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Intern  Joined: 26 Sep 2016
Posts: 7
Re: Elimination strategy  [#permalink]

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

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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:

$$[3.4]=3$$, $$=2$$, $$[-7.5]=-8$$, ...

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 V
Joined: 02 Sep 2009
Posts: 58464
Re: If [x] denotes the greatest integer less than or equal to x  [#permalink]

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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:

$$[3.4]=3$$, $$=2$$, $$[-7.5]=-8$$, ...

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.
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Joined: 09 Sep 2014
Posts: 3
If [x] denotes the greatest integer less than or equal to x  [#permalink]

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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:

$$[3.4]=3$$, $$=2$$, $$[-7.5]=-8$$, ...

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?
Thanks for your help..
Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Re: If [x] denotes the greatest integer less than or equal to x  [#permalink]

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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:

$$[3.4]=3$$, $$=2$$, $$[-7.5]=-8$$, ...

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?
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:

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

Check other Rounding Functions Questions in our Special Questions Directory.
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Joined: 29 Oct 2016
Posts: 24
Re: If [x] denotes the greatest integer less than or equal to x  [#permalink]

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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 

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

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

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

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!
Intern  B
Joined: 20 Jan 2019
Posts: 3
Re: If [x] denotes the greatest integer less than or equal to x  [#permalink]

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As [x]<=x. So x cannot be negative as it violates [-1]=1>-1.
So, 1. 5x+1=3+2x
x = 3/2, positive sufficient,
2. As x is greater than 0 it is sufficient.
SO answer is D Re: If [x] denotes the greatest integer less than or equal to x   [#permalink] 31 Jan 2019, 09:33

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