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Bunuel
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There are 20 students participating in an after-school program offerin 13 May 2019, 00:55
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72% (02:13) correct 28% (02:25) wrong based on 268 sessions

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There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are 10 students taking yoga, 13 taking bridge, and 9 taking painting. There are 9 students taking at least two classes. How many students are taking all three classes?

A. 1
B. 2
C. 3
D. 4
E. 5
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C
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There are 20 students participating in an after-school program offerin 13 May 2019, 02:14
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Bunuel
There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are 10 students taking yoga, 13 taking bridge, and 9 taking painting. There are 9 students taking at least two classes. How many students are taking all three classes?

A. 1
B. 2
C. 3
D. 4
E. 5
Show more

solve using formula for three set
total = a+b+c-both-all-neither
20=10+13+9-9-all
-3=-all
all= 3
IMO C
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There are 20 students participating in an after-school program offerin 03 Feb 2020, 01:57
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Bunuel
There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are 10 students taking yoga, 13 taking bridge, and 9 taking painting. There are 9 students taking at least two classes. How many students are taking all three classes?

A. 1
B. 2
C. 3
D. 4
E. 5

solve using formula for three set
total = a+b+c-both-all-neither
20=10+13+9-9-all
-3=-all
all= 3
IMO C
Show more

Archit3110

can u plz explain a more above highlighted formula
or give me link expaining same :)

thx
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There are 20 students participating in an after-school program offerin 03 Feb 2020, 02:03
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Rohit2015
please see below link for chapter theory on venn diag
https://gmatclub.com/forum/gmat-math-book-87417.html

Rohit2015
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Bunuel
There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are 10 students taking yoga, 13 taking bridge, and 9 taking painting. There are 9 students taking at least two classes. How many students are taking all three classes?

A. 1
B. 2
C. 3
D. 4
E. 5

solve using formula for three set
total = a+b+c-both-all-neither
20=10+13+9-9-all
-3=-all
all= 3
IMO C

Archit3110

can u plz explain a more above highlighted formula
or give me link expaining same :)

thx
Show more
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There are 20 students participating in an after-school program offerin 03 Feb 2020, 03:28
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Bunuel
There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are 10 students taking yoga, 13 taking bridge, and 9 taking painting. There are 9 students taking at least two classes. How many students are taking all three classes?

A. 1
B. 2
C. 3
D. 4
E. 5

solve using formula for three set
total = a+b+c-both-all-neither
20=10+13+9-9-all
-3=-all
all= 3
IMO C

Archit3110

can u plz explain a more above highlighted formula
or give me link expaining same :)

thx
Show more


The scenario is shown in the diagram below:

Attachment:
11.JPG
11.JPG [ 25.48 KiB | Viewed 11137 times ]

In the diagram, 'p', 'q', and 'r' denote students who play 1 game; 'a', 'b', and 'c' denote students who participate in 2 classes and 'd' denotes students who participate in all 3 classes

Since there are 20 students: \(p+q+r + a+b+c + d = 20\)

Also: a+b+c+d = 9 (since 9 students take at least 2 classes i.e. 2 or 3 classes)

If we add Yoga, Bridge and Painting, we end up adding the regions 'a', 'b', 'c' twice each and the region 'd' thrice

Yoga + Bridge + Painting = \((p+q+r) + 2(a+b+c) + 3d\)

\(10 + 13 + 9 = (p+q+r + a+b+c + d) + (a+b+c + d) + d\)

=> 32 = 20 + 9 + d

=> d = Students who participate in all three classes = 3


Alternate approach:

From the diagram:

Total = Yoga + Bridge + Painting - [(Yoga & Bridge) + (Yoga & Painting) + (Bridge & Painting)] + (Yoga & Bridge & Painting)

\(=> 20 = 10 + 13 + 9 - [(a+d) + (b+d) + (c+d)] + d\)

\(=> 20 = 32 - (a+b+c+3d) + d\)

\(=> 20 = 32 - [(a+b+c+d) + 2d] + d\)

\(=> 20 = 32 - 9 - d\)

\(=> d = 3\)


Answer C
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There are 20 students participating in an after-school program offerin 03 Jan 2026, 04:10
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