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# For all z, [z] denotes the least integer greater than or equal to z. I

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Intern
Joined: 14 May 2011
Posts: 9
For all z, [z] denotes the least integer greater than or equal to z. I  [#permalink]

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06 Sep 2011, 18:18
1
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:08) correct 31% (01:10) wrong based on 217 sessions

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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

How to determine the range for |x+0.5| = 1 ?

I considered two ranges X<0 and X>0.

X>0:
x+0.5 =1
x=0.5

X<0:
-(x+0.5) = 1
x=-1.5

But it looks like I'm missing something.In OG they have given the range as -0.5<x<=0.5

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-all-z-denotes-the-least-integer-greater-than-or-equ-167640.html
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1327
Re: For all z, [z] denotes the least integer greater than or equal to z. I  [#permalink]

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06 Sep 2011, 19:13
2
2
klueless7825 wrote:
For all z,|z| denotes the least integer greater than or equal to z.Is |x| = 0?

(Source:Q 96 - GMAT Quantitative Review 2nd Edition.)

1) -1 < X <-0.1
2) |x+0.5| = 1

How to determine the range for |x+0.5| = 1 ?

I considered two ranges X<0 and X>0.

X>0:
x+0.5 =1
x=0.5

X<0:
-(x+0.5) = 1
x=-1.5

But it looks like I'm missing something.In OG they have given the range as -0.5<x<=0.5

This is not a 'modulus' question at all, which is surely the source of your confusion. The question defines a completely different function, one you may never have seen before (sometimes called the 'ceiling function'), and probably won't ever see again (so this question is not likely to be that useful to study). In any case, the question tells us that [x] is equal to the smallest integer which is greater than or equal to x. From that definition, [3.6] would be equal to 4, for example, and [-0.7] would be equal to 0. We just round up the value inside the square brackets to the nearest integer.

So if -1 < x < -0.1, then to find [x], we'd round up to the nearest integer, so we'd round up to 0, and Statement 1 is sufficient. If [x+0.5] = 1, however, we cannot be sure of the value of [x]. It might be that x = 0.2, for example, so [x] is also equal to 1. Or it might be that x = -0.2, in which case [x] = 0. So Statement 2 is not sufficient, and the answer is A.
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Intern
Joined: 14 May 2011
Posts: 9
Re: For all z, [z] denotes the least integer greater than or equal to z. I  [#permalink]

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06 Sep 2011, 19:37
Got it.Thanks a lot for pointing the error,Ian.

In general,how do we determine the range for the below modulus function?

|x+0.5| = 1.How many solutions this modulus function can have?

I considered two ranges X<0 and X>0.Is there any other ranges need to be considered?

X>0:
x+0.5 =1
x=0.5

X<0:
-(x+0.5) = 1
x=-1.5

I see only 0.5 and -1.5 satisfying the equation.
Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: For all z, [z] denotes the least integer greater than or equal to z. I  [#permalink]

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08 Dec 2014, 03:18
4
12
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.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: for-all-z-denotes-the-least-integer-greater-than-or-equ-167640.html
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Re: For all z, [z] denotes the least integer greater than or equal to z. I  [#permalink]

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21 Oct 2018, 02:50
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Re: For all z, [z] denotes the least integer greater than or equal to z. I &nbs [#permalink] 21 Oct 2018, 02:50
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