Question 64046
Ignore student gender and tally all information as students
S = Soccer B = baseball T = Tennis
S = 25
S + B = 7
B = 14
T = 9
S + T = 6
B + T = 4
S + B + T = 2
Draw up the 3 circle Venn Diagram. Put 2 (S + B + T) in the central section.
The two sections between B and T total 4. One already has a 2 so the other section must be 2 as well.
The two sections between S and B total 7. One already has a 2 so the other must be 5.
The two sections between S and T total 6. One already has a 2 so the other must be 4.
The soccer total is 25 and the three numbers already in the soccer sections are 4, 2 and 5. So the last section in soccer is 14.
Similarly you should be able to work out the last section of baseball is 5 and the last section of tennis is 1.
Students playing only one sport = 14 + 5 + 1 = 20.
Students playing soccer but not tennis or baseball = 14.
Students playing soccer and baseball but not tennis = 5


Redraw the Venn Diagram using girl only data.
s + B = 3
B = 4
S + T = 3
B + T = 1
S + B + T = 1
The central section is 1.
The two sections between B and T total 1. One already has a 1 so the other section must be 0.
The two sections between S and B total 3. One already has a 1 so the other must be 2.
The two sections between S and T total 3. One already has a 1 so the other must be 2.
B = 4 and the three baseball sections filled in total 3 so the last baseball section must be 1.
Therefore 1 girl played baseball only.