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

1)in english and mathematics but not science
2)in mathmatics and sciecnce but not in english
3)in mathematics only
more than one subject only

Answer 1

there are 4 students who passed in all subjects, we can say that 2 students passed in English and Mathematics, 3 students passed in Mathematics and Science only, and no one passed in English and Science only.

Explanation:

Given that we have deduced the number of students who passed in only two subjects, we can now solve for the number of students who passed only one subject.

English = 15 - (4 + 2 + 0) = 9

Mathematics = 12 - (4 + 3 + 2) = 3

Science = 8 - (4 + 3 + 0) = 1

1. In English but not in Science,

9 + 2 = 11

2. In Mathematics and Science but not in English

3 + 3 + 1 = 7

3. In Mathematics only

= 3

3. More than one subject only

3 + 4 + 2 + 9 = 18

Answer 2

Because there are 4 students who passed in all subjects, we can say that only 2 students passed in English and Mathematics only, only 3 students passed in Mathematics and Science only, and no one passed in English and Science only.

Given that we have deduced the number of students who passed in two subjects, we can now solve for the number of students who passed only one subject.
English = 15 - (4 + 2 + 0) = 9
Mathematics = 12 - (4 + 3 + 2) = 3
Science = 8 - (4 + 3 + 0) = 1

1. In English but not in Science,
9 + 2 = 11
2. In Mathematics and Science but not in English
3 + 3 + 1 = 7
3. In Mathematics only
= 3
3. More than one subject only
3 + 4 + 2 + 9 = 18

It will really be helpful if you draw yourself a Venn Diagram for this item.