Similar questions help needed!! OG 2nd ed #96 and#102

[joshua868]

#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!!

[Frankenstein]

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.

[joshua868]

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!

[cans]

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