Question #f86db

1 Answer
Aug 13, 2017

The answer is #25# students passed both tests. See explanation.

Explanation:

Let's start with following variables (sets):

#A# - set of students which passed Oral test

#B# - set of students which passed Listening test

#Omega# - set of all students.

#A'nnB'# set of students who failed both tests

From the task we know that:

#|Omega|=40#

#|A|=26#

#|B|=37#

#|A'nnB'|=2#

Using the last information we know that #|AuuB|=38# which means that #38# students passed either oral test or listening test.

Now to calculate the number of students who passed both tests we use:

#|A|+|B|-|AnnB|=|AuuB|#

If we substitute the numbers we get:

#26+37-|AnnB|=38#

#-|AnnB|=38-37-26#

#-|AnnB|=-25#

#|AnnB|=25#