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If \([z]\) denotes the greatest integer less than or equal to \(z\) and \([z] = -1,\) which of the following statements

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If \([z]\) denotes the greatest integer less than or equal to \(z\) and \([z] = -1,\) which of the following statements

by Gmat_mission » Sat Jun 06, 2020 4:59 am

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If \([z]\) denotes the greatest integer less than or equal to \(z\) and \([z] = -1,\) which of the following statements must be true?

A. \(z = -1\)
B. \(-2 \leq z < -1\)
C. \(-2 < z \leq -1\)
D. \(-1 \leq z < 0\)
E. \(-1 < z \leq 0\)

[spoiler]OA=D[/spoiler]

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Re: If \([z]\) denotes the greatest integer less than or equal to \(z\) and \([z] = -1,\) which of the following stateme

by RaghavKhanna » Sun Jun 07, 2020 2:55 am
[z] = greatest integer less than or equal to z
eg: [5.3] = 5
[-2.4] = -3

Now,
it is given that [z] = -1
=> z<0 because if z=0, then [z] = 0

Also, if z< -1, then [z] < -1
eg: [-1.5] = -2
=> z>=-1

Range of z => [-1,0)
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Re: If \([z]\) denotes the greatest integer less than or equal to \(z\) and \([z] = -1,\) which of the following stateme

by Scott@TargetTestPrep » Fri Jun 12, 2020 1:51 pm
Gmat_mission wrote: ↑
Sat Jun 06, 2020 4:59 am
 If \([z]\) denotes the greatest integer less than or equal to \(z\) and \([z] = -1,\) which of the following statements must be true?

A. \(z = -1\)
B. \(-2 \leq z < -1\)
C. \(-2 < z \leq -1\)
D. \(-1 \leq z < 0\)
E. \(-1 < z \leq 0\)

[spoiler]OA=D[/spoiler]

Solution:

If z = -1, [z] = -1. If z = -0.5, [z] = -1. If z = -0.0001, [z] = -1. However, if z = 0, then [z] = 0. So -1 ≤ z < 0.

Answer: D

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