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Difficulty:
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93% (01:49) correct
7%
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wrong
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In school V, all students must take at least one of Mathematics, Physics, or Biology. If none of the students took 3 classes, the number of students who took Mathematics class is 18, the number of students who took Physics class is 23, and the number of students who took Biology class is 20. And also 3 students took both Mathematics class and Physics class, 8 students took both Physics class and Biology class, and 6 students took both Biology class and Mathematics class. What is the total number of students in school V?
A. 11
B. 22
C. 33
D. 44
E. 55
A. 11
B. 22
C. 33
D. 44
E. 55
12 Jan 2017, 18:11
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A useful formula for three overlapping sets is as follows.
If you were to count everybody in group 1 and than count everybody in group 2 and then count everybody in group three, you'd end up with a number that is bigger than the actual total, because you would have counted the people in multiple groups more than once.
To make up for the over-counting you'd have to subtract one version of everybody you counted exactly twice, and you'd have to subtract two versions of everybody you counted three times.
That's the logic behind this formula:
Total = Group 1 + Group 2 + Group 3 - ('doubles,' those in 2 groups but not three) - 2('triples,' those in all three groups)
So, here, plugging in, we get:
18 + 23 + 20 - (3 + 8 + 6) - 2(0)
61 - 17 = 44
If you were to count everybody in group 1 and than count everybody in group 2 and then count everybody in group three, you'd end up with a number that is bigger than the actual total, because you would have counted the people in multiple groups more than once.
To make up for the over-counting you'd have to subtract one version of everybody you counted exactly twice, and you'd have to subtract two versions of everybody you counted three times.
That's the logic behind this formula:
Total = Group 1 + Group 2 + Group 3 - ('doubles,' those in 2 groups but not three) - 2('triples,' those in all three groups)
So, here, plugging in, we get:
18 + 23 + 20 - (3 + 8 + 6) - 2(0)
61 - 17 = 44
16 Jan 2024, 19:32
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Aren't you also supposed to add 'Neither'?
I though the total formula follows as:
Group1 + Group2 + Neither - Both = Total
I though the total formula follows as:
Group1 + Group2 + Neither - Both = Total
