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# If denotes the greatest integer less than or equal to x then

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Intern
Joined: 24 Jun 2009
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If denotes the greatest integer less than or equal to x then [#permalink]

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22 Jul 2009, 15:32
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If [x] denotes the greatest integer less than or equal to x then is [x]=0?
a) [2x]=0
b0 [3x]=0

Manager
Joined: 03 Jul 2009
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Kudos [?]: 83 [2] , given: 13

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22 Jul 2009, 15:45
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bassiseema,

I think the answer is D.

1) If [2x]=0
Then, following the definition of [x]
We know that if [2x] = 0, this means that 0<2x<1
Resolving we have 0<x<0.5
For any value of x, we will have [x] = 0

2) Following the same reasoning, we get almost the same results
0<3x<1
0<x<0.3333
For any value of x, we will have [x] = 0

Thus each one is sufficient.

PS.: If that is right consider a kudo I am trying to get kudos enough to have access to the tests...
Intern
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22 Jul 2009, 16:53
hi could you please explain how you got 0<2x<1 and 0<3x<1.
I am not able to follow this bit. thanks!
Manager
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22 Jul 2009, 17:11
I got from the definition of [x]

[x] says that it is the greatest integer less then or equal to x.

In other words, this means that
for x = 4.5, then [x] = 4
for x = 11.5, then [x] = 11
for x = 1546.456465, then [x] = 1546
for x = 5, then [x] = 5
for x = 0.9, then [x] = 0
for x = 0.000015466879, then [x] = 0

So if [anything]=0, this means that the "anything" is "0.something"
So if [2x]=0, this means that "2x" is "0.something", or "2x" is between 0 and 1.
That is why I wrote $$0<2x<1$$

Am I clear now, or I just make it worst? Let me know! Sometimes it is hard to explain only through text.
Intern
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22 Jul 2009, 17:20
understood. kind of rounding down. is that correct?
thanks!
but i could not understand this from "the greatest integer less than equal to x"
Manager
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22 Jul 2009, 17:30
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You got it.

"the greatest integer less than equal to x" = rounding down.

Thanks as well
Manager
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22 Jul 2009, 20:45
Thanks for the explaination.
Director
Joined: 01 Apr 2008
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Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
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23 Jul 2009, 00:42
bassiseema wrote:
If [x] denotes the greatest integer less than or equal to x then is [x]=0?
a) [2x]=0
b0 [3x]=0

Another approach..

a) [2x] = 0, here we know that the greatest integer less than or equal to 2 is 2.
=> 2[x]= 0, i.e. 2 multiplied by some real number is 0 => [x] is 0.
b) Same as a.
>> wrong approach

We cannot assume that this operation can be split. i.e we cannot say [2x] = 2[x]...we can only do that if [] indicates multiplication..here it is 'some function'.

So, we can only use the approach mentioned by coelholds (+1 for you)
Though, I got the right answer , approach is wrong..sorry for the confusion
But it makes concepts more clear
Re: Greatest integer   [#permalink] 23 Jul 2009, 00:42
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