GMAT 2008, p.362

[mehrasa]

The table below shows the enrollment in
various classes at a certain college.
Class Number of Students
Biology 50
Physics 35
Calculus 40
Although no student is enrolled in all three
classes, 15 are enrolled in both Biology and
Physics, 10 are enrolled in both Biology and
Calculus, and 12 are enrolled in both Physics
and Calculus. How many different students
are in the three classes?
A. 51
B. 88
C. 90
D. 125
E. 162

any help?

[GMATGuruNY]

The table below shows the enrollment in
various classes at a certain college.
Class Number of Students
Biology 50
Physics 35
Calculus 40
Although no student is enrolled in all three
classes, 15 are enrolled in both Biology and
Physics, 10 are enrolled in both Biology and
Calculus, and 12 are enrolled in both Physics
and Calculus. How many different students
are in the three classes?
A. 51
B. 88
C. 90
D. 125
E. 162

any help?

Here's the big idea with overlapping groups: subtract the overlaps.

In the problem above, for example, there is an overlap between the biology group and the physics group: 15 students study both subjects. Thus, when we count the total number in the bio group (60) and the total number in the physics group (35), the 15 students who take both classes get counted twice. So we need to subtract these 15 students from our total so that they don't get double-counted.

Thus, to solve the problem above, we need to add together the number of students in all the classes and subtract all the overlaps so that we don't double-count the students who take 2 classes:

50+35+40-15-10-12 = 88.

The correct answer is B.

[rishab1988]

Let P denote only Physics
B denote only Biology
C denote only Calculus

a(B+P)=15
b(P+C)=12
c(B+C)=10

We know from Question

B+a+c=50
B=50-15-10=25

P+a+b=35
P=35-15-12=8

C+b+c=40
C=40-12-10=18

Therefore, P+B+C+a+b+c= 25+8+18+15+12+10=88

[goyalsau]

The table below shows the enrollment in
various classes at a certain college.
Class Number of Students
Biology 50
Physics 35
Calculus 40
Although no student is enrolled in all three
classes, 15 are enrolled in both Biology and
Physics, 10 are enrolled in both Biology and
Calculus, and 12 are enrolled in both Physics
and Calculus. How many different students
are in the three classes?
A. 51
B. 88
C. 90
D. 125
E. 162

any help?

If you have problem in overlapping sets , you must go through this link, Rahul Has given a brilliant explanation,
https://www.beatthegmat.com/venn-diagram ... tml#316739