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  4. Suppose that the number of elements in the set S is 105 and that S is split into n subsets 11m + 2 elements each. If m is an integer, then m is

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Q. Suppose that the number of elements in the set S is 105 and that S is split into n subsets 11m + 2 elements each. If m is an integer, then m is

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Solution:

Number of elements in each set = 11m+2
Number of elements in n subsets = n(11m+2)
$n(11 m + 2) = 105 = 21 \times 5 = 3 \times 7 \times 5$
$ n = 3 \, \Rightarrow \, 11 m + 2 = 35 \, \Rightarrow m = 3$