Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 May 2017, 10:43

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

‎[x] denotes to be the least integer no less than x. Is [2d]

Author Message
TAGS:

Hide Tags

Manager
Joined: 29 Nov 2011
Posts: 80
Followers: 1

Kudos [?]: 322 [0], given: 37

‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

17 Apr 2012, 19:53
18
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:22) correct 47% (01:13) wrong based on 551 sessions

HideShow timer Statistics

‎[x] denotes to be the least integer no less than x. Is [2d] = 0?

(1) [d] = 0
(2) [3d] = 0
[Reveal] Spoiler: OA
Manager
Joined: 17 Sep 2011
Posts: 180
Concentration: Strategy, Operations
Schools: ISB '15
GMAT 1: 720 Q48 V40
GPA: 3.18
WE: Supply Chain Management (Manufacturing)
Followers: 13

Kudos [?]: 66 [1] , given: 34

Show Tags

17 Apr 2012, 20:49
1
KUDOS
1
This post was
BOOKMARKED
Smita04 wrote:
‎[x] denotes to be the least integer no less than x. Is [2d] = 0?
(1) [d] = 0
(2) [3d] = 0

'no less than' indicated [x]$$>=$$ x....with the equality holding when x is an integer

st1: [d]=0 indicates -1<d<0 (eg. -0.5) => -2<2d<0(2x -0.5=-1) =>[2d]=-1
but if d= -0.3......2d= -0.6.....[2d]= 0 (not -1 as -1< -0.6)
NOT Sufficient

st2: -1<3d<0 => -1/3<d<0
d can be -0.65...then [2d]=0..... d can be [-0.01]....[d]=0....
(taking extreme values )
Suffecient

Last edited by Dreaming on 17 Apr 2012, 23:43, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38828
Followers: 7717

Kudos [?]: 105887 [0], given: 11593

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

17 Apr 2012, 21:17
Expert's post
13
This post was
BOOKMARKED
‎[x] denotes to be the least integer no less than x. Is [2d] = 0?

[x] denotes to be the least integer no less than x, means that some function [] rounds UP a number to the nearest integer, for example:
$$[1.5] = 2$$ since 2 is the least integer which no less than 1.5;
$$[-0.5]=0$$ since 0 is the least integer which no less than -0.5;
$$[1] = 1$$ since 1 itself is the least integer which no less than 1;
...

(1) [d] = 0 --> $$-1<d\leq{0}$$. Now, if $$d=0$$ then $$[2d]=[0]=0$$ but if $$d=-0.5$$ then $$[2d]=[-1]=-1$$. Not sufficient.

Or: $$-1<d\leq{0}$$ --> $$-2<d\leq{0}$$ --> $$[2d]=0$$ (if $$-1<2d\leq{0}$$) or $$[2d]=-1$$ (if $$-2<2d\leq{-1}$$). Not sufficient.

(2) [3d] = 0 --> $$-1<3d\leq{0}$$ --> $$-\frac{1}{3}<d\leq{0}$$. Even if $$d=-\frac{1}{3}$$ then $$[2d]=[-\frac{2}{3}]=0$$ (again since 0 is the least integer which no less than -2/3). Sufficient.

Or: $$-1<3d\leq{0}$$ --> $$-\frac{2}{3}<2d\leq{0}$$ --> $$[2d]=0$$. Sufficient.

Similar questions to practice:
if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
for-all-z-denotes-the-least-integer-greater-than-or-110561.html

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38828
Followers: 7717

Kudos [?]: 105887 [0], given: 11593

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

21 Jun 2013, 02:51
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Functions and Custom Characters questions: search.php?search_id=tag&tag_id=40
All PS Functions and Custom Characters questions: search.php?search_id=tag&tag_id=61

_________________
Intern
Joined: 22 May 2013
Posts: 49
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 18 [0], given: 10

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

22 Jun 2013, 03:56
Smita04 wrote:
‎[x] denotes to be the least integer no less than x. Is [2d] = 0?

(1) [d] = 0
(2) [3d] = 0

I did not jump into the equations, but tried to solve logically. Please let me know if wrong.

We need to find out if [2d] = 0?

Again its a YES or NO, question, getting Either in the statements will help us to the solutions.

(1) [d] = 0

Now according to the question [x] = integer no less than x

Hence, considering two extremes for evaluating this particular case, Lets take
[0.12] = 0 as well as [0.99] = 0 (both are valid for [d] =0)

therefore, [2d], i.e. taking the same values as above
[0.24] = 0, but [1.98] = 1
so we cant say most definitely that [2d] =0

Not Sufficient.

