Last visit was: 21 Jul 2024, 12:06 It is currently 21 Jul 2024, 12:06
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
SORT BY:
Date
Tags:
Difficulty: 555-605 Level,   Functions and Custom Characters,                        
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94440
Own Kudos [?]: 642781 [179]
Given Kudos: 86716
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94440
Own Kudos [?]: 642781 [87]
Given Kudos: 86716
Send PM
Tutor
Joined: 16 Oct 2010
Posts: 15126
Own Kudos [?]: 66768 [12]
Given Kudos: 436
Location: Pune, India
Send PM
General Discussion
Manager
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 291 [6]
Given Kudos: 35
Location: India
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
4
Kudos
2
Bookmarks
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.
avatar
Intern
Intern
Joined: 18 May 2014
Posts: 41
Own Kudos [?]: 77 [3]
Given Kudos: 6
Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE:Analyst (Consulting)
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
3
Kudos
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!!
Current Student
Joined: 10 Mar 2013
Posts: 359
Own Kudos [?]: 2738 [1]
Given Kudos: 200
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.7
WE:Marketing (Telecommunications)
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
1
Bookmarks
(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
User avatar
Manager
Manager
Joined: 15 Aug 2014
Status:Always try to face your worst fear because nothing GOOD comes easy. You must be UNCOMFORTABLE to get to your COMFORT ZONE
Posts: 221
Own Kudos [?]: 562 [0]
Given Kudos: 470
Concentration: Marketing, Technology
GMAT 1: 570 Q44 V25
GMAT 2: 600 Q48 V25
WE:Information Technology (Consulting)
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
Bunuel wrote:


Please advise how below statement can be formed :

(2) [x + 0.5] = 1 --> 0<x+0.5≤1
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11479
Own Kudos [?]: 34502 [1]
Given Kudos: 323
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
1
Kudos
Expert Reply
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...
avatar
Intern
Intern
Joined: 27 Dec 2014
Posts: 4
Own Kudos [?]: 1 [0]
Given Kudos: 2
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
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.
Manager
Manager
Joined: 03 Jul 2017
Status:IF YOU CAN DREAM IT, YOU CAN DO IT
Posts: 145
Own Kudos [?]: 33 [0]
Given Kudos: 27
Location: India
Concentration: Finance, International Business
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
Sorry does this 2nd statement show modulus??
Math Expert
Joined: 02 Sep 2009
Posts: 94440
Own Kudos [?]: 642781 [0]
Given Kudos: 86716
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
Expert Reply
longhaul123 wrote:
Sorry does this 2nd statement show modulus??


No. The stem introduces a function [], which rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ... The second statement also has the same function.
Senior Manager
Senior Manager
Joined: 05 Feb 2018
Posts: 308
Own Kudos [?]: 829 [1]
Given Kudos: 325
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
1
Kudos
1) -1 < x < -0.1
[x] = 0 when -1 < x ≤ 0
Sufficient.

(2) [x+0.5] = 1
Range of x is -0.5 < x < 0.5
If x is -0.4 then it rounds up to 0
If x is 0.4 then it rounds up to 1
Not sufficient.

A number line can be helpful to visualize.
Director
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [2]
Given Kudos: 432
Location: United States
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
2
Bookmarks
For all z, [z] denotes the least integer greater than or equal to z. Is [x] = 0 ?

The least integer greater than or equal to z means we round up. [5.5] = 6, [5] = 5.

(1) -1< x < -0.1

[x] = 0. SUFFICIENT.

(2) [x + 0.5] = 1

If x = 0 then, [0] = 0
If x = 0.5 then [0.5] = 1

INSUFFICIENT.

Answer is A.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22687 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
Expert Reply
Bunuel wrote:
For 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



Solution:

We need to determine whether [x] = 0 where [x] denotes the least integer greater than or equal to x.

Statement One Alone:

Since the least integer greater than any number whose value is between -1 and -0.1 is 0, [x] = 0. Statement one alone is sufficient.

Statement Two Alone:

If [x + 0.5] = 1, then we have:

0 < x + 0.5 ≤ 1

-0.5 < x ≤ 0.5

We see that if x = -0.4, then [x] = 0. However, if x = 0.4, then [x] = 1. Statement two alone is not sufficient.

Answer: A
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34037
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: For all z, [z] denotes the least integer greater than or equal to z. [#permalink]
Moderator:
Math Expert
94440 posts