Question

Solve the given problem using Venn Diagram. Show your solution

A group of 50 students went on a tour in Palawan province Out of 50 students, 24 joined the trip to Coron; 18 went to Tubbataha Reef, 20 visited El Nido: 12 made a trip to Coron and Tubbataha Reef 15 saw the Tubbataha Reef and El Nido, 11 made a trip to Coron and El Nido: 10 saw the three tourist spots.

1. How many students went to Coron only?
2. How many students went to Tubbataha Reef only?
3. How many joined the El Nido trip only? 4. How many did not go to any of the tourist spot?

(Please kindly help me. I have answered this problem, but it seems not to be correct.)​​

Answer 1

1. 11

2. 1

3. 4

4. 16

Explanation:

Start with the number visiting all 3 spots, i.e. 10, this goes in the middle (the triple overlap zone);

Then, the number of those visiting two of the 3 spots less 10 will go into each dual overlap zone;

Finally, the total number of those visiting a single spot less anything in any overlap zone of that circle needs to go in the singular outer zone;

What this means is:

In the case of Coron:

10 visited Coron and the other 2 spots;

11 visited Coron and El Nido, but 10 of these also visited the Reef as well, leaving only 1 who visited just Coron and El Nido;

Similarly, 12 went to Coron and the Reef, 10 of these went to El Nido as well so just 2 visited only Coron and the Reef;

Then 24 in total visited Coron, 10 of these visited the two other spots as well, 1 visited Coron and El Nido and 2 visited Coron and the Reef;

So 13 (= 10 + 1 + 2) visited Coron and one or more of the other two spots, leaving 11 (=24 - 13) who visited Coron alone;

Do the same thing with El Nido and the Reef to get the answers to the other questions;

This is all represented in the Venn diagram shown;

The last question is calculated by summing all the values in each zone and subtracting the total from 50, which is the total number of students;

This gives 16.