Last visit was: 06 Nov 2024, 08:48 It is currently 06 Nov 2024, 08:48
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
User avatar
goodyear2013
Joined: 21 Oct 2013
Last visit: 29 May 2020
Posts: 392
Own Kudos:
5,296
 [140]
Given Kudos: 289
Posts: 392
Kudos: 5,296
 [140]
9
Kudos
Add Kudos
131
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,608
Own Kudos:
Given Kudos: 87,946
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,608
Kudos: 674,526
 [23]
13
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
User avatar
BrentGMATPrepNow
User avatar
GMAT Club Legend
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,790
Own Kudos:
31,833
 [5]
Given Kudos: 799
Location: Canada
Expert reply
Posts: 6,790
Kudos: 31,833
 [5]
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 06 Nov 2024
Posts: 2,010
Own Kudos:
2,248
 [3]
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,010
Kudos: 2,248
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[x] is defined as the least integer greater than or equal to 0 and [x]=0
So, x has to be between -1 and 0
x cannot be equal to -1 as [x] = -1 in that case and x can be equal to 0 as in that case also [x]=0
so, -1< x <= 0

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,608
Own Kudos:
674,526
 [2]
Given Kudos: 87,946
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,608
Kudos: 674,526
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
goodyear2013
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0
B. 0 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1x\leq{0}\): any number from this range when rounded up gives 0.

Answer: E.

Check other Rounding Functions Questions in our Special Questions Directory.
avatar
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,552
Own Kudos:
7,450
 [1]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,552
Kudos: 7,450
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
goodyear2013
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0
B. 0 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0


The answer for this is 0 < = x < = 1

However it is not available in the options. The match to the above is -1 < x <= 0

Answer = E
avatar
buddyisraelgmat
Joined: 14 Jul 2014
Last visit: 07 Jun 2015
Posts: 67
Own Kudos:
96
 [1]
Given Kudos: 49
Posts: 67
Kudos: 96
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
goodyear2013
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0
B. 0 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1x\leq{0}\): any number from this range when rounded up gives 0.

Answer: E.


Hi Bunuel

So just to clarify, if x = -1, then [x] = -1
But since its given that [x] = 0, hence x can be at the least -0.99 and max 0

I think the trap here is greater than or equal to x Thats why "D" is wrong

Is this understanding correct?

Thanks
avatar
OptimusPrepJanielle
Joined: 06 Nov 2014
Last visit: 08 Sep 2017
Posts: 1,787
Own Kudos:
Given Kudos: 23
Expert reply
Posts: 1,787
Kudos: 1,405
Kudos
Add Kudos
Bookmarks
Bookmark this Post
goodyear2013
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0
B. 0 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

Least integer GREATER THAN or EQUAL to x means [x] when rounded off to the nearest integer is GREATER THAN or EQUAL to [x].
Given that [x] = 0
So, [x] can take any value from -1 to 0 (excluding -1 and including 0), it will always be equal to 0.
Hence option (E).

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,608
Own Kudos:
674,526
 [3]
Given Kudos: 87,946
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,608
Kudos: 674,526
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
buddyisraelgmat
Bunuel
goodyear2013
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0
B. 0 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Hence, since [x] = 0, then it must be true that \(-1x\leq{0}\): any number from this range when rounded up gives 0.

Answer: E.


Hi Bunuel

So just to clarify, if x = -1, then [x] = -1
But since its given that [x] = 0, hence x can be at the least -0.99 and max 0

I think the trap here is greater than or equal to x Thats why "D" is wrong

Is this understanding correct?

Thanks

[x] = 0, means that \(-1<x\leq{0}\): any number from this range when rounded up gives 0.

D is wrong because x can be 0, while D excludes this possibility.
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,813
Own Kudos:
11,970
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,813
Kudos: 11,970
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi healthjunkie,

When a question asks "which of the following statements MUST be true?", you can interpret this to mean "which of the following statements is ALWAYS TRUE no matter how many different examples we can come up with?"

In this question, we're told that [X] is the least integer GREATER THAN OR EQUAL to X. We're also told that [X] = 0.

So, while X = 0 is a potential value for X (since 0 is the least integer that is greater than or equal to 0), it is NOT the only potential value.

As an example, X COULD be -1/2

The least integer that is greater than or equal to -1/2 IS 0. Thus, Answer A is NOT always true. With these types of questions, you have to make sure that you're doing enough work to prove when something is ALWAYS true vs. when something is SOMETIMES true.

GMAT assassins aren't born, they're made,
Rich
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,813
Own Kudos:
11,970
 [3]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,813
Kudos: 11,970
 [3]
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Hi All,

This is an example of a Symbolism question; these types of questions provide you with a "made up" math symbol, tell you what it "means" mathematically, then ask you to perform a calculation with it.

