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

Question

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

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

CareerGeek · Accepted Answer

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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farharajeev · Answer

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)

ScottTargetTestPrep · Answer

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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saad166 · Answer

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

Praful_0810 · Answer

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

So given that," If at least 10% of the club's members participate in neither kickboxing nor rowing"
10% of 212 = 21.2/ Since members cannot be decimal, Minimum value can be 22.

So Maximum participation activity = 212 - 22 = 190

We need to calculate: what's the minimum number of members who participate in both?

We are given that only kickboxing + only rowing + both = 240

So 240 - 190 = 50

So option D is correct answer.

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

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

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