It is currently 21 Nov 2017, 05:30

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If [x] denotes the greatest integer less than or equal to x

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15582

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If denotes the greatest integer less than or equal to x, is [#permalink]

Show Tags

New post 11 May 2016, 07:01
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 907 [0], given: 5

Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

Show Tags

New post 14 May 2016, 06:20
Expert's post
1
This post was
BOOKMARKED
musabber wrote:
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1



Solution:

We need to determine whether [x] = 0 where [x] denotes the greatest integer less than or equal to x. If the rule is hard to follow, let’s use a few examples.

[12.53] = 12, since 12 is the greatest integer less than or equal to 12.53.

[-1/2] = -1, since -1 is the greatest integer less than or equal to -1/2.

[1/2] = 0, since 0 is the greatest integer less than or equal to 1/2.

Using this last example, we know that if x is a positive fraction between zero and one, or is zero itself, the answer will be yes.

Statement One Alone:

5x + 1 = 3 + 2x

Let’s first simplify the equation.

5x + 1 = 3 + 2x

3x = 2

x = 2/3

Since 0 is the greatest integer less than or equal to 2/3, we see that [2/3] = 0.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

0 < x < 1

Because 0 < x < 1, x is a number between 0 and 1 (but, of course, not including 0 nor 1). Thus, the greatest integer less than or equal to such a number will always be zero. Statement two alone is also sufficient to answer the question.

The answer is D.
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 907 [0], given: 5

Intern
Intern
User avatar
Joined: 26 Sep 2016
Posts: 7

Kudos [?]: [0], given: 2

Re: Elimination strategy [#permalink]

Show Tags

New post 04 Oct 2016, 12:13
musabber wrote:
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1

hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...


Statement 1 gives x = 0.67
Statement 2 i.e 0 < x < 1 includes statement 1 data, so both statements have same information with respect to the question.

This means answer will be either D or E, so A, B ,C eliminated

If x = 0.67 rounded down then [x] = 0, satisfied from statement 1, therefore E cannot be the answer.

Only remaining option is D

Kudos [?]: [0], given: 2

Manager
Manager
avatar
B
Joined: 30 Jun 2015
Posts: 62

Kudos [?]: 2 [0], given: 87

CAT Tests
Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

Show Tags

New post 30 Nov 2016, 12:24
Great explanation.

For [x]=0, the inequality is -1<x<=0 but what if the question states [x] = 5.. What will the inequality be in that case?

will it still be -1<x<=0 ?? Please explain


Bunuel wrote:
musabber wrote:
hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1


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

Here \(x\) is not said to be an integer. Stem defines some function, represented by the symbol \([]\), as the function which rounds down any number to an integer value:

\([3.4]=3\), \([2]=2\), \([-7.5]=-8\), ...

Q: is \([x]=0\)? Or is \(0\leq{x}<1\)?

(1) 5x + 1 = 3 + 2x --> \(x=\frac{2}{3}\) --> \([\frac{2}{3}]=0\). Sufficient.

(2) 0 < x < 1 --> any \(x\) from this range will round down to 0, so \([x]=0\). Sufficient.

Answer: D.

Hope it helps.

Kudos [?]: 2 [0], given: 87

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [0], given: 12391

Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

Show Tags

New post 30 Nov 2016, 23:48
Expert's post
1
This post was
BOOKMARKED
cuhmoon wrote:
Great explanation.

For [x]=0, the inequality is -1<x<=0 but what if the question states [x] = 5.. What will the inequality be in that case?

will it still be -1<x<=0 ?? Please explain


Bunuel wrote:
musabber wrote:
hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1


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

Here \(x\) is not said to be an integer. Stem defines some function, represented by the symbol \([]\), as the function which rounds down any number to an integer value:

\([3.4]=3\), \([2]=2\), \([-7.5]=-8\), ...

Q: is \([x]=0\)? Or is \(0\leq{x}<1\)?

(1) 5x + 1 = 3 + 2x --> \(x=\frac{2}{3}\) --> \([\frac{2}{3}]=0\). Sufficient.

