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.

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you rock Bunuel! Explanation is so good compared to that given in OG!