of 250 candidates writing a exam, 147 passed in math,150 pass in chemistry and 85 pass subjects

Question

B)calculate the number of students who pass
i)pass math only
ii)pass chemistry only
iii)passed neither
iv)pass only one subject

Answer 1

Let's use a Venn diagram to help us solve this problem.

Let M be the set of students who passed math.
Let C be the set of students who passed chemistry.
Let T be the total number of students (250 in this case).

We are given the following:
| M ∪ C | = T (the total number of students)
| M | = 147 (students passed in math)
| C | = 150 (students passed in chemistry)
|M ∩ C | = 85 (students pass both subjects)

Now, let's calculate the following:
i) | M - C | (students passed only in math)
To find the number of students who passed only in math, we need to subtract the number of students who passed in both math and chemistry: | M - C | = | M | - | M ∩ C | = 147 - 85 = 62 students.

ii) | C - M | (students passed only in chemistry)
To find the number of students who passed only in chemistry, we need to subtract the number of students who passed in both math and chemistry: | C - M | = | C | - | M ∩ C | = 150 - 85 = 65 students.

iii) (students who passed neither)
To find the number of students who passed neither math nor chemistry, we can use the formula for the total number of students:
| M ∪ C | = | M - C | + | M ∩ C | + | C - M | + |neither|

Now we can substitute our known values into the equation and solve for the number of students who passed neither:
250 = 62 + 85 + 65 + |neither|
250 = 212 + |neither|
|neither| = 250 - 212 = 38 students

iv) (students who passed only one subject)
To find the number of students who passed only one subject, we can simply add the number of students who passed only in math and those who passed only in chemistry: 62 + 65 = 127 students.

In summary, the number of students who
i) passed math only: 62
ii) passed chemistry only: 65
iii) passed neither: 38
iv) passed only one subject: 127