November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50715

For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
18 Feb 2014, 02:38
Question Stats:
68% (01:45) correct 32% (01:46) wrong based on 929 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionFor all z, [z] denotes the least integer greater than or equal to z. Is [x] = 0 ? (1) 1< x < 0.1 (2) [x + 0.5] = 1 Data Sufficiency Question: 96 Category: Algebra Operations with real numbers Page: 160 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 50715

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
18 Feb 2014, 02:38




Manager
Joined: 20 Dec 2013
Posts: 234
Location: India

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
18 Feb 2014, 03:07
Option A.
From S1:x=any value greater than 1 but less than 0.1.For every value of x, [x]=0 only.Sufficient.
From S2:x=0.1,0.2,0.3,...,0.5 OR x=0.1,0.2,0.3,0.4. Therefore,[x]=0 or 1.Not sufficient.



Math Expert
Joined: 02 Sep 2009
Posts: 50715

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
22 Feb 2014, 05:42



Manager
Joined: 18 May 2014
Posts: 59
Location: United States
Concentration: General Management, Other
GMAT Date: 07312014
GPA: 3.99
WE: Analyst (Consulting)

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
18 May 2014, 09:33
et us do [2.4] What are the integers greater than or equal to 2.4? 3,4,5... What is the least among them? 3 So [2.4] = 3
What is [5]? Integers greater than or equal to 5 are 5,6,7,... Leats among them is 5. so [5] = 5
[] is called a step function. because, the graph looks like steps.
Hope this helps!!



Director
Joined: 10 Mar 2013
Posts: 512
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
26 Jul 2015, 03:48
(1) 1 < x < 0.1. It'S Sufficient, as it's within the range  IXI = 0 (2) [x + 0.5] = 1 > 0<x+0.5≤1 > −0.5<x≤0.5 Not sufficient, if x=0,2 > IXI = 0, if x=0,3 > IXI = 1
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Senior Manager
Status: Always try to face your worst fear because nothing GOOD comes easy. You must be UNCOMFORTABLE to get to your COMFORT ZONE
Joined: 15 Aug 2014
Posts: 291
Concentration: Marketing, Technology
GMAT 1: 570 Q44 V25 GMAT 2: 600 Q48 V25
WE: Information Technology (Consulting)

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
14 May 2016, 04:09
Bunuel wrote: Please advise how below statement can be formed : (2) [x + 0.5] = 1 > 0<x+0.5≤1
_________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.”  Eric Thomas
I need to work on timing badly!!



Math Expert
Joined: 02 Aug 2009
Posts: 7038

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
14 May 2016, 06:40
sairam95 wrote: Bunuel wrote: Please advise how below statement can be formed : (2) [x + 0.5] = 1 > 0<x+0.5≤1 hi [b]For all z, [z] denotes the least integer greater than or equal to z. so if [x+0.5] =1, x+0.5 has to be between 0 and 1 including 1.. if x+0.5 is between 0.999999 and 0, inclusive, then [x+0.5] =0.. basically what ever is betwen [] takes the higher integer value or same value if it is integer...
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 27 Dec 2014
Posts: 4

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
02 Sep 2016, 07:09
Could you please explain the logic for the statement 2 .I understood [z] denotes the least integer greater than or equal to z is meant by −1<x≤0.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8574
Location: Pune, India

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
05 Sep 2016, 01:34
Ishanvs wrote: Could you please explain the logic for the statement 2 .I understood [z] denotes the least integer greater than or equal to z is meant by −1<x≤0. "Least integer greater than or equal to z implies that [z] >= z but [z] takes the least value that it can. So if z = 0.3, [z] = 1 If z = 1.98, [z] = 2 Ques: Is [x] = 0? When will [x] be 0? When 1 < x <= 0 So we need to know whether 1 < x <= 0? Stmnt 2: [x + 0.5] = 1 Say, x + 0.5 = z Given: [z] = 1 If [z] = 1, then we know that 0 < z <= 1. Note that if z is 0, [z] = 0. If z > 1, then [z] > 1 too. This implies that 0 < x + 0.5 <= 1 Subtracting 0.5 from the inequality, we get 0.5 < x <= 0.5 We know that x lies between 0.5 and 0.5. Some of these values lie in the 1 to 0 range and some do not. Hence we can't say whether x will lie in the 1 to 0 range. Not sufficient alone.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Director
Joined: 12 Nov 2016
Posts: 743
Location: United States
GPA: 2.66

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
22 Feb 2017, 14:37
Okay has anyone actually seen a question like this on the actual GMAT? Maybe I'm crazy, but with Kaplan for example, there were lots of practice questions that did not prepare me for the actual GMAT. On the QA of the actual GMAT I took, there were much more questions like those on Veritas' prep CAT's lots of exponents, lots of algebra, lots of functions



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8574
Location: Pune, India

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
22 Feb 2017, 19:40
Nunuboy1994 wrote: Okay has anyone actually seen a question like this on the actual GMAT? Maybe I'm crazy, but with Kaplan for example, there were lots of practice questions that did not prepare me for the actual GMAT. On the QA of the actual GMAT I took, there were much more questions like those on Veritas' prep CAT's lots of exponents, lots of algebra, lots of functions This question is from the Official Quant guide. So you could definitely see something like this in the actual GMAT.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 205
Location: India
Concentration: Finance, International Business

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
06 Nov 2017, 23:18
Sorry does this 2nd statement show modulus??



Math Expert
Joined: 02 Sep 2009
Posts: 50715

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
06 Nov 2017, 23:24



Intern
Joined: 20 May 2018
Posts: 5

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
14 Jul 2018, 12:40
Bunuel  For statement 1, do we not consider 0.05? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 50715

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
14 Jul 2018, 22:48



Intern
Joined: 20 May 2018
Posts: 5

Re: For all z, [z] denotes the least integer greater than or equ
[#permalink]
Show Tags
15 Jul 2018, 04:29
My mistake, I did not see the minus. Sorry about that.




Re: For all z, [z] denotes the least integer greater than or equ &nbs
[#permalink]
15 Jul 2018, 04:29






