In a group of 210 students, 120 students study Math, 150 students study Physics, and 110 students study Chemistry. If 30 students study all three subjects, 40 students study only Math and Physics, 50 students study only Physics and Chemistry, and 25 students study only Math and Chemistry, how many students study exactly one subject?
Question
In a group of 210 students, 120 students study Math, 150 students study Physics, and 110 students study Chemistry. If 30 students study all three subjects, 40 students study only Math and Physics, 50 students study only Physics and Chemistry, and 25 students study only Math and Chemistry, how many students study exactly one subject?
Solution
To find out how many students study exactly one subject, we first need to find out how many students study at least two subjects.
- We know that 30 students study all three subjects.
- 40 students study only Math and Physics.
- 50 students study only Physics and Chemistry.
- 25 students study only Math and Chemistry.
So, the total number of students who study at least two subjects is 30 + 40 + 50 + 25 = 145.
Next, we need to find out how many students study at least one subject.
- 120 students study Math.
- 150 students study Physics.
- 110 students study Chemistry.
So, the total number of students who study at least one subject is 120 + 150 + 110 = 380.
Now, to find out how many students study exactly one subject, we subtract the number of students who study at least two subjects from the number of students who study at least one subject.
So, 380 - 145 = 235.
Therefore, 235 students study exactly one subject.
Similar Questions
In a class of 150 students, 50 students passed in mathematics, 40 students failed only in chemistry and 20 students failed in both the subjects . How many students passed exactly in one subject?
In a class of 55 students, the number of students studying different subjects are, 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is
In a class test, 30 students passed in Mathematics, 30 in Physics, and 35 in Chemistry. 20 students passed in exactly two subjects while 65 passed in at least one of the three subjects. How many passed in all the three subjects?105150
In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone? 35 48 60 22
In a survey involving 60 students, it was found that 26 like Chemistry, 24 like Physics, 18 like Mathematics, 12 both Chemistry and Physics, 10 Chemistry and Mathematics, 10 Physics and Mathematics and 15 none of the three subjects. Find the number of students that like all the three subjects.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.