GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Jan 2020, 10:03

### 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

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

# If [x] denotes the least integer greater than or equal to x and [x] =

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 408
If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

29 Aug 2014, 07:09
4
56
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:05) correct 33% (01:10) wrong based on 680 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 60727
If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

29 Aug 2014, 07:22
8
5
goodyear2013 wrote:
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 $$-1<x\leq{0}$$: any number from this range when rounded up gives 0.

_________________
##### General Discussion
GMAT Tutor
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 635
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

29 Aug 2014, 07:18
3
[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

Hope it helps!

goodyear2013 wrote:
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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 60727
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

29 Aug 2014, 07:24
1
1
Bunuel wrote:
goodyear2013 wrote:
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.

Check other Rounding Functions Questions in our Special Questions Directory.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1721
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

01 Oct 2014, 22:00
1
goodyear2013 wrote:
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

Manager
Joined: 14 Jul 2014
Posts: 88
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

30 Mar 2015, 10:13
1
Bunuel wrote:
goodyear2013 wrote:
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.

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
SVP
Joined: 06 Nov 2014
Posts: 1868
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

31 Mar 2015, 04:04
goodyear2013 wrote:
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: http://www.optimus-prep.com/gmat-on-demand-course
Math Expert
Joined: 02 Sep 2009
Posts: 60727
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

31 Mar 2015, 04:47
1
2
buddyisraelgmat wrote:
Bunuel wrote:
goodyear2013 wrote:
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.

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.
_________________
Intern
Joined: 14 Oct 2013
Posts: 42
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

29 May 2015, 19:20
E totally makes sense and I went for that option as well but can someone explain why A is wrong?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15997
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

29 May 2015, 21:14
1
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
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15997
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

03 Mar 2018, 15:28
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

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 20 Feb 2017
Posts: 161
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

05 May 2018, 21:26
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
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15997
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

06 May 2018, 16:24
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
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 14 Oct 2017
Posts: 231
GMAT 1: 710 Q44 V41
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

07 May 2018, 08:25
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
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15997
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

07 May 2018, 12:39
1
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
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9158
Location: United States (CA)
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

08 May 2018, 11:26
goodyear2013 wrote:
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 03 Aug 2018
Posts: 65
Location: India
Concentration: Strategy, Operations
GMAT 1: 590 Q45 V26
GPA: 3.5
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

16 Dec 2018, 02:33
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

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.
Math Expert
Joined: 02 Sep 2009
Posts: 60727
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

16 Dec 2018, 02:42
1
proabhinav wrote:
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

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.
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3230
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

16 Dec 2018, 12:11

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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 14007
Re: If [x] denotes the least integer greater than or equal to x and [x] =  [#permalink]

### Show Tags

16 Jan 2020, 00:49
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.
_________________
Re: If [x] denotes the least integer greater than or equal to x and [x] =   [#permalink] 16 Jan 2020, 00:49
Display posts from previous: Sort by