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# For all z, [z] denotes the least integer greater than or equ

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For all z, [z] denotes the least integer greater than or equ  [#permalink]

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18 Feb 2014, 02:38
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

For all z, [z] denotes the least integer greater than or equal to z. Is [x] = 0 ?

(1) -1< x < -0.1
(2) [x + 0.5] = 1

Data Sufficiency
Question: 96
Category: Algebra Operations with real numbers
Page: 160
Difficulty: 650

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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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18 Feb 2014, 02:38
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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18 Feb 2014, 03:07
2
Option A.

From S1:x=any value greater than -1 but less than -0.1.For every value of x,
[x]=0 only.Sufficient.

From S2:x=0.1,0.2,0.3,...,0.5
OR x=-0.1,-0.2,-0.3,-0.4.
Therefore,[x]=0 or 1.Not sufficient.
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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22 Feb 2014, 05:42
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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18 May 2014, 09:33
et us do [2.4]
What are the integers greater than or equal to 2.4?
3,4,5...
What is the least among them?
3
So [2.4] = 3

What is [5]?
Integers greater than or equal to 5 are 5,6,7,...
Leats among them is 5.
so [5] = 5

[] is called a step function. because, the graph looks like steps.

Hope this helps!!
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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26 Jul 2015, 03:48
(1) -1 < x < -0.1. It'S Sufficient, as it's within the range - IXI = 0

(2) [x + 0.5] = 1 --> 0<x+0.5≤1 --> −0.5<x≤0.5 Not sufficient, if x=-0,2 -> IXI = 0, if x=0,3 -> IXI = 1
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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14 May 2016, 04:09
Bunuel wrote:

Please advise how below statement can be formed :

(2) [x + 0.5] = 1 --> 0<x+0.5≤1
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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14 May 2016, 06:40
sairam95 wrote:
Bunuel wrote:

Please advise how below statement can be formed :

(2) [x + 0.5] = 1 --> 0<x+0.5≤1

hi

[b]For all z, [z] denotes the least integer greater than or equal to z.
so if [x+0.5] =1, x+0.5 has to be between 0 and 1 including 1..
if x+0.5 is between -0.999999 and 0, inclusive, then [x+0.5] =0..
basically what ever is betwen [] takes the higher integer value or same value if it is integer...
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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02 Sep 2016, 07:09
Could you please explain the logic for the statement 2 .I understood [z] denotes the least integer greater than or equal to z is meant by −1<x≤0.
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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05 Sep 2016, 01:34
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Ishanvs wrote:
Could you please explain the logic for the statement 2 .I understood [z] denotes the least integer greater than or equal to z is meant by −1<x≤0.

"Least integer greater than or equal to z implies that [z] >= z but [z] takes the least value that it can.

So if z = 0.3, [z] = 1
If z = 1.98, [z] = 2

Ques: Is [x] = 0?
When will [x] be 0? When -1 < x <= 0
So we need to know whether -1 < x <= 0?

Stmnt 2: [x + 0.5] = 1

Say, x + 0.5 = z
Given: [z] = 1
If [z] = 1, then we know that 0 < z <= 1. Note that if z is 0, [z] = 0. If z > 1, then [z] > 1 too.

This implies that 0 < x + 0.5 <= 1
Subtracting 0.5 from the inequality, we get
-0.5 < x <= 0.5
We know that x lies between -0.5 and 0.5. Some of these values lie in the -1 to 0 range and some do not. Hence we can't say whether x will lie in the -1 to 0 range.
Not sufficient alone.
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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22 Feb 2017, 14:37
Okay has anyone actually seen a question like this on the actual GMAT? Maybe I'm crazy, but with Kaplan for example, there were lots of practice questions that did not prepare me for the actual GMAT. On the QA of the actual GMAT I took, there were much more questions like those on Veritas' prep CAT's- lots of exponents, lots of algebra, lots of functions
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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22 Feb 2017, 19:40
Nunuboy1994 wrote:
Okay has anyone actually seen a question like this on the actual GMAT? Maybe I'm crazy, but with Kaplan for example, there were lots of practice questions that did not prepare me for the actual GMAT. On the QA of the actual GMAT I took, there were much more questions like those on Veritas' prep CAT's- lots of exponents, lots of algebra, lots of functions

This question is from the Official Quant guide. So you could definitely see something like this in the actual GMAT.
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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06 Nov 2017, 23:18
Sorry does this 2nd statement show modulus??
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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06 Nov 2017, 23:24
longhaul123 wrote:
Sorry does this 2nd statement show modulus??

No. The stem introduces a function [], which rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ... The second statement also has the same function.
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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14 Jul 2018, 12:40
Bunuel - For statement 1, do we not consider 0.05?

Thanks
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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14 Jul 2018, 22:48
eishan123 wrote:
Bunuel - For statement 1, do we not consider 0.05?

Thanks

(1) says: -1 < x < -0.1. Is 0.05 in that range?
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Re: For all z, [z] denotes the least integer greater than or equ  [#permalink]

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15 Jul 2018, 04:29
My mistake, I did not see the minus. Sorry about that.
Re: For all z, [z] denotes the least integer greater than or equ &nbs [#permalink] 15 Jul 2018, 04:29
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# For all z, [z] denotes the least integer greater than or equ

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