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Question

Let A1,A2,...,Am be non-empty subsets of {1,2,3,...,100} satisfying the following conditions:
(1) the numbers |A1|,|A2|,...,|Am| are distinct ;
(2) A1,A2,...,Am are pairwise disjoint.
(Here |A| denotes the number of elements in the set A).
Then the maximum possible value of m is

A
13
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B
14
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C
15
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D
16
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Solution

The correct option is A 13
The possibility is,|A1|=1;|A2|=2;|A3|=3;...;|Am|=m1+2+3+...+m100 (all are disjoint)m(m+1)2100m(m+1)200Since, mZm13Max. possible value of m=13

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