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# M19 Q36

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Senior Manager
Joined: 20 Feb 2008
Posts: 295
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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12 Nov 2008, 22:26
[x] denotes biggest integer smaller than $$x$$ . Is $$[x] \gt [-x]$$ ?

1. $$x = [x] + 1$$
2. $$x + 1 \gt 0$$
SVP
Joined: 17 Jun 2008
Posts: 1548

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12 Nov 2008, 22:44
It should be E.

From stmt1: x is an integer. But, if x is a positive integer, the inequality is true. However, if x is a negative integer, the inequality is not true.

From stmt2: x > -1. Again, for positive x, inequality is true and for negative x, inequality is not true.

Combining both, x > -1 and x is integer.

Hence, x = 0,1,2,3,4,.....

For x > 0, inequality holds true. However, for x = 0, it does not hold true.
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Joined: 29 Aug 2007
Posts: 2473

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12 Nov 2008, 22:52
ventivish wrote:
[x] denotes biggest integer smaller than $$x$$ . Is $$[x] \gt [-x]$$ ?

1. $$x = [x] + 1$$
2. $$x + 1 \gt 0$$

1: x is an integer and it is true for every integer. not suff.
2: if x+1 > 0, x is >-1. nsf..

togather, x is neither - nor + fraction but it could be 0 or +ve integer.

if x is 0, [x] = -1 and [-x] = 1. so [x] < [-x].
if x is 1, [x] = 0 and [-x] = 0. so [x] = [-x]
if x is 2, [x] = 1 and [-x] = -1. so [x] > [-x]
nsf...

got E...
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Manager
Joined: 16 Feb 2011
Posts: 194
Schools: ABCD

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20 Jul 2012, 08:44
What does x = [x] + 1 mean?

If x = 2 (say integer), [x] = 2 => x = 2+1 = 3; how is that possible ?

Thoughts?
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)

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20 Jul 2012, 08:54
voodoochild wrote:
What does x = [x] + 1 mean?

If x = 2 (say integer), [x] = 2 => x = 2+1 = 3; how is that possible ?

Thoughts?

[2] = 1, being the greatest integer smaller than 2. But [2.5] = 2.
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Re: M19 Q36   [#permalink] 20 Jul 2012, 08:54
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# M19 Q36

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