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

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Joined: 10 Jan 2013
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If [x] denotes the least integer greater than or equal to x  [#permalink]

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Updated on: 26 May 2014, 02:22
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Difficulty:

45% (medium)

Question Stats:

64% (01:25) correct 36% (01:28) wrong based on 877 sessions

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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?

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

Originally posted by GeorgeA023 on 25 May 2014, 18:02.
Last edited by Bunuel on 26 May 2014, 02:22, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 60646
Re: If [x] denotes the least integer greater than or equal to x  [#permalink]

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26 May 2014, 02:48
12
16
GeorgeA023 wrote:
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?

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

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

Hence, since [x/2] = 0, then it must be true that $$-1<\frac{x}{2}\leq{0}$$: any number from this range when rounded up gives 0.

$$-1<\frac{x}{2}\leq{0}$$ --> $$-2<x\leq{0}$$, Only option B is in this range.

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Hope it helps.
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Re: If [x] denotes the least integer greater than or equal to x  [#permalink]

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26 May 2014, 10:06
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.
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Re: If [x] denotes the least integer greater than or equal to x  [#permalink]

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05 Dec 2015, 11:32
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3
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]?

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

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17 May 2016, 18:44
1
Attached is a visual that should help.

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

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

Screen Shot 2016-05-17 at 6.42.19 PM.png [ 148.14 KiB | Viewed 16900 times ]

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Re: If [x] denotes the least integer greater than or equal to x  [#permalink]

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02 Oct 2017, 23:31
1
GeorgeA023 wrote:
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?

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

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..

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

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05 Oct 2017, 10:17
2
2
GeorgeA023 wrote:
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?

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

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

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.

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Re: If [x] denotes the least integer greater than or equal to x  [#permalink]

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20 Jan 2019, 07:35
3
Top Contributor
GeorgeA023 wrote:
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?

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

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

Only -3/2 falls inside that range.

Cheers,
Brent
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Re: If [x] denotes the least integer greater than or equal to x   [#permalink] 20 Jan 2019, 07:35
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