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If [x] denotes the greatest integer less than or equal to x Updated on: 05 Mar 2020, 00:24
Originally posted by musabber on 23 May 2010, 09:06.
Last edited by Bunuel on 05 Mar 2020, 00:24, edited 3 times in total.
Edited the question and added the OA
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If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1

Show Spoiler
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...
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D
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If [x] denotes the greatest integer less than or equal to x 23 May 2010, 10:40
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musabber
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
Show more

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.

Answer: D.

Hope it helps.
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If [x] denotes the greatest integer less than or equal to x 21 May 2014, 07:23
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Why bother solve statement-1? From st-1 we can tell that we will get the exact value of 'x' for sure and that's all we need to answer the question one way or the other. So sufficient. Is my logic right mods?
Show more

Absolutely.

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If [x] denotes the greatest integer less than or equal to x 29 Oct 2010, 11:08
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Hi all,

this is from OG 12 q.100/p.281

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1

The answer mentions that this [x] = 0 is equivalent to 0 ≤ x < 1.

I have hard time understanding it.

What would be [x] = 5 ?

5 <= x < 6 ???
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If [x] denotes the greatest integer less than or equal to x 29 Oct 2010, 11:17
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lordspace
Hi all,

this is from OG 12 q.100/p.281

If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1

The answer mentions that this [x] = 0 is equivalent to 0 ≤ x < 1.

I have hard time understanding it.

What would be [x] = 5 ?

5 <= x < 6 ???
Show more

Merging similar topics. Please refer to the solution above.

As for your question:
If \([x]=5\) then yes, \(5\leq{x}<6\), as ANY \(x\) from this range if round down to the integer gives 5. The same way if \([x]=0\) then \(0\leq{x}<1\), as ANY \(x\) from this range if round down to the integer gives 0.

Hope it's clear.
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If [x] denotes the greatest integer less than or equal to x 29 Oct 2010, 22:02
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Thanks Bunuel for the answer & merging my question with other questions.
I understand the the lower limit but find it hard to grasp the upper limit.
can the upper limit always be x+1 for [x] ?
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If [x] denotes the greatest integer less than or equal to x 31 Oct 2010, 09:47
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Thanks Bunuel for the answer & merging my question with other questions.
I understand the the lower limit but find it hard to grasp the upper limit.
can the upper limit always be x+1 for [x] ?
Show more

No upper limit is not x+1 for [x]. For example if [x]=5 then x<6 because if it's more than or equal to 6 then 5 won't be the greatest integer less than or equal to x.

More examples:

[5]=5;
[5.3]=5;
[5.9]=5;
[6]=6;
[-0.1]=-1;
...

Hope it's clear.
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If [x] denotes the greatest integer less than or equal to x 02 Jul 2011, 21:56
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(1)

3x = 2

=> x = 2/3 ~ 0.67

So [x] = 0

Sufficient

(2)

x = 0.5, 0.9

So [x] = 0

Sufficient

Answer - D
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If [x] denotes the greatest integer less than or equal to x 04 Jul 2011, 00:56
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I've seen this exact formula used before. Basically, they are just telling you that the brackets mean to round down to the nearest integer. The solution above is correct. Both statements indicate that x is a fraction between 0 and 1, and would therefore round down to 0.
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If [x] denotes the greatest integer less than or equal to x 18 Dec 2012, 01:12
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What value of x would give [x]=0?
According to the rule given in the problem: [x] denotes the greatest integer less than or equal to x.
\(0<= x < 1\) will give us [x] = 0.

(1) 5x + 1 = 3 + 2x
3x = 2
x = 2/3 which satisfies 0 <= x < 1 Thus SUFFICIENT.

(2) 0 < x < 1 SUFFICIENT.

Answer: D
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If [x] denotes the greatest integer less than or equal to x 21 May 2014, 07:18
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Why bother solve statement-1? From st-1 we can tell that we will get the exact value of 'x' for sure and that's all we need to answer the question one way or the other. So sufficient. Is my logic right mods?
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If [x] denotes the greatest integer less than or equal to x 14 May 2016, 06:20
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If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1

Show more

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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If [x] denotes the greatest integer less than or equal to x 30 Nov 2016, 12:24
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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
musabber
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.

Answer: D.

Hope it helps.
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If [x] denotes the greatest integer less than or equal to x 30 Nov 2016, 23:48
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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
musabber
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.

Answer: D.

Hope it helps.
Show more

[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 09 Jul 2017, 05:04
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Bunuel
musabber
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.

Answer: D.

Hope it helps.
Show more


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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If [x] denotes the greatest integer less than or equal to x 10 Jul 2017, 02:27
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Bunuel
musabber
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.

Answer: D.

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..
Show more

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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If [x] denotes the greatest integer less than or equal to x 04 Mar 2020, 14:18
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musabber
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.

Answer: D.

Hope it helps.
Show more
Hello Bunuel
Thanks for the nice explanation.
Here i need to add one more thing. As we still don't know what is going on in both statements (Can we refrain our eyes from statements for some moments?) we should rephrase the question stem ( \([x]=0\) ?) as \(-1 <x≤ 0\) too. Am I missing anything?
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If [x] denotes the greatest integer less than or equal to x 05 Mar 2020, 01:03
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Bunuel
musabber
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.

Answer: D.

Hope it helps.
Hello Bunuel
Thanks for the nice explanation.
Here i need to add one more thing. As we still don't know what is going on in both statements (Can we refrain our eyes from statements for some moments?) we should rephrase the question stem ( \([x]=0\) ?) as \(-1 <x≤ 0\) too. Am I missing anything?
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No. If \(-1 <x< 0\), then the greatest integer less than or equal to x, will be -1, not 0. For example, if x = -1/2, then the greatest integer less than or equal to -1/2 is -1.
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If [x] denotes the greatest integer less than or equal to x 06 Mar 2020, 06:34
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Bunuel
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Bunuel


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.

Answer: D.

Hope it helps.
Hello Bunuel
Thanks for the nice explanation.
Here i need to add one more thing. As we still don't know what is going on in both statements (Can we refrain our eyes from statements for some moments?) we should rephrase the question stem ( \([x]=0\) ?) as -1 <x≤ 0 too. Am I missing anything?

No. If \(-1 <x< 0\), then the greatest integer less than or equal to x, will be -1, not 0. For example, if x = -1/2, then the greatest integer less than or equal to -1/2 is -1.
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Thanks for the response Bunuel
I am talking when the scenario is -1 <x≤ 0 (not -1 <x< 0). So, what if the value of x=0? Shouldn't it be the greatest integer less than or equal to x, is [x] = 0?
Thanks_-
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If [x] denotes the greatest integer less than or equal to x 06 Mar 2020, 06:36
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Thanks for the response Bunuel
I am talking when the scenario is -1 <x≤ 0 (not -1 <x< 0). So, what if the value of x=0? Shouldn't it be the greatest integer less than or equal to x, is [x] = 0?
Thanks_-
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If x = 0, then then the greatest integer less than or equal to 0 is 0 itself. So, \(0\leq{x}<1\) in the solution above is correct.
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