Here, we're told that [X] = the LEAST INTEGER that is greater than or equal to X.

In these situations, it helps to come up with some quick examples, so that you are clear on the concept:

For example:
[1] = 1
[1/2] = 1
[-2.5] = -2
Etc.

With this prompt, we're asked to figure out this…

[X] = 0

So what COULD X be so that the LEAST integer that would be greater than (or equal) X is 0?

X COULD be 0, of course.
X would have to be negative….
BUT it CAN'T be -1, since [-1] = -1

It would have be 0 and any negative fraction greater than -1

Final Answer:

GMAT assassins aren't born, they're made,
Rich
avatar
Raksat
Joined: 20 Feb 2017
Last visit: 11 Jun 2024
Posts: 153
Own Kudos:
Given Kudos: 489
Location: India
Concentration: Operations, Strategy
WE:Engineering (Other)
Posts: 153
Kudos: 466
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why can' it be A. If x is 0 ; then is it [x] = 1 or 0 . Hence it cannot be the answer.


Posted from my mobile device

Posted from my mobile device
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,813
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,813
Kudos: 11,970
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Raksat,

This question asks what MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples you can come up with?"). Answer A is SOMETIMES true (X COULD be 0, but it could also be other values).

GMAT assassins aren't born, they're made,
Rich
User avatar
Masterscorp
Joined: 14 Oct 2017
Last visit: 30 Mar 2021
Posts: 188
Own Kudos:
Given Kudos: 385
GMAT 1: 710 Q44 V41
GMAT 1: 710 Q44 V41
Posts: 188
Kudos: 275
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is the first time I encountered those [] marks in the GMAT quant section. Is it something that could also appear or already has appeared on the actual test?

I am aware that it isn't that complex, but it is surprising to encounter something completly new to me after studying for the GMAT for a few months :oops:
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,813
Own Kudos:
11,970
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,813
Kudos: 11,970
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Masterscorp,

This is an example of a Symbolism question; these types of questions provide you with a "made up" math symbol, tell you what it "means" mathematically, then ask you to perform a calculation with it. To reiterate: these [ ] marks are a made up math symbol that applies to THIS question ONLY; they don't represent some branch of math that you're unaware of.

GMAT assassins aren't born, they're made,
Rich
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 06 Nov 2024
Posts: 19,689
Own Kudos:
23,747
 [1]
Given Kudos: 287
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,689
Kudos: 23,747
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
goodyear2013
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

A. x = 0
B. 0 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

We are given that [x] denotes the least integer greater than or equal to x and that [x] = 0.

So some numbers x can be include: 0, -0.1, -0.5, -0.9 and -0.999.

Thus, we see that x must be greater than -1 but less than or equal to 0.

Answer: E
User avatar
proabhinav
Joined: 03 Aug 2018
Last visit: 10 Jul 2024
Posts: 60
Own Kudos:
Given Kudos: 263
Location: India
Concentration: Strategy, Operations
GMAT 1: 590 Q45 V26
GPA: 3.5
GMAT 1: 590 Q45 V26
Posts: 60
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

B. 0 <= x < 1
E. -1 < x <= 0

Please can someone advice how option B cannot be the right answer for this.

I was in doubt between B & E.

If x= 0.4, least integer would be 0 ( supports B ).
If x= 0.8, least integer still would be 0 ( as X < 1) , support B ?

Please can someone help me understand why B is incorrect.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,608
Own Kudos:
674,526
 [2]
Given Kudos: 87,946
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,608
Kudos: 674,526
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
proabhinav
If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

B. 0 <= x < 1
E. -1 < x <= 0

Please can someone advice how option B cannot be the right answer for this.

I was in doubt between B & E.

If x= 0.4, least integer would be 0 ( supports B ).
If x= 0.8, least integer still would be 0 ( as X < 1) , support B ?

Please can someone help me understand why B is incorrect.

If [x] denotes the least integer greater than or equal to x.

If x = 0.4, then the least integer which is GREATER than x is 1, NOT 0.
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,699
Own Kudos:
Given Kudos: 165
Expert reply
Posts: 3,699
Kudos: 18,099
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution



Given:
    • [x] denotes the least integer greater than or equal to x.

Approach and Working:

[x] = x, if x is an integer.
And if x is not an integer then [x]= Least integer greater than x.

Now, [x]=0 for x=0 and when -1 < x <0.

Therefore, the correct answer is option E.
Answer: E
User avatar
TBT
Joined: 09 Aug 2020
Last visit: 26 Nov 2023
Posts: 316
Own Kudos:
Given Kudos: 494
Location: India
Concentration: Marketing, General Management
Posts: 316
Kudos: 389
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can x be -1? not with respect to these options but otherwise.
 1   2   
Moderator:
Math Expert
96608 posts