Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

Answer 2

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