If $$[x]$$ denotes the least integer greater than or equal to $$x$$ and $$[x] = 0,$$ which of the following statements

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If $$[x]$$ denotes the least integer greater than or equal to $$x$$ and $$[x] = 0,$$ which of the following statements

by Vincen » Thu Dec 02, 2021 8:30 am

00:00

A

B

C

D

E

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If $$[x]$$ denotes the least integer greater than or equal to $$x$$ and $$[x] = 0,$$ which of the following statements must be true?

A. $$x = 0$$
B. $$0 \le x < 1$$
C. $$0 < x \le 1$$
D. $$-1 \le x < 0$$
E. $$-1 < x\le 0$$

Source: GMAT Prep

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Re: If $$[x]$$ denotes the least integer greater than or equal to $$x$$ and $$[x] = 0,$$ which of the following statemen

by [email protected] » Thu Dec 02, 2021 11:04 am
Vincen wrote:
Thu Dec 02, 2021 8:30 am
If $$[x]$$ denotes the least integer greater than or equal to $$x$$ and $$[x] = 0,$$ which of the following statements must be true?

A. $$x = 0$$
B. $$0 \le x < 1$$
C. $$0 < x \le 1$$
D. $$-1 \le x < 0$$
E. $$-1 < x\le 0$$

Source: GMAT Prep
First, let's take a moment to get a good idea of what this strange notation means.
A few examples:
[5.1] = 6 since 6 is the smallest integer that's greater than or equal to 5.1
 = 3 since 3 is the smallest integer that's greater than or equal to 3
[8.9] = 9 since 9 is the smallest integer that's greater than or equal to 8.9
[-1.4] = -1 since -1 is the smallest integer that's greater than or equal to -1.4
[-13.6] = -13 since -13 is the smallest integer that's greater than or equal to -13.6

So, if [x] = 0, then -1 < x ≤ 0