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555-605 (Medium)|   Functions and Custom Characters|                           
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If [x] denotes the least integer greater than or equal to x 25 Nov 2022, 13:47
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Bunuel
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Question: is \([x]=0\)? --> is \(-1<x\leq{0}\)?

(1) -1< x< 1. Not sufficient.
(2) x < 0. Not sufficient.

(1)+(2) -1<x<0. Sufficient.

Answer: C.

Similar questions to practice:
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https://gmatclub.com/forum/help-data-su ... 99856.html
https://gmatclub.com/forum/if-denotes-t ... 94687.html
https://gmatclub.com/forum/denotes-to-b ... 30841.html

Hope it helps.
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does the symbol, [], always denote this operation or is it just for this question?
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If [x] denotes the least integer greater than or equal to x 20 Jan 2023, 01:37
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Stanindaw
Bunuel
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [-1.5]=-1, ...

Question: is \([x]=0\)? --> is \(-1<x\leq{0}\)?

(1) -1< x< 1. Not sufficient.
(2) x < 0. Not sufficient.

(1)+(2) -1<x<0. Sufficient.

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/how-x-become ... 94687.html
https://gmatclub.com/forum/awkward-ds-105416.html
https://gmatclub.com/forum/help-data-su ... 99856.html
https://gmatclub.com/forum/if-denotes-t ... 94687.html
https://gmatclub.com/forum/denotes-to-b ... 30841.html

Hope it helps.


does the symbol, [], always denote this operation or is it just for this question?
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Hello Stanindaw,



The function [x] is generally used in GMAT to denote one of the following functions:

  1. Greatest integer function: Per this definition, [x] denotes the greatest integer less than or equal to x.
    For example: If x = 2.4, then [x] = the greatest integer less than or equal to 2.4 = 2.

    OR
  2. Least integer function: [x] denotes the least integer greater than or equal to x. (Note: This is the definition used in this question.)
    For example: If x = 2.4, then [x] = the least integer greater than or equal to 2.4 = 3.

To summarize, the function [x] does not have a strict definition that is all-time adhering. You must check the definition provided in the question and use just that to get the value of [x].


Hope this helps!


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Ashish,
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If [x] denotes the least integer greater than or equal to x 11 Feb 2024, 01:16
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I agree with this response. In some questions, where one is not sure of the logic or definition presented, one can always test a few values to get a sense of the definition/logic. It may seem very time-consuming, but with practice, it comes naturally. 
CrackverbalGMAT
The least integer function takes any real number as the input; the output is the smallest integer greater than/equal to the number provided as the input.
For example, if x = 3.7, [x] = 4 since the smallest integer bigger than 3.7 is 4.

Strategy to solve least integer functions:

1) Plot the given value on the number line
2) The least integer for the given value will be the closest integer to the right, on the number line.

The original question stem, “Is [x] = 0?” can be rephrased as “Is -1<x≤0?”.

Statement I alone is insufficient to answer the question. Answer options A and D can be eliminated. Possible answer options are B, C or E

Statement II alone is insufficient to answer the question. Answer option B can be eliminated. Possible answer options are C or E.

Combining the data given in statements I and II, the common range is -1<x<0. This is sufficient to answer the question with a definite YES.
Statements I and II are sufficient when taken together. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!
Aravind B T
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If [x] denotes the least integer greater than or equal to x 18 Apr 2025, 10:16
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[x] denotes the least integer greater than or equal to x, is [x] = 0?

For [x] = 0, x should be -1<x<=0

Statement 1
-1< x< 1
[x] = 0 or 1 depending if x <0 or x>0
Insufficient

Statement 2
x < 0
This could be any value -1,-2,-100,...
Insufficient

Combined, we have -1< x< 0
This is what we needed
Sufficient


macwanjason
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

(1) -1< x< 1
(2) x < 0
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If [x] denotes the least integer greater than or equal to x 24 Feb 2026, 12:56
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macwanjason
If [x] denotes the least integer greater than or equal to x, is [x] = 0?

(1) -1< x< 1
(2) x < 0
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