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

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

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11 May 2016, 07:01
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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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14 May 2016, 06:20
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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

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.
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Re: Elimination strategy [#permalink]

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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

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

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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.

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

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30 Nov 2016, 23:48
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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:

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

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

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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?
Thanks for your help..

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

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

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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!

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

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