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 must be true?

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

Answer: E

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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. \(-1 < x\le 0\)

Answer: E

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] = 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

Answer: E

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Brent
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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. \(-1 < x\le 0\)

Answer: E

Source: GMAT Prep
\([x]\) is defined as the least integer greater than or equal to \(0\) and \([x]=0\)

So, \(x\) has to be between \(-1\) and \(0\)

\(x\) cannot be equal to \(-1\) as \([x] = -1\) in that case and \(x\) can be equal to \(0\) as in that case also \([x]=0\)

So, \(-1 < x \leq 0\)

So, the correct answer is E

Hope this helps!