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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gmattesttaker2
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sukriti2hats
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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
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
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GMATGuruNY
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We can PLUG IN THE ANSWERS, which represent the value of x.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
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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Brent@GMATPrepNow
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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
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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gmattesttaker2
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Hi Sukriti,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
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] = 0 since [x] denotes the least integer greater than or equal to x?
Thanks,
Sri
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gmattesttaker2
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Hello Brent,Brent@GMATPrepNow 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
Thanks a lot for the practice questions.
Best Regards,
Sri
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Jeff@TargetTestPrep
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We are given that [x] denotes the least integer greater than or equal to x and [x/2] = 0.
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
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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Brent@GMATPrepNow
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First, let's take a moment to get a good idea of what this strange notation means.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
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
Cheers,
Brent
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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: B
GMAT assassins aren't born, they're made,
Rich
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: B
GMAT assassins aren't born, they're made,
Rich
