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

Bunuel


Thank you for the response. When I was taking the GMAT Prep test yesterday and this question appeared, I just could not figure out what it was asking.

Thank you for the explanation.

Hi All,

This is an example of a 'Symbolism' question - the prompt 'makes up' a math symbol, tells you what it means, then asks you to perform a calculation using it. When dealing with these types of symbols, it often helps to jot down a few examples, so that you understand the work that will be required of you when you deal with the actual question that is asked.

Here, we're told that [X] is the LEAST INTEGER greater than or equal to X. Thus...

[2] = 2
[.5] = 1
[-1.5] = -1
Etc.

When we're told that [X/2] = 0, this implies that whatever is inside the symbol is a limited range that is LESS THAN OR EQUAL TO 0....

For example:
[0] = 0
[-.5] = 0
[-.9999] = 0
Etc.

With this information, finding the value of X shouldn't be too hard...which answer will fit this pattern when you plug it into [X/2]?

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Attached is a visual that should help.

A) \([ \frac{-2}{-1} ] = [ -1 ] = -1\)

B) \([ \frac{-3}{4} ] = 0\)

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 i decimal part of x

So [x/2] = 0
-1 < x/2 < = 0
-2 < x <= 0

Only -3/2 lies in between this range..

Answer B..

We are given that [x] denotes the least integer greater than or equal to x and [x/2] = 0.

Let’s analyze each answer choice:

A) -2

[-2/2] = [-1]

This is not correct since the least integer greater than or equal to -1 is -1, which is not 0.

B) -3/2

[(-3/2)/2] = [-3/4]

This is correct since the least integer greater than or equal to -3/2 is 0.

Answer: B

I just have question

If [x] denotes a least number greater or equal to x, then doesn't [x] need to be bigger than x?
For example: [3.1] = 3; [4.3] = 4

Hi Yesul,

This is an example of a 'Symbolism' question - the prompt 'makes up' a math symbol, tells you what it means, then asks you to perform a calculation using it. When dealing with these types of symbols, it often helps to jot down a few examples, so that you understand the work that will be required of you when you deal with the actual question that is asked.

Here, we're told that [X] is the LEAST INTEGER greater than or equal to X. Thus...

[2].... so what is the least integer that is greater than or equal to 2?.... [2] = 2
[0.5]... so what is the least integer that is greater than or equal to 0.5?.... [0.5] = 1
[-1.5]... so what is the least integer that is greater than or equal to -1.5?.... [-1.5] = -1
Etc.

GMAT assassins aren't born, they're made,
Rich

\([1] = 1\)
\([1.2] = 2\)
\([-1.3] = -1\)

Lets go through the choices:

A. [-2/2] = [-1] = -1

B. [-3/2/2] = [-3/4] = 0. CORRECT

C. [1/2/2] = [1/4] = 1

D. [1/2] = 1

E. [2/2] = 1

Answer is B.

What you are thinking of is the greatest integer less than or equal to x.
What we have here is the least integer greater than or equal to x.

So [x] will be equal to x or greater than it.

Say x = 3.1. Then [x] = 4
Say x = 4.3. Then [x] = 5

You are given that [something] = 0
This means something is either 0 or between -1 and 0.
So x/2 is either 0 or between -1 and 0.
When x = -3/2, x/2 is -3/4 which is between -1 and 0.

Answer (B)

Bunuel - Tag can be updated - source of this is Gmatprep

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Added the tag. Thank you!