# The maximum number of elements that can be drawn from {1,2,3,.......,2001,2002,2003,2004} such that no two of them add up to 2005 is A)1002 B)1003 C)1004 D)1005 E)2004

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There are only 1002 pairs of numbers that add up to 2005:(1,2004),(2,2003),...........,(1002,1003).Now by just picking one number from each pair we get 1002 numbers such that no two of the numbers add up to 2005.It is easy to see that 1003 numbers with this property can't be drawn.