Q. In a school where each student has to take at least one of two languages, French and German, it is found that 520 students have taken French and 400 have taken German. Find the maximum and minimum possible number of students in that school(Using Venn diagram and it's formulae)
• (Step-wise explanation)
Answers
Answer:
In a group of 50 students, 31 are taking French, 17 are taking Spanish, and 10 are taking neither French nor Spanish. How many students are taking both French and Spanish?
This can be explained through a Venn Diagram
C depicts both French and Spanish.
The answer is 8.
In a class of 60 students, 30 students like math, 25 like science and 15 like both. What is the number of students who like either mathematics or science?
In a class of 30 students, 18 students study Spanish, 15 study French and 5 students study neither Spanish nor French. How many students study both Spanish and French?
In a school with 100 students, 60 will study French, 60 will study German, and 60 will study Spanish. What is the minimum number of students who will study all three languages?
In a class of 60 students, 35 read French and 25 read English. If 10 students read none of the subjects, how many read both subjects?
In a group of 30 high school students, 8 take French, 12 take Spanish and 3 take both languages. How many students of the group take neither?
A general tip is to break down a hard problem into smaller easier problems. I also get the feeling that you are a lot like me (need to visualize the solution).
For example:
First of all, let’s work with smaller numbers to make it easier to both calculate and visualize.
Lets say there are instead 6 students:
3 of these students studies French:
2 students study Spanish:
So this will be our first simple problem to solve:
Right now we will interpret these parameters as:
3 students study French
2 students study Spanish
3 + 2 = 5 students studies a language
Also, 1 student doesn’t study any language (at least
All right so, the trick here is that 31+17+10 = 58 which is greater than your headcount. If you look at the groups:
A = French
B = Spanish
C= Neither
You see that group A and B can overlap (this is the answer you are looking for) but A and B cannot overlap with C.
So 8 people more than your headcount,that means 8 people have been counted twice (because we said nobody can be in C and in A or B, otherwise it would be more complicated) .
So you can easily conclude that you have 8 Students in both groups A and B as these are the only two groups anybody can belong to at the same time .
8 people have taken French and Spanish