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

Question

If   denotes the least integer greater than or equal to x and   = 0, which of the following could be the value of x?

A. -2
B. -3/2
C. 1/2
D. 1
E. 2

https://gmatclub.com/forum/download/file_private.php?id=88386

Bunuel · Accepted Answer

Some function rounds UP a number to the nearest integer. For example =2, =2, =-1, ... Hence, since = 0, then it must be true that -1<\frac{x}{2}\leq{0} : any number from this range when rounded up gives 0. -1<\frac{x}{2}\leq{0} --> -2if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html is-x-an-odd-integer-1-x-2-2x-99856.html for-all-z-denotes-the-least-integer-greater-than-or-110561.html denotes-to-be-the-least-integer-no-less-than-x-is-130841.html for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html if-is-the-greatest-integer-less-than-or-equal-to-x-what-144277.html how-x-become-fraction-if-its-been-said-an-integer-94687.html awkward-ds-105416.html help-data-sufficiency-equation-and-inequalities-99856.html if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html denotes-to-be-the-least-integer-no-less-than-x-is-130841.html is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html if-denotes-the-greatest-integer-less-than-or-equal-to-z-162078.html if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html for-all-z-denotes-the-least-integer-greater-than-or-equ-167640.html Hope it helps.

BrentGMATPrepNow · Answer

First, let's take a moment to get a good idea of what this strange notation means. 
A few examples: 
  = 6 
  = 3 
  = 9 
  = -1 
  = -13

So, if   = 0, then we know that  -1 < x/2 ≤ 0 
Multiply all sides of the inequality by 2 to get:   -2 < x ≤ 0

Check the answer choices....
Only -3/2 falls inside that range.

Answer: B

Cheers,
Brent

GeorgeA023 · Answer

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.

EMPOWERgmatRichC · Answer

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   is the LEAST INTEGER greater than or equal to X. Thus...

= 2
  = 1
  = -1
Etc.

When we're told that   = 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
  = 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  ?

Final Answer:  B

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

mcelroytutoring · Answer

Attached is a visual that should help.

A)    =   = -1

B)    = 0

shashankism · Answer

Since   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   = 0 
-1 < x/2 < = 0
-2 < x <= 0

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

Answer B..

ScottTargetTestPrep · Answer

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

Let’s analyze each answer choice:

A) -2

=

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

B) -3/2

=

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

Answer: B

Yesul · Answer

I just have question

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

EMPOWERgmatRichC · Answer

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   is the LEAST INTEGER greater than or equal to X. Thus...

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

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

Basshead · Answer

= 1 
   = 2 
   = -1

Lets go through the choices:

A.   =   = -1

B.   =   = 0. CORRECT

C.   =   = 1

D.   = 1

E.   = 1

Answer is B.

KarishmaB · Answer

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   will be equal to x or greater than it.

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

You are given that   = 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)

TargetMBA007 · Answer

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

Bunuel · Answer

_________________________
Added the tag. Thank you!

bumpbot · Answer

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

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