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Question

The minimum possible value of |x1|+|x2|++|x100| is

A
4900
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B
2500
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C
2550
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D
2450
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Solution

The correct option is B 2500
Critical points are 1,2,3,,99,100
Minimum value occurs at x=median{1,2,3,,99,100}=50 or 51
For x=50,
|x1|+|x2|++|x100|
=49+48++1+0+1++49+50
=2(1+2++49)+50
2500

Note: The minimum value occurs at any value in [50,51]

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