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

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

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New post Updated on: 26 May 2014, 02:22
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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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Re: If [x] denotes the least integer greater than or equal to x  [#permalink]

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New post 26 May 2014, 02:48
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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.

Answer: B.

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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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New post 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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New post 05 Dec 2015, 11:32
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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:

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

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

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

B) \([ \frac{-3}{4} ] = 0\)
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Screen Shot 2016-05-17 at 6.42.19 PM.png
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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New post 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..

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

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New post 05 Oct 2017, 10:17
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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.

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

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New post 20 Jan 2019, 07:35
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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

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

Answer: B

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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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