Data Sufficiency

HI,

I have a question from the 2nd Edition GMAT Quantitive Review.

They are Question 96 and 102 from the Data Sufficiency section.

96. 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

What does least integer greater than or equal to z mean?

Question 102 also has a similar question

102. [y] denotes the greatest integer less than or equal to y. Is d<1?
(1) d=y-[y]
(2) [d] = 0

Thanks.

96. 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

What does least integer greater than or equal to z mean?

[x] =x is x is integer.
[x]=whole number... if x>0 and non-integer. (lets say x=0.5, then 1 > 0.5 and 1 is smallest of all such integers..)

A) -1<x<-0.1
as x is not an integer, [x]=0
B) [x+0.5]=1
thus 0< x+0.5 <=1
-0.5<x<=0.5
if -0.5<x<=0, [x]=0 but if 0<x<=0.5, [x]=1
insufficient
IMO A

[y] denotes the greatest integer less than or equal to y. Is d<1?
(1) d=y-[y]
(2) [d] = 0

B) [d]=0 -> 0<=d<1
sufficient

A) d=y-[y]
if y is integer, d=0. sufficient
if y=5.6, [y]=5. d<1 sufficient
if y=-0.6, [y]=-1
d = 0.4 <1
IMO D

Thanks. Took me a while to review the answers given to get it but I finally got it!