Van Diagram II

Total # of signups that all students made is 77 (22 + 27 + 28 = 77)

Assume that:

x = # of students who signed up for 1 class

y = # of students who signed up for 2 classes

z = # of students who signed up for 3 classes


Based on the conditions of the question, we know the following 3 equations are true:

1. 77 = x + 2y + 3z

2. x + y + z = 59

3. y = 6 (since 6 students signed up for exactly 2 classes)


So then, we can deduce the value for x

x = 59 - y - z = 59 - 6 -z = 53 - z

Finally, we can calculate a value for z

77 = (53 - z) + 2*6 + 3z = 65 + 2z

2z = 77 - 65 = 12

z = 6

I could not attach the Venn diagram, so you got to visualize here. Consider the following variables

p - no. of student JUST attending Poetry club
h - no of students attending JUST the history club
w - no. of students attending JUST the writing club
x - just attending poetry and history(part above all 3 area)
y - just attending history and writing
z - just attending writing and poetry
c - attending all the 3 (which we intend to find).

The equations are:
p+h+w+(x+y+z)+c = 59 =>p+h+w+c = 59-6=53 .......1
p+x+z+c = 22.........2
h+x+y+c = 27.........3
w+y+z+c = 28.........4

adding 2, 3 and 4
p+h+w+2(x+y+z)+3c = 77
=>p+w+h+3c = 65 ................5

5-1 gives
2c = 12 => c = 6.

The equations might seems daunting at first, but once iu have the venn diagram in front of you, these are effortless and moreover you dont have to remember any formulae. This system follows from the question stem but one has to be careful with the calculations as with any GMAT problem.



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