Neither = at least 10% = 21.2 = 22 members minimum

Formula: Total - Neither = A + B - Both
—> Both = 130 + 110 - 212 + Neither
—> Both = 28 + Neither
—> Minimum value of Both = 28 + 22 = 50

IMO Option D

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Total members = kick boxing members + rowing members - both +neither

212 = 130 + 110 - both + neither

-28 = - both +neither

28= both - neither

28 + neither = both.

thus for both to be minimum, neither should be minimum. Minimum of neither is \(\frac{10}{100}\) x 212 = 21.2, i.e., 22 members.

then the minimum for both = 28+22= 50 (D)

Solution:

We can use the formula:

Total = Set A + Set B - Both + Neither

Since we are asking to determine Both, we can isolate it as:

Both = Set A + Set B + Neither - Total

Since at least 10% of the club’s members participate in neither kickboxing nor rowing, at least 22 members participate in neither. Since we need the minimum number of members who participate in Both, we want to minimize Neither also (notice that Total, Set A and Set B are fixed). So we should let Neither = 22 and thus we have:

Both = 130 + 110 + 22 - 212

Both = 50

Answer: D

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