Question: 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

Solution and Explanation:

Approach Solution 1:
It is a MUST BE TRUE question for ALL values. A cannot be true. You would have stopped at option A itself and gone on to the next question if this had been a "might be true" question.
But, because this question MUST BE TRUE, you must ensure that [z] =-1 is satisfied only by z =-1 among the available possibilities (and not by any other option). A "must be true" inquiry has a valid response, which rules out all other possibilities. This is a crucial factor to keep in mind. While we do not dispute that z = -1 is false, we do question whether it is the only option available. Z = -0.5 may or may not also satisfy the specified criterion.
Hence, if z = -0.5 also meets the stated criterion, option D is also true (along with option A, per your statement). There can never be two right answers to a question.
As I already stated, a MUST BE TRUE question

1. Find the choice or options that satisfy the stated requirement.
2. Rule out all but one possibility. The best response will be the final choice. There will always be compelling arguments to rule out alternatives. You are lacking some crucial information if you are unable to eliminate choices.

You cannot be certain of your response unless you consider both possibilities.
I used the next approach for this inquiry:

1. Using z = -0.5 to rule out choices A through C
2. To rule out option E, set z = 0. If z = 0, [z] = 0, and z -1

Following the previous two phases, only option D remained, and this is the right response.
Correct Answer: D

Approach Solution 2:
To answer this GMAT question, apply the data provided in the question. These issues pertain to many different branches of mathematics. This query relates to number theory. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
Make sure we comprehend what this sign, [], implies.
Here are a few illustrations:
[3.1] = 3
[5.8] = 5
[0.7] = 0
[-0.9] = -1
[-4.6] = -5
Thus, if [z] = -1, -1 < z < 0
Hence,
Correct Answer: D

Approach Solution 3:
That must be true for all values. Not possible. If this question was "may be true," you would have stopped at option A and moved on.
This is a MUST BE TRUE question, thus make sure [z] =-1 is only satisfied by z =-1 from the offered possibilities (and not by any other option). Answering a MUST BE TRUE question correctly eliminates all other options. Remember this crucial point. z = -1 is true, but is it the only choice? z = -0.5 may not satisfy the criterion.
Option D is true if z = -0.5 meets the requirement (along with option A, per your statement). Two valid responses are impossible.
As mentioned, in a MUST BE TRUE inquiry,

1. Find options that meet a requirement.
2. Remove everything but one. The final answer is correct. There are always valid reasons to eliminate alternatives. Eliminating alternatives is crucial.

You can't be sure unless you consider both alternatives.
I answered this question this way:

1. Eliminated A-C with z=-0.5
2. Eliminated option E with z=0. For z=0, [z] = 0, and z is not equal to -1.

D is the only option left and the correct answer.
Correct Answer: D

“If [z] denotes the greatest integer less than or equal to z and [z] =" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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