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

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For all z, [z] denotes the least integer greater than or [#permalink] New post 08 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?

(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, 12:51, edited 1 time in total.
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Re: 2nd edition problems 96,102 [#permalink] New post 09 Mar 2011, 17:16
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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.

Answer: A.

[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.

Answer: D.

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

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Re: 2nd edition problems 96,102 [#permalink] New post 12 Mar 2011, 06:48
Thanks for your reply.
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Re: 2nd edition problems 96 [#permalink] New post 12 Mar 2011, 14:16
Spidy001 wrote:
Uploaded the question 96 now..


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] New post 22 Dec 2012, 18:09
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.

Answer: A.

[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.

Answer: D.

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, 18:09
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