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# In a recreation club with 212 members, 130 participate in kickboxing

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Re: In a recreation club with 212 members, 130 participate in kickboxing [#permalink]
Bunuel wrote:
In a recreation club with 212 members, 130 participate in kickboxing and 110 participate in rowing. If at least 10% of the club's members participate in neither kickboxing nor rowing, what's the minimum number of members who participate in both?

A. 22
B. 38
C. 49
D. 50
E. 60

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

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Re: In a recreation club with 212 members, 130 participate in kickboxing [#permalink]
Dillesh4096 wrote:
Bunuel wrote:
In a recreation club with 212 members, 130 participate in kickboxing and 110 participate in rowing. If at least 10% of the club's members participate in neither kickboxing nor rowing, what's the minimum number of members who participate in both?

A. 22
B. 38
C. 49
D. 50
E. 60

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

Pls Hit kudos if you like the solution

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sir why is 21.2 rounded to 22 shouldnt it be 21 as it will be the minimum members who dont take part in either
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Re: In a recreation club with 212 members, 130 participate in kickboxing [#permalink]
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Re: In a recreation club with 212 members, 130 participate in kickboxing [#permalink]
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