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## Number property question

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### Number property question

by mikepamlyla » Fri Nov 15, 2013 8:52 am
Here is a problem that I am having a tough time figuring out what the question is asking.
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by Brent@GMATPrepNow » Fri Nov 15, 2013 9:05 am
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

Target question: Is [x] = 0?

Given: For all z, [z] denotes the least integer greater than or equal to z.
So, for example, [1.3] = 2, since 2 is the smallest INTEGER that's greater than 1.3
Likewise, [8.8] = 9, since 9 is the smallest INTEGER that's greater than 8.8
[-3.5] = -3, since -3 is the smallest INTEGER that's greater than -3.5
[-0.9] = 0, since 0 is the smallest INTEGER that's greater than -0.9

Statement 1: -1 < x < -0.1
If -1 < x < -0.1, then [x] must equal 0, since 0 will be the always be smallest INTEGER that's greater than x
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: [x + 0.5] = 1
If [something] = 1, then 0 < something < 1
So, if [x + 0.5] = 1 then 0 < x + 0.5 < 1
Solve, to get -0.5 < x < 0.5

There are several values of x that satisfy this condition. Here are two:
Case a: x = -0.3, in which case [x] = 0
Case b: x = 0.3, in which case [x] = 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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by theCodeToGMAT » Fri Nov 15, 2013 9:11 am
[z] = least INT >=z

To find : [x] = 0

Statement 1:
x > -1
x < -0.1
I.e. x lies between -0.1 and -1, exclusive
if x = -0.2 ==> 0
if x = -0.9 ==> 0
SUFFICIENT

Statement 2:
[x+0.5] = 1
that means "x" can be
x + 0.5 = 0.1
x = -0.4
[x] = 0
or
x + 0.5 = 0.9
x = 0.4
[x] = 1
INSUFFICIENT