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

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

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18 Feb 2014, 03:38
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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, 03:38
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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, 04:07
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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, 06:42
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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, 10:33
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, 04:48
(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, 05:09
Bunuel wrote:

(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, 07:40
sairam95 wrote:
Bunuel wrote:

(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, 08:09
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, 02:34
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 12 Nov 2016 Posts: 776 Location: United States Schools: Yale '18 GMAT 1: 650 Q43 V37 GRE 1: 315 Q157 V158 GPA: 2.66 Re: For all z, [z] denotes the least integer greater than or equ [#permalink] ### Show Tags 22 Feb 2017, 15:37 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 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8079 Location: Pune, India Re: For all z, [z] denotes the least integer greater than or equ [#permalink] ### Show Tags 22 Feb 2017, 20:40 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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07 Nov 2017, 00:18
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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07 Nov 2017, 00:24
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] 07 Nov 2017, 00:24
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