denotes the greatest integer less than or equal to x means


Every real number can be placed between two consecutive integers, such that k\leq{x}<k+1.
For every given x, the integer kwith the above property is unique. By definition, then [x] = k.
You can always write [x]\leq{x}<[x]+1.
If x=5, [5]=5. If x=5.67, [x]=5.
[0]=0, [0.84]=0, but [-0.34]=-1.

If x is an integer, than [x] is simply x.
For non-integer x, try to visualize the number line. The closest integer to x from the left is [x].
We used to call it the integer part function. For positive numbers, just ignore the decimal part and leave the integer part of the number.
For negative numbers, don't forget to look at the left of your number. [-2.7] = -3 and not -2.

So, if [x] = 0, then certainly 0\leq{x}<1, meaning x can be any number between 0 and 1, 0 inclusive, 1 exclusive.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Expert Post
Manhattan GMAT Instructor
User avatar
Joined: 05 Jun 2012
Posts: 73
Location: United States
Schools: UCSD (Rady) - Class of 2011
GMAT 1: 760 Q49 V44
GPA: 3.7
WE: Education (Education)
Followers: 194

Kudos [?]: 90 [0], given: 3

Re: questions including [x] [#permalink] New post 11 Aug 2012, 20:51
Expert's post
EvaJager wrote:

It's not a function made up by GMAT :o)
Carl Friedrich Gauss introduced the square bracket notation [x] for the floor function, which indeed, associates to every x the greatest integer less than or equal to x. Much later, in computer science, Iverson introduced different notations for the floor \lfloor{x}\rfloor (and ceiling \lceil{x}\rceil) function. In mathematics both notations are used.


HA that's great, I totally didn't know that! I usually teach my students that this is the equivalent of the RoundDown function on Excel, but I think I like this history lesson better :)
_________________

Ryan Jacobs | Manhattan GMAT Instructor | San Francisco

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | View Instructor Profile

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [0], given: 43

Re: questions including [x] [#permalink] New post 11 Aug 2012, 22:10
rjacobsMGMAT wrote:
EvaJager wrote:

It's not a function made up by GMAT :o)
Carl Friedrich Gauss introduced the square bracket notation [x] for the floor function, which indeed, associates to every x the greatest integer less than or equal to x. Much later, in computer science, Iverson introduced different notations for the floor \lfloor{x}\rfloor (and ceiling \lceil{x}\rceil) function. In mathematics both notations are used.


HA that's great, I totally didn't know that! I usually teach my students that this is the equivalent of the RoundDown function on Excel, but I think I like this history lesson better :)


I know this is not the place, but I see I can't send you a PM (personal message) through the site. Thank you for the Kudos, but I think I didn't do much to earn it in this case:o)

BTW, I thoroughly enjoyed your post "Winning ugly on the GMAT", Kudos for it!
I cannot deny Agassi's achievements, but my all times favorites is still Sampras.
Although he never won Roland Garros, he had a superb game at the net, which today's player lack so much.
Definitely, Agassi made the maximum of what he had at hand.
Great message and amazing idea to connect tennis with GMAT!

For those who didn't read the article yet:
http://www.manhattangmat.com/blog/index ... -the-gmat/
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.


Last edited by EvaJager on 12 Aug 2012, 07:19, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23355
Followers: 3604

Kudos [?]: 28717 [0], given: 2820

Re: questions including [x] [#permalink] New post 12 Aug 2012, 06:29
Expert's post
Questions testing this function to practice:
if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html
is-x-an-odd-integer-1-x-2-2x-99856.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html
for-all-z-denotes-the-least-integer-greater-than-or-110561.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1152

Kudos [?]: 5349 [0], given: 165

Re: questions including [x] [#permalink] New post 16 Aug 2012, 22:07
Expert's post
Pillah wrote:
does anyone know what [x] means?

eg: If [x] denotes the greatest integer less than or equal to x, is [x] = 0

I'm having trouble understanding what If [x] denotes the greatest integer less than or equal to x means


When working on Floor or Ceiling functions, a useful technique is to think of the number line.

Say x lies somewhere on the number line. The floor function, often denoted by [x], is the integer closest to x on the left hand side i.e. it is the largest number which is smaller than x (or equal to x if x is an integer). It is easy to comprehend in case of positive numbers. e.g.
[3.4] = 3,
[5.789] = 5 etc
You should be a little more careful while dealing with negative numbers
[-2.45] = -3
This is why the number line perspective helps.
_________________

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

Re: questions including [x]   [#permalink] 16 Aug 2012, 22:07
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic does real GMAT exam include OG questions? imrandesai 1 08 Oct 2014, 07:44
2 Experts publish their posts in the topic Many English adjectives, when included in questions, nishtil 4 04 May 2013, 23:15
DOES PRINCETON INCLUDE EXPERIMENTAL QUESTIONS IN ITS CAT soumyamalani 1 02 Aug 2011, 05:31
Cultural question: Does base salary includes OT? asdert 3 06 Jan 2009, 04:54
Essay Question include or not? Ozmba 5 02 Jan 2007, 09:34
Display posts from previous: Sort by

questions including [x]

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.