swerve wrote:
The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?
A. 68
B. 69
C. 74
D. 79
E. 84
The values in the chart DOUBLE-COUNT any student who belongs to 2 of the 3 clubs.
The totals for chess and drama -- 40 and 30 -- double-count the
10 students who belong to both chess AND drama.
The totals for chess and math -- 40 and 25 -- double-count the
5 students who belong to both chess AND math.
The totals for drama and math -- 30 and 25 -- double-count the
6 students who belong to both drama AND math.
Since the students in red have been double-counted, they must be SUBTRACTED from the total.
Resulting equation:
Number of students = (total in chess) + (total in drama) + (total in math) - (red students who have been double-counted).
Thus:
Number of students = 40 + 30 + 25 - (10+5+6) = 74.
The correct answer is
C.
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