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

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Director
Joined: 01 Feb 2011
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For all z, [z] denotes the least integer greater than or [#permalink]

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08 Mar 2011, 19:16
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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

[y] denotes the greatest integer less than or equal to y. Is d < 1?

(1) d=y-[y]
(2) [d] =0

Last edited by Bunuel on 01 Feb 2012, 13:51, edited 1 time in total.
Edited the question
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Posts: 40413
Re: 2nd edition problems 96,102 [#permalink]

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09 Mar 2011, 18:16
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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.

[y] denotes the greatest integer less than or equal to y. Is d < 1?

The same here: some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Question: is $$d<1$$?

(1) d=y-[y] --> if y is an integer then $$[y]=y$$ and $$d=y-[y]=0<1$$, if y is not an integer [y] is nearest integer less than y and still $$d=y-[y]<1$$ (for example: $$y=1.5$$ --> $$d=1.5-[1.5]=1.5-1=0.5<1$$ or $$y=-1.5$$ --> $$d=-1.5-[-1.5]=-1.5-(-2)=0.5<1$$ ). Sufficient.

(2) [d] =0 --> $$0\leq{d}<1$$. Sufficient.

Similar questions:
how-x-become-fraction-if-its-been-said-an-integer-94687.html
awkward-ds-105416.html
help-data-sufficiency-equation-and-inequalities-99856.html

P.S. Please post one question per topic.
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Director
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Re: 2nd edition problems 96,102 [#permalink]

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12 Mar 2011, 07:48
Director
Status: No dream is too large, no dreamer is too small
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Re: 2nd edition problems 96 [#permalink]

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12 Mar 2011, 15:16
Spidy001 wrote:

Spidy001 wrote:
Does anyone have a better explanation for the problems 96,102 in 2nd edition DS?

option (1) giving the limit of the value and within the limit only greatest integer is ''0''. suf.
in op (2) x could be 0.1 or 0 as O+0.5=1 and 0.20+0.5=(0.7)1
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Re: 2nd edition problems 96,102 [#permalink]

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22 Dec 2012, 19:09
Bunuel wrote:
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.

[y] denotes the greatest integer less than or equal to y. Is d < 1?

The same here: some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...

Question: is $$d<1$$?

(1) d=y-[y] --> if y is an integer then $$[y]=y$$ and $$d=y-[y]=0<1$$, if y is not an integer [y] is nearest integer less than y and still $$d=y-[y]<1$$ (for example: $$y=1.5$$ --> $$d=1.5-[1.5]=1.5-1=0.5<1$$ or $$y=-1.5$$ --> $$d=-1.5-[-1.5]=-1.5-(-2)=0.5<1$$ ). Sufficient.

(2) [d] =0 --> $$0\leq{d}<1$$. Sufficient.

Similar questions:
how-x-become-fraction-if-its-been-said-an-integer-94687.html
awkward-ds-105416.html
help-data-sufficiency-equation-and-inequalities-99856.html

P.S. Please post one question per topic.

you rock Bunuel! Explanation is so good compared to that given in OG!
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Re: 2nd edition problems 96,102   [#permalink] 22 Dec 2012, 19:09
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