Solution
Understanding the Set:
There are four Online Teaching-Learning Platforms (OTLP):
F1: Own software for OTLP
F2: Trained teachers for OTLP
F3: Training materials for OTLP
F4: All students have laptops
These platforms are used by 600 schools.
Now, there are four features (F1 to F4), and 600 schools were surveyed.
Each student may be using one, two, three, or even all four features.
This directly translates to a Venn diagram-based set.
Lets first see the data we can directly add to the table :
- Clue 1 says,
80 schools did not have any of the four facilities – F1, F2, F3, F4
- Clue 2 says,
40 schools had all four facilities.
- Clue 3 says,
number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.
Clue 4 says,
number of schools with exactly three of the facilities was the same irrespective of which three were considered.
Let that be "x"
Clue 5 says,
313 schools had F2.
Also, clue 6 says,
26 schools had only F2 and F3 (but neither F1 nor F4).
Clue 7 says,
Among the schools having F4, 24 had only F3, and 45 had only F2.
=> Only F4 & F3 = 24
AND, Only F4 & F2 = 45
Clue 8 says,
162 schools had both F1 and F2.
(Here please be careful its F1 + F2 not, Only F1 & F2)
Let Only F1 & F2 be "a"
=> a + x + 40 + x =
=> a + 2x = .......eq (1)
Now, We know, F2 had 313 schools (clue 5)
=>
=> .........eq (2)
Now, solving eq 1 and 2 we get;
a =
And x =
Clue 9 says,
The number of schools having F1 was the same as the number of schools having F4.
Now, we only have two missing values let that be - 'a' and 'b'.
According to the clue,
F1 = F4
=>
=>
=>
Now, we know,
total schools =
Out of which has no facility
=> total schools with atleast one facility =
=>
=>
Number of schools having exactly three of the four facilities = 50 + 50 + 50 + 50 = 200