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

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

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23 May 2010, 09:06
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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

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...
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Dec 2012, 10:30, edited 2 times in total.
Edited the question and added the OA
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Re: How x become fraction if its been said an integer [#permalink]

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23 May 2010, 09:30
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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

x is not defined as an integer here. the function [x] is defined as an integer, therefore x can be a fraction

[4] = 4
[4.9] = 4
[3/2] = 1

get it?
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Re: How x become fraction if its been said an integer [#permalink]

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23 May 2010, 10:40
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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: How x become fraction if its been said an integer [#permalink]

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23 May 2010, 11:05
Thank you Gmat guys for ur reply, Now i m clear....Well...kinda tricky problem indeed!!!.....
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If [x] denotes the greatest integer ... [#permalink]

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29 Oct 2010, 11:08
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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Re: If [x] denotes the greatest integer ... [#permalink]

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29 Oct 2010, 11:17
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lordspace wrote:
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 ???

Merging similar topics. Please refer to the solution above.

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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Re: How x become fraction if its been said an integer [#permalink]

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29 Oct 2010, 22:02
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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Re: How x become fraction if its been said an integer [#permalink]

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31 Oct 2010, 09:47
lordspace wrote:
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] ?

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

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02 Jul 2011, 21:27
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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
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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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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

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

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

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04 Jul 2011, 01:07
Is x less than 1?

1) s
2) s

D

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

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04 Jul 2011, 01:18
Pike, you can't rephrase as "is x<1?", or you'll hurt the negative numbers' feelings! For instance, if x = -2.5, then [x] = -3, not 0.
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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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18 Dec 2012, 01:12
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.

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

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21 May 2014, 07:18
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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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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21 May 2014, 07:23
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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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21 May 2014, 07:29
thanks for validating my logic. thanks also for similar questions.
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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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13 Aug 2014, 10:20
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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

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...

For what it's worth, I learned the 'greatest integer less than or equal to' function as the 'floor' function, and the 'least integer greater than or equal to' as the 'ceiling' function. It's an image that really helps me.
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Re: If [x] denotes the greatest integer less than or equal to x [#permalink]

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19 Dec 2015, 06:52
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Statement 1, on solving, gives x=0.66. The greatest integer smaller than that is 0. Sufficient

Statement 2 implies the value to be any decimal that one can conjure from the imagination with a calue less than 1 and more than 0. In that case too, the greatest integer less than the value is 0. Hence, Sufficient.

Hence, D
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Re: If [x] denotes the greatest integer less than or equal to x   [#permalink] 19 Dec 2015, 06:52

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