(2) [3d] = 0

again considering etremes here,

lets take
Minimum value => 3d = 0.12 (you can take less then this as well, i am just taking this for easy divisibility purpose, as anything less then 0.12 will also result in 0 we already know that)
and
Maximum value => 3d = 0.99
[3d] = 0 holds for both the values.

now, [2d]
minimum= [0.8] =0
maximum= [0.22] =0

hence, no matter what range we take for 3d, 2d will always be less then that.
Thus, if [3d]= 0, holds true, then [2d] =0 should hold true as well.

Hence, B
_________________

Intern
Joined: 22 May 2013
Posts: 49
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 18 [0], given: 10

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

23 Jun 2013, 06:53
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Functions and Custom Characters questions: search.php?search_id=tag&tag_id=40
All PS Functions and Custom Characters questions: search.php?search_id=tag&tag_id=61

Hi Bunuel,

Please let me know if the above approach is correct?
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 38828
Followers: 7717

Kudos [?]: 105887 [0], given: 11593

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

24 Jun 2013, 01:59
kpali wrote:
Smita04 wrote:
‎[x] denotes to be the least integer no less than x. Is [2d] = 0?

(1) [d] = 0
(2) [3d] = 0

I did not jump into the equations, but tried to solve logically. Please let me know if wrong.

We need to find out if [2d] = 0?

Again its a YES or NO, question, getting Either in the statements will help us to the solutions.

(1) [d] = 0

Now according to the question [x] = integer no less than x

Hence, considering two extremes for evaluating this particular case, Lets take
[0.12] = 0 as well as [0.99] = 0 (both are valid for [d] =0)

therefore, [2d], i.e. taking the same values as above
[0.24] = 0, but [1.98] = 1
so we cant say most definitely that [2d] =0

Not Sufficient.

(2) [3d] = 0

again considering etremes here,

lets take
Minimum value => 3d = 0.12 (you can take less then this as well, i am just taking this for easy divisibility purpose, as anything less then 0.12 will also result in 0 we already know that)
and
Maximum value => 3d = 0.99
[3d] = 0 holds for both the values.

now, [2d]
minimum= [0.8] =0
maximum= [0.22] =0

hence, no matter what range we take for 3d, 2d will always be less then that.
Thus, if [3d]= 0, holds true, then [2d] =0 should hold true as well.

Hence, B

No, that's not correct. Function [] rounds UP a number to the nearest integer, thus [0.12] = 1, not 0 and [0.99] = 1, not 1.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15401
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

21 Aug 2014, 06:14
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.
_________________
Manager
Joined: 05 Jun 2014
Posts: 72
GMAT 1: 630 Q42 V35
Followers: 1

Kudos [?]: 26 [0], given: 51

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

13 Sep 2014, 00:37
Meaning that even -0.99 will round UP to 0 and not -1??
Math Expert
Joined: 02 Sep 2009
Posts: 38828
Followers: 7717

Kudos [?]: 105887 [0], given: 11593

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

13 Sep 2014, 07:16
Meaning that even -0.99 will round UP to 0 and not -1??

Yes. The function rounds UP a number to the nearest integer. The nearest integer greater than -0.99 is 0, thus [-0.99] = 0.

Check other Rounding Functions Questions in our Special Questions Directory.

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15401
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

23 Sep 2015, 09:55
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 Legend
Joined: 09 Sep 2013
Posts: 15401
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: ‎[x] denotes to be the least integer no less than x. Is [2d] [#permalink]

Show Tags

29 Nov 2016, 21:04
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: ‎[x] denotes to be the least integer no less than x. Is [2d]   [#permalink] 29 Nov 2016, 21:04
Similar topics Replies Last post
Similar
Topics:
6 If [x] denotes the greatest integer less than or equal to x for any nu 7 10 Feb 2017, 22:00
23 [x] denotes the greatest integer less than or equal to x. 7 04 Oct 2016, 19:49
102 If [x] denotes the least integer greater than or equal to x 14 13 Jan 2017, 06:26
2 If @x denotes the greatest integer that is less than 6 24 Oct 2010, 04:50
47 If [x] denotes the greatest integer less than or equal to x 24 30 Nov 2016, 23:48
Display posts from previous: Sort by