Question: If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?
- -2
- -3/2
- 1/2
- 1
- 2
Correct Answer: B
Solution and Explanation
Approach Solution 1:
Given: x denotes the least integer greater than or equal to x and [x/2] = 0
Find out: The value of x
First, let's take a moment to get a good idea of what this strange notation means.
A few examples:
[5.1] = 6
[3] = 3
[8.9] = 9
[-1.4] = -1
[-13.6] = -13
So, if [x/2] = 0, then
As per the basic arithmetic function, we know that -1 < x/2 ≤ 0
If we Multiply all sides of the inequality by 2 we get:
-2 < x ≤ 0
As per the answer choices given in the question,
Only -3/2 falls inside that range (-2 < x ≤ 0)
Hence, the correct answer is B.
Approach Solution 2:
Given: x denotes the least integer greater than or equal to x and [x/2] = 0
Find out: The value of x
Since [x] denotes the least integer greater than or equal to x
This means x = I , if x is an integer and x = I
x = i+1, if x is not an integer and x = i + d where i is integral part of x and d is decimal part of x
So [x/2] = 0
-1 < x/2 < = 0
-2 < x <= 0
Only -3/2 which is equal to -1.5 lies in between this range.
Hence, the correct answer is option B.
Approach Solution 3:
If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.
Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.
Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.
“If [x] denotes the least integer greater than or equal to x”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review 2017". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
Suggested GMAT Problem Solving Questions
- The Owner of A Local Jewellery Store Hired 3 Watchmen to Guard his Diamonds GMAT Problem Solving
- What is the smallest integer n for which 25^n>5^12 GMAT Problem Solving
- Ten Coins are Tossed Simultaneously. In how many of the Outcomes GMAT Problem Solving
- A Pool can be Filled in 4 Hours and Drained in 5 Hours GMAT Problem Solving
- If x^2 − 2 < 0, which of the following specifies all the possible GMAT Problem Solving
- A Train Approaches A Tunnel AB. Inside The Tunnel Is A Cat Located GMAT Problem Solving
- A Dairyman Pays Rs. 6.40 Per Liter Of Milk GMAT Problem Solving
- John is 20 years older than Brian. 12 years ago, John was twice as old GMAT Problem Solving
- A Train Overtakes Two Persons Who Are Walking In The Same Direction GMAT Problem Solving
- If 1/x − 1/x+1= 1/x+4, Then x could be GMAT Problem Solving
- If x = - |x|, Then Which One of the Following Statements GMAT Problem Solving
- A Bag Contains 4 Red and 3 Black Balls. A Second Bag Contains 2 Red GMAT Problem Solving
- A Mixture of 40 Litres of Milk and Water, Contains 20% of Water GMAT Problem Solving
- A Candidate is Required to Answer 6 Out of 10 Questions Divided into 2 Groups GMAT Problem Solving
- Company XYZ had $498.2 Million in Profits for the Year GMAT Problem Solving
- If -2 < a < 11 and 3 < b < 12, Then Which of the Following is NOT Always True GMAT Problem Solving
- Karan and Arjun run a 100-metre Race, Where Karan Beats Arjun by 10 metres GMAT Problem Solving
- Set T consists of all points (x, y) such that \(x^2+y^2=1\) GMAT Problem Solving
- How Many Natural Numbers Not Exceeding 4321 can be Formed GMAT Problem Solving
- The Figure below Shows an Equilateral Triangle ABC Tangent GMAT Problem Solving
- In an Isosceles Triangle PQR, If ∠Q = 80 Degrees, Then What is The GMAT Problem Solving
- If x=10^{10},\frac{x^2+2x+7}{3x^2-10x+200} is closest to GMAT Problem Solving
- If set S Consists of all Different Solutions of Equation |x – 4| = x, What is the Range of Set S GMAT Problem Solving
- Two Members of a Club are to be Selected to Represent the Club GMAT Problem Solving
- The Square Root of 24336 is Exactly GMAT Problem Solving
- A Certain Purse Contains 30 Coins, Each Coin is either a Nickel or GMAT Problem Solving
- Which of the Following is Equal to the Value of 2^5+2^5+3^5+3^5+3^5 ? GMAT Problem Solving
- The Price of a Certain Painting Increased By 20% During the First Year GMAT Problem Solving
- The Population of the Village is 5500. If the Number of Males Increase GMAT Problem Solving
- Two Vessels A and B Contain Milk and Water Mixed in the Ratio 8:5 GMAT Problem Solving
- A Dealer Offers a Cash Discount of 20%. Further, a Customer Bargains GMAT Problem Solving
- There are Two Vessels A and B. Vessel A is Containing 40 Litres of GMAT Problem Solving
- At A Certain Fruit Stand, The Price Of Each Apple Is 40 Cents GMAT Problem Solving
- The Coordinates Of Vertices P And Q Of An Equilateral Triangle PQR Are GMAT Problem Solving
- A Certain Roller Coaster has 3 Cars, and A Passenger is Equally Likely GMAT Problem Solving
- A Manufacturer Produces a Certain Men's Athletic Shoe in GMAT Problem Solving
- In The Figure Shown Below, The Area of Square Region ACEG is 729 GMAT Problem Solving
- How Many Dimes are There in 4x - 1 Cents? (1 dime = 10 cents) GMAT Problem Solving
- In How Many Ways The Letter Of The Word "Family" Can Be When GMAT Problem Solving
- A Fair Coin Is Tossed 4 Times. What Is The Probability Of Getting At GMAT Problem Solving
- In A Sequence 1, 2, 4, 8, 16, 32, ... Each Term After The First Is Twice GMAT Problem Solving
- What Is The Sum Of Odd Integers From 35 To 85, Inclusive? GMAT Problem Solving
- If 2p + 1/p = 4, Then what is the Value of p^3 + 1/8p^3 ? GMAT Problem Solving
- There are 12 Pipes that are Connected to a Tank. Some of them are fill GMAT Problem Solving
- A wire is cut into three equal parts. The resulting segments are then cut GMAT Problem Solving
- If x = -3, What Is The Value Of -3x^2? GMAT Problem Solving
- There Were R Red Balls And Y Yellow Balls In A Bag. Three Red Balls GMAT Problem Solving
- With An Average Speed Of 40 Km/H, A Train Reaches Its Destination On GMAT Problem Solving
- A Photographer Will Arrange 6 People Of 6 Different Heights GMAT Problem Solving
- What Is The Radius Of The Incircle Of The Triangle Whose Sides Measure GMAT Problem Solving
Comments