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

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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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SOLUTION

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

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Question: is \([x]=0\)? --> is \(-1<x\leq{0}\)?

(1) -1 < x < -0.1. Sufficient.

(2) [x + 0.5] = 1 --> \(0<x+0.5\leq{1}\) --> \(-0.5<x\leq{0.5}\). Not sufficient.

Answer: A.

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

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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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SOLUTION

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

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Question: is \([x]=0\)? --> is \(-1<x\leq{0}\)?

(1) -1 < x < -0.1. Sufficient.

(2) [x + 0.5] = 1 --> \(0<x+0.5\leq{1}\) --> \(-0.5<x\leq{0.5}\). Not sufficient.

Answer: A.

Similar questions to practice:
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denotes-to-be-the-least-integer-no-less-than-x-is-130841.html
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if-denotes-the-greatest-integer-less-than-or-equal-to-z-162078.html
if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html
is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html

Hope it helps.
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 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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New post 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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New post 14 May 2016, 05:09
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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New post 14 May 2016, 07:40
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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New post 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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New post 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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Re: For all z, [z] denotes the least integer greater than or equ [#permalink]

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New post 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

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

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

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New post 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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Re: For all z, [z] denotes the least integer greater than or equ   [#permalink] 07 Nov 2017, 00:24
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