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

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

by gmattesttaker2 » Mon Jun 02, 2014 10:02 pm
Hello,

Can you please tell me how to solve this:

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

OA: B

Thanks a lot,
Sri

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by sukriti2hats » Mon Jun 02, 2014 11:02 pm
Hi gmattesttaker2,

This is a problem based on greatest integer function [x] . In greatest integer function, x takes the value of the greatest nearest integer. For example if x=2.3 then [x]=[2.3]=3 and if x=-2.3 then [-2.3] = -2.

In this case it is given [x/2]=0, this can happen only when x/2 lies between -1 and 0: -1< x/2 < 0
In the given options, only x=-3/2 satisfies this condition : -3/2 divided by 2 = -3/4 = -0.75
[-0.75] = 0

Cheers
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by GMATGuruNY » Tue Jun 03, 2014 1:59 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

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 can PLUG IN THE ANSWERS, which represent the value of x.
When the correct answer choice is plugged in, [x/2] = 0.

Answer choice D: 1
[x/2] = [1/2] = the least integer greater than or equal to 1/2 = 1.
Eliminate D.
The correct answer must SMALLER.

Answer choice B: -3/2
[x/2] = [ (-3/2)/2 ] = [-3/4] = the least integer greater than or equal to -3/4 = 0.
Success!

The correct answer is B.
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by [email protected] » Tue Jun 03, 2014 2:55 am
Hey Sri,

Now that you've seen a couple of approaches, here are two more questions to practice with:
- https://www.beatthegmat.com/ds-t276593.html
- https://www.beatthegmat.com/number-prope ... 71768.html

Cheers,
Brent

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by gmattesttaker2 » Wed Jun 04, 2014 6:18 pm
sukriti2hats wrote:Hi gmattesttaker2,

This is a problem based on greatest integer function [x] . In greatest integer function, x takes the value of the greatest nearest integer. For example if x=2.3 then [x]=[2.3]=3 and if x=-2.3 then [-2.3] = -2.

In this case it is given [x/2]=0, this can happen only when x/2 lies between -1 and 0: -1< x/2 < 0
In the given options, only x=-3/2 satisfies this condition : -3/2 divided by 2 = -3/4 = -0.75
[-0.75] = 0

Cheers
Sukriti
Hi Sukriti,

Thanks for the explanation. I was just wondering if the in-equality will be -1 < x/2 <= 0 since if x/2 = 0 then [x/2] =  = 0 since [x] denotes the least integer greater than or equal to x?

Thanks,
Sri

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by gmattesttaker2 » Wed Jun 04, 2014 6:41 pm
[email protected] wrote:Hey Sri,

Now that you've seen a couple of approaches, here are two more questions to practice with:
- https://www.beatthegmat.com/ds-t276593.html
- https://www.beatthegmat.com/number-prope ... 71768.html

Cheers,
Brent
Hello Brent,

Thanks a lot for the practice questions.

Best Regards,
Sri

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by [email protected] » Fri Jan 05, 2018 7:27 am

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 -3/4 is 0.

Answer: B

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by [email protected] » Sun Jan 20, 2019 6:27 am
gmattesttaker2 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
[8.9] = 9
[-1.4] = -1
[-13.6] = -13

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

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

Answer: B

Cheers,
Brent

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by [email protected] » Sun Jan 20, 2019 12:03 pm
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
[.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
[-.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: B

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Rich

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