Data Sufficiency

#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

#102)[y] denotes the greatest integer less than or equal to y. Is d<1?

1) d=y-[y]
2) [d]=0

In explanation can you please include any tips on how to deal with </> in GMAT questions that's my weak area. Thanks!!

Hi,
#96)
From(1):-1<x<-0.1 For any value of x in this range, 0 is the least integer greater than or equal to x
sufficient
From(2):[x+0.5]=1 => 0<x+0.5<=1 => -0.5<x<=0.5
If x=-0.4, [x] is 0
If x=+0.4, [x] is 1
Insufficient

Hence, A

#102)

from (1): d=y-[y]
By definition [y]<=y<[y]+1
So, [y]-[y]<=y-[y]<[y]+1-[y]
So, 0<=d<1
Sufficient
from(2) : [d]=0
By definition [d]<=d<[d]+1 i.e. 0<=d<1
Sufficient

Hence, D

I did not understand "how to deal with </> in GMAT questions ". Can you be more clear on this.

greater than or less than sign for some reason always confuses me in DS questions. And can you please explan more #96 i still don't get it. Thanks!

joshua868 wrote:greater than or less than sign for some reason always confuses me in DS questions. And can you please explan more #96 i still don't get it. Thanks!

[z] is least integer greater than or equal to z.
a)-1<x<-0.1
[-1]=-1
but as x>-1, it means its not an integer and thus the min value is something like -.999999999999999
now [-.99999999999999999]=0 (integer greater than or equal to -.9999999999 is 0)
also [-0.1]=0
thus [x]=0
Sufficient. (just remember that for a -ve number say -2.6, [] = -2 (remove the fraction))
b)[x+0.5]=1
it means 0<x+0.5<=1 (not equal to 0 because then [x+0.5]=0)
or -0.5<x<=0.5
Insufficient (as [-0.49]=0 and [0.49]=1)
IMO A