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![If [x] denotes the greatest integer less than or equal to x](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If [x] denotes the greatest integer less than or equal to x"){kind=icon}
06 Mar 2020, 10:39
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Bunuel
Asad
Thanks for the response Bunuel
I am talking when the scenario is -1 <x≤ 0 (not -1 <x< 0). So, what if the value of x=0? Shouldn't it be the greatest integer less than or equal to x, is [x] = 0?
Thanks_-
I am so sorry to bother you @bunuel!I am talking when the scenario is -1 <x≤ 0 (not -1 <x< 0). So, what if the value of x=0? Shouldn't it be the greatest integer less than or equal to x, is [x] = 0?
Thanks_-
If x = 0, then then the greatest integer less than or equal to 0 is 0 itself. So, \(0\leq{x}<1\) in the solution above is correct.
Thank you..
06 Mar 2020, 10:51
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musabber
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1
hello GMAT guy!!
well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...
well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...
Here, the notation [x] is to make the problem harder than it seems. Just replace [x] with another variable which is easier and more natural to grasp - y. The question can be rephrased as: "If y denotes the greatest integer less than or equal to x, is y = 0 ?"
Integers comprise of the set of numbers which can be written without a fractional component. They can be positive, negative or zero.
Let's go to the follow on equations given. The first equation can be solved as x= 2/3. In which case, y would be 0 (greatest integer less than or equal to x). So, we can answer this question with option (1) alone.
The second inequality equation mentions x is in between 0 and 1. Hence, y would be 0 again because it is the greatest integer less than or equal to x which is a fraction between 0 and 1. Hence, option (2) alone is also sufficient to answer the question.
So the answer to this question is option D - EACH statement ALONE is sufficient.
11 Mar 2020, 09:45
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Bunuel
musabber
hello GMAT guy!!
well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1
well i m confused about a certain problem [ 100th data sufficieny on OG 12th ed] here they define x as a integer but in the explanation they solve it as if x is is a fraction not an integer...can any one have better explanation...
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?[data suff prob number 100 from OG 12th edition]
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
Here \(x\) is not said to be an integer. Stem defines some function, represented by the symbol \([]\), as the function which rounds down any number to an integer value:
\([3.4]=3\), \([2]=2\), \([-7.5]=-8\), ...
Q: is \([x]=0\)? Or is \(0\leq{x}<1\)? Thanks in advance!
(1) 5x + 1 = 3 + 2x --> \(x=\frac{2}{3}\) --> \([\frac{2}{3}]=0\). Sufficient.
(2) 0 < x < 1 --> any \(x\) from this range will round down to 0, so \([x]=0\). Sufficient.
Answer: D.
Hope it helps.
Hi Bunuel
I read your responses to other similar questions but I'm not able to grasp how you came up with this equation \(0\leq{x}<1\)
Is it just by logically understanding the definition of what [] means or some other way as in how we solve inequalities?
