If [x] Denotes the Least Integer Greater Than or Equal to x and [x] = GMAT Problem Solving

Question: If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be true?

1. x = 0
2. 0 <= x < 1
3. 0 < x <= 1
4. -1 <= x < 0
5. -1 < x <= 0

Correct Answer: E

Solution and Explanation
Approach Solution 1:

It is given in the question that [x] denotes the least integer greater than or equal to x and the value of [x] = 0
[x] is defined as the smallest integer greater than or equal to 0; therefore, [x]=0.
As a result, x must be between -1 and 0.
As you know x cannot be equal to -1
because [x] = -1
nor can it be equal to 0
because [x]=0
so, -1< x <= 0
The answer is E which is -1< x <= 0.

Approach Solution 2:

There is another approach to solve this question which is pretty simple and could help in finding the answer more quickly, let us look at the reasoning below-
Least integer GREATER THAN or EQUAL to x means [x] is GREATER THAN or EQUAL to [x] when rounded off to the nearest integer.
Since it is already given that
Given that [x] = 0
So, while [x] can take any value between -1 and 0 (excluding -1 and including 0), it will always equal 0.
so, -1< x <= 0
The answer is E which is -1< x <= 0.

Approach Solution 3:
Given:

•  [x] denotes the least integer greater than or equal to x.

[x] = x, if x is an integer.
And if x is not an integer then [x]= Least integer greater than x.

Now, [x]=0 for x=0 and when -1 < x <0.

Therefore, the correct answer is option E.

“If [x] denotes the least integer greater than or equal to x and [x] =”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018 Quantitative Review".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.

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