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
[x] denotes the least integer greater than or equal to x ...
This topic has expert replies

 Legendary Member
 Posts: 641
 Joined: 14 Feb 2012
 Thanked: 11 times
 Followed by:8 members

 Junior  Next Rank: 30 Posts
 Posts: 20
 Joined: 30 May 2014
 Thanked: 1 times
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
 GMATGuruNY
 GMAT Instructor
 Posts: 15532
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1897 members
 GMAT Score:790
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.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15422
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
Hey Sri,
Now that you've seen a couple of approaches, here are two more questions to practice with:
 https://www.beatthegmat.com/dst276593.html
 https://www.beatthegmat.com/numberprope ... 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/dst276593.html
 https://www.beatthegmat.com/numberprope ... 71768.html
Cheers,
Brent

 Legendary Member
 Posts: 641
 Joined: 14 Feb 2012
 Thanked: 11 times
 Followed by:8 members
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 inequality 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

 Legendary Member
 Posts: 641
 Joined: 14 Feb 2012
 Thanked: 11 times
 Followed by:8 members
Hello Brent,[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/dst276593.html
 https://www.beatthegmat.com/numberprope ... 71768.html
Cheers,
Brent
Thanks a lot for the practice questions.
Best Regards,
Sri
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 1460
 Joined: 09 Apr 2015
 Location: New York, NY
 Thanked: 39 times
 Followed by:20 members
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
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15422
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
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 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
GMAT/MBA Expert
 [email protected]
 Elite Legendary Member
 Posts: 10347
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:508 members
 GMAT Score:800
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