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A question i just dont understand from the OG

Expert replies
by hongwang9703 » Sat Nov 28, 2009 6:14 pm
for all z, [z] denotes the least integer greater than or equal to z. is [x] = 0??

(1)-1 < x <-0.1
(2) [x+.5] = 1

the answer is A;

i cant even understand the explaination, but there is the jist of it:
Determining if [x]=0 is equivalent to determining if -1<x<=0. <= is smaller or equal to

This can be inferred by examining a few representative examples, such as [-1.1]=-1, [-1]=-1, [-0.9]=0, [-0.1]=0, [0]=0, and [0.1]=1.

then it goes on to explain 1 and 2.

could anyone who understands this problem explain this question is layman's term please?
i got utterly defeated by the gmat.
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Source: — Data Sufficiency |

by papgust » Sat Nov 28, 2009 8:13 pm
(1)-1 < x <-0.1

[x] is the least integer >= x. Now for x, we have values between -1 and -0.1.
So what is the next integer after -0.1? It is 0 (Remember 0 is also an integer which is neither +ve nor -ve).

0 is least integer >= -0.1. So it answers the questions (is [x] = 0?). So its A.

--------

Let's see why stmt 2 is insufficient,

(2) For, [x+.5] = 1, the possible values of x can be (It is enough to consider just 2 values)

x=-0.1, so x+0.5 = 0.4. Therefore [x+0.5]=1.
x=0.2, so x+0.5 = 0.6. Therefore [x+0.5]=1.

For [x+0.5] to be equal to 1, we have 2 possible values for x ==> -0.1, 0.2

Now take [x],
For x=-0.1, [x] = 0 (YES)
For x=0.2, [x] = 1 (NO)

You get multiple answers to the question. So it is insufficient.

Hope this clarifies your doubt.!
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