GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Nov 2019, 15:10 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # ‎[x] denotes to be the least integer no less than x. Is [2d]

Author Message
TAGS:

### Hide Tags

Manager  Joined: 29 Nov 2011
Posts: 71
‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

2
43 00:00

Difficulty:   65% (hard)

Question Stats: 56% (01:49) correct 44% (01:39) wrong based on 1010 sessions

### HideShow timer Statistics

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

(1) [d] = 0
(2) [3d] = 0
Math Expert V
Joined: 02 Sep 2009
Posts: 59095
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

7
19
‎[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;
$$ = 1$$ since 1 itself is the least integer which no less than 1;
...

(1) [d] = 0 --> $$-1<d\leq{0}$$. Now, if $$d=0$$ then $$[2d]==0$$ 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.
_________________
##### General Discussion
Manager  Joined: 17 Sep 2011
Posts: 164
Concentration: Strategy, Operations
Schools: ISB '15
GMAT 1: 720 Q48 V40 GPA: 3.18
WE: Supply Chain Management (Manufacturing)

### Show Tags

1
3
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

Originally posted by Dreaming on 17 Apr 2012, 20:49.
Last edited by Dreaming on 17 Apr 2012, 23:43, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 59095
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

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: 43
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

1
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
_________________
PS: Like my approach? Please Help me with some Kudos. Intern  Joined: 22 May 2013
Posts: 43
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

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?
_________________
PS: Like my approach? Please Help me with some Kudos. Math Expert V
Joined: 02 Sep 2009
Posts: 59095
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

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.
_________________
Manager  Joined: 05 Jun 2014
Posts: 60
GMAT 1: 630 Q42 V35 Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

Meaning that even -0.99 will round UP to 0 and not -1??
Math Expert V
Joined: 02 Sep 2009
Posts: 59095
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

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.
_________________
Intern  B
Joined: 27 Apr 2015
Posts: 39
GMAT 1: 370 Q29 V13 Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

Smita04 wrote:
‎[x] denotes to be the least integer no less than x. Is [2d] = 0?

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

Given [x] LI no less than x i.e [x]>=x
Find Is [2d]=0

Now [2d]=0 possible if 2d satisfies the inequality/range -1<2d<=0 ---equ(a)

Statement 1 [d]=0
=> Since [d]=0 so d lies in -1<d<=0
=> Multiplying the above inequality by 2 we have -2<2d<=0. So this range makes 2 cases
=> Case 1 When -2<2d<=-1 then [2d]=-1
=> Case 2 When -1<2d<=0 then [2d]=0
=> Since no unique sol. So NOT sufficient

Statement 2 [3d]=0
Since [3d]=0 so 3d lies in -1<3d<=0
=> Multiplying the above inequality by 2/3 we have -2/3<2d<=0.
=> So the above range satisfy equ (a)
=> Therefore [2d]=0
=> Since unique sol. So SUFFICIENT

Therefore "B"

Thanks
Non-Human User Joined: 09 Sep 2013
Posts: 13602
Re: ‎[x] denotes to be the least integer no less than x. Is [2d]  [#permalink]

### Show Tags

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 Dec 2018, 12:49
Display posts from previous: Sort by

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