(2) 0 < x < 1 --> any \(x\) from this range will round down to 0, so \([x]=0\). Sufficient.

Answer: D.

Hope it helps.


[x] = 5 would mean that \(5\leq{x}<6\). Any number from that range when rounded down to the integer gives 5.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [0], given: 12391

Intern
Intern
avatar
B
Joined: 09 Sep 2014
Posts: 5

Kudos [?]: 1 [0], given: 12

If [x] denotes the greatest integer less than or equal to x [#permalink]

Show Tags

New post 09 Jul 2017, 05:04
Bunuel wrote:
musabber wrote:
hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1


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

Here \(x\) is not said to be an integer. Stem defines some function, represented by the symbol \([]\), as the function which rounds down any number to an integer value:

\([3.4]=3\), \([2]=2\), \([-7.5]=-8\), ...

Q: is \([x]=0\)? Or is \(0\leq{x}<1\)?

(1) 5x + 1 = 3 + 2x --> \(x=\frac{2}{3}\) --> \([\frac{2}{3}]=0\). Sufficient.

(2) 0 < x < 1 --> any \(x\) from this range will round down to 0, so \([x]=0\). Sufficient.

Answer: D.

Hope it helps.



Hello.. I wanted to ask why is 2/3 rounded to zero and not to 1 ?? O.667 so since 6 is greater than 4, shouldn't it be rounded up?
Thanks for your help..

Kudos [?]: 1 [0], given: 12

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [0], given: 12391

Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

Show Tags

New post 10 Jul 2017, 02:27
reemel3bd wrote:
Bunuel wrote:
musabber wrote:
hello GMAT guy!!

well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1


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

Here \(x\) is not said to be an integer. Stem defines some function, represented by the symbol \([]\), as the function which rounds down any number to an integer value:

\([3.4]=3\), \([2]=2\), \([-7.5]=-8\), ...

Q: is \([x]=0\)? Or is \(0\leq{x}<1\)?

(1) 5x + 1 = 3 + 2x --> \(x=\frac{2}{3}\) --> \([\frac{2}{3}]=0\). Sufficient.

(2) 0 < x < 1 --> any \(x\) from this range will round down to 0, so \([x]=0\). Sufficient.

Answer: D.

Hope it helps.



Hello.. I wanted to ask why is 2/3 rounded to zero and not to 1 ?? O.667 so since 6 is greater than 4, shouldn't it be rounded up?
Thanks for your help..


0.667 rounded to the nearest integer is indeed 1. But the function we have does not simply rounds number. Given function, represented by the symbol \([]\), rounds down any number to an integer value:

\([3.4]=3\), \([2]=2\), \([-7.5]=-8\), ... So, \([\frac{2}{3}]=0\).

Check other Rounding Functions Questions in our Special Questions Directory.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [0], given: 12391

Intern
Intern
avatar
B
Joined: 29 Oct 2016
Posts: 24

Kudos [?]: 1 [0], given: 12

Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

Show Tags

New post 04 Nov 2017, 16:04
Hi,

I was able to get this question right but I want to confirm if my concepts/understanding is correct for the four different situations:

If [x] is let's say, [4.3], and the question said:

1. [x] is the greatest integer that is less than or equal to x, this would mean [4.3] rounds down to [4]

2. [x] is the greatest integer that is more than or equal to x, this would mean [4.3] rounds up to [5]

3. [x] is the least integer that is less than or equal to x, this would mean [4.3] rounds down to [4]

4. [x] is the least integer that is more than or equal to x, this would mean [4.3] rounds up to [5]

Is the above correct? I am kind of confused about situations 3 and 4 above because I'm not exactly sure what 'least integer' means. Perhaps there are other examples that can help to explain 'least integer' cases further? Thank you!

Kudos [?]: 1 [0], given: 12

Re: If [x] denotes the greatest integer less than or equal to x   [#permalink] 04 Nov 2017, 16:04

Go to page   Previous    1   2   [ 28 posts ] 

Display posts from previous: Sort by

If [x] denotes the greatest integer less than or equal to x

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.