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Maximum number of elements in a set

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by Rahul@gurome » Mon Jul 26, 2010 8:15 pm
Solution:
Let us check for the possibilities of elements of B.
Now since the sum of no two elements is 203, there will be some constraints while selecting the elements.
Let 0, 1 and 2 belong to B. Then there is no other element with which they combine to give a sum of 203. So they can easily belong to B without limiting the presence of any other element.
Let 3 belong to B. Then 200 cannot belong to B because their sum will give 203.
So either 3 or 200 will be in B.
Similarly either 4 or199, 5 or 198, 6 or 197............100 or 103, 101 or 102 can belong to B.
So the possible elements of B are {0,1,2, 3,...............101} or {0,1,2, 200, 199, 198............,102}.
In any case there will be a maximum of 102 elements in B.

The correct answer is (C).
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by selango » Mon Jul 26, 2010 8:15 pm
200+3=203
.
.
.
.
103+100
102+101


In set B, the integers from 102 to 200 or 3 to 101 must not included such that the sum of no two integers in B is 203.

99 integers must not be included.

Remaining in set B=201-99=102

Pick C
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by winnerhere » Wed Jul 28, 2010 9:45 am
Thanks guys :)
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