Question

out of 100 students ; 15 passed in English, 12 passed in mathematics, 8 in science, 6 in English and mathematics, 7 in mathematics and science, 4 in English and science, 4 in all three. find how many passed.(i) in English and mathematics but not in science (ii) in mathematics and science but not in English (iii) in mathematics only. (iv) in more than one subject only.​

Answer 1

Answer:

Step-by-step explanation:

Hi, you need to start by drawing Venn diagram, and label each circle with its' subject.  

Now onto working out the data:

Start by identifying the mid section, where all 3 circles connect - this section represents the students who have passed in all 3 subjects - and we know that's 4!  So 4 goes in that part!  This part is vital as it affects all other data given.... please follow carefully.

Next you will find 3 section on the venn diagram where two circles overlap:

1st: For English and maths

2nd: for English and Science  

3rd: for Science and maths

let's take the 1st overlap (English and maths): you know that 6 students passed in english and maths.  The key here is to look out for the number in the mid section (4).  So in the overlap area you will write 2 only.  That's because 6 students passed but the diagram already contains data for 4 (so you do 6 take away 4 = 2)

For the 2nd overlap English and Science: 4 students passed.  On the overlap you will write...... 0 .  That's because 4 students passed minus the 4 students in the mid section equals 0.  

For the 3rd overlap English and maths, 6 students minus the 4 in the middle section equals 2.  

Now you know 8 students passed in Science (remember to minus the middle data and that in the overlaps (8-4-3=1).  You enter 1 for Science

Repeat the same thing for the other 2 subjects: so for mathematics (12 - 4 - 3 - 2 = 3)  so for maths it's 3 only.  For english (15 - 4 - 2=9 students).  

Once you've completed this, you can answer the questions.  

How many passed in

(i) English and mathematics but not in science = 2

in mathematics and science but not in English = 3

in mathematics only = 3

in more than one subject only = (for this part, add all the overlaping areas, i.e. 3 + 4+ 2 = 9)

Hope this helps.