Please help with venn diagram

[Marcia]

Hello,

My name is Marcia I'm a new member, can someone help me with this problem please?

Out of 150 candidates taking exams, 115 passed in Maths and 123 passed in English, 96 passed both subjects. How many failed both subjects?


Thank you.

[asquare]

There are several ways to approach this, but here is an easy one:

Of the 115 who passed maths, 96 passed English also. That means that 19 (115-96) passed maths but not English.

Of the 123 who passed English, 96 passed maths also. So 27 (123-96) passed English only.

Now, you know that everyone either passed both, passed English only, passed maths only, or passed neither. We have figured out the numbers in each of the first three groups: 96 passed both, 27 passed English only, and 19 passed maths only. Add those up, and you get 142 people. The remainder of the 150 candidates must be in the last group, passed neither subject. So, 8 people (150-142) failed both subjects.

[Marcia]

Thank you asquare for your response, I will work it out with your help.