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

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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?

by BTGmoderatorDC » Wed Jun 15, 2022 5:06 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 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

OA E

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 statements must be t

by [email protected] » Wed Jun 15, 2022 10:36 am
BTGmoderatorDC wrote:
Wed Jun 15, 2022 5:06 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 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

OA 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 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