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

 It is currently 22 Jun 2018, 11:45

### 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

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Sep 2016
Posts: 7

### Show Tags

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
Manager
Joined: 30 Jun 2015
Posts: 60
Location: Malaysia
Schools: Babson '20
GPA: 3.6
Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

### Show Tags

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.

Hope it helps.
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

### Show Tags

30 Nov 2016, 23:48
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.

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.
_________________
Intern
Joined: 09 Sep 2014
Posts: 4
If [x] denotes the greatest integer less than or equal to x [#permalink]

### Show Tags

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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

### Show Tags

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.

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?

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.
_________________
Intern
Joined: 29 Oct 2016
Posts: 27
Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

### Show Tags

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!
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   [ 26 posts ]

Display posts from previous: Sort by