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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?

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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 » Sat Apr 04, 2020 8:35 pm

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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

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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 Brent@GMATPrepNow » Sun Apr 05, 2020 5:41 am
BTGmoderatorDC wrote: ↑
Sat Apr 04, 2020 8:35 pm
 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
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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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 Scott@TargetTestPrep » Thu Apr 09, 2020 4:04 am
BTGmoderatorDC wrote: ↑
Sat Apr 04, 2020 8:35 pm
 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

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We are given that [x] denotes the least integer greater than or equal to x and that [x] = 0.

So some numbers x can be include: 0, -0.1, -0.5, -0.9 and -0.999.

Thus, we see that x must be strictly greater than -1 but less than or equal to 0.

Answer: E

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