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Question from Quantitative Review

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by parasite8 » Fri Sep 23, 2011 2:23 pm
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.
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Source: — Data Sufficiency |
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by cans » Fri Sep 23, 2011 7:59 pm
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
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Cans!!
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by Anurag@Gurome » Fri Sep 23, 2011 8:00 pm
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
(1) -1 < x < -0.1
For any value of x in the above range, 0 is the least integer, which is greater than or equal to x; SUFFICIENT.

(2 [x + 0.5] = 1 implies 0 < x + 0.5 <= 1 => -0.5 < x <= 0.5
If x = -0.4, [x] is 0.
If x = +0.4, [x] is 1; NOT sufficient.

The correct answer is A.
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by cans » Fri Sep 23, 2011 8:05 pm
[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
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by parasite8 » Sun Sep 25, 2011 1:32 pm
Thanks. Took me a while to review the answers given to get it but I finally got it! :D
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