If [z] denotes the greatest integer less than or equal to z and [z] = GMAT Problem-Solving

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.

Suggested GMAT Problem Solving Questions:

• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT Problem Solving
• How many factors does \(36^2\) have? GMAT Problem Solving
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively GMAT Problem Solving
• Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes GMAT Problem Solving
• A milkman cheats his customers by adding water to the milk he sells GMAT Problem Solving
• if 80 lamps can be lighted, 5 hours per day for 10 days for $21.25, then the number of lamps, GMAT Problem Solving
• Few of the corporate contributions to the earthquake relief fund, aside from Pterocom GMAT Problem Solving
• X is Older Than Y, Z Is Younger Than W And V Is Older Than Y GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• Find the Greatest Number That Will Divide 43,91 and 183 So as to Leave GMAT Problem Solving
• A Right Angled Triangle has its Sides in Arithmetic Progression and Being Integers GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 seconds Respectively GMAT Problem Solving
• A Man can Hit a Target Once with 4 Shots. If He Fires 4 Shots in Success GMAT Problem Solving
• A is twice as good a workman as B and together they finish a piece of GMAT Problem Solving
• Frances can complete a job in 12 hours, and Joan can complete the same GMAT Problem Solving
• The Average Age of Chief Executive Officers (CEO’s) in a Large Sample of Companies is 57 GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines can GMAT Problem Solving
• If a and b are positive integers such that a – b and a/b are both even GMAT Problem Solving
• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333²²² is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving
• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married to Each Other? GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
• If tu=xytu=xyand ty=uxty=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving
• A Farm has Chickens, Cows and Sheep. The Number of Chickens and Cows Combined is 3 Times the Number of Sheep. GMAT Problem Solving
• In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• The product of the first 10 prime numbers is closest to which of the following? GMAT Problem Solving
• There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5 GMAT Problem Solving
• An equilateral triangle ABC is inscribed in square ADEF, forming three right triangles GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B. The Selling Price of Model A is $120 GMAT Problem Solving
• A contractor combined x tons of a gravel mixture that contained 10 percent gravel G GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution GMAT Problem Solving
• Jug Contains Water And Orange Juice In The Ratio 5:7 . Another Jug Contains Water And Orange J GMAT Problem Solving
• The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated GMAT Problem Solving
• A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour GMAT Problem Solving
• The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. GMAT Problem Solving
• y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT Problem Solving