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

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:17 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 ≤ z < –1
C) –2 < z ≤ –1
D) –1 ≤ z < 0
E) –1 < z ≤ 0

Answer: D
Source: GMATPrep test

Since [z] = –1, the value of z would lie between 0, excl. and –1, incl.

z cannot be 0 since [0] = 0, greatest integer, equal to 0. z cannot be less than – 1, say – 1.5 since if were so, [–1.5] = –2.

Thus, Option D is the correct answer.

The correct answer: D

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:17 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 ≤ z < -1
C) -2 < z ≤ -1
D) -1 ≤ z < 0
E) -1 < z ≤ 0

Answer: D
Source: GMATPrep test

Let's make sure we understand what this [] symbol means.
Here are a few examples:
[3.1] = 3
[5.8] = 5
[0.7] = 0
[-0.9] = -1
[-4.6] = -5

So, if [z] = -1, then -1 ≤ z < 0

Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Tue Mar 10, 2020 7:17 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 ≤ z < -1
C) -2 < z ≤ -1
D) -1 ≤ z < 0
E) -1 < z ≤ 0

Answer: D
Source: GMATPrep test

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