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!