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 do not study any one of the subject? Options 5 15 10 20

To solve this problem, we need to find the number of students who study each subject individually, then subtract this from the total number of students.

First, let's find the number of students who study each subject individually:

• Math: 120 students study Math. But this includes students who also study Physics and/or Chemistry. So we subtract the students who study Math and Physics (40), the students who study Math and Chemistry (25), and the students who study all three subjects (30). This gives us 120 - 40 - 25 - 30 = 25 students who study only Math.

• Physics: 150 students study Physics. We subtract the students who study Physics and Math (40), the students who study Physics and Chemistry (50), and the students who study all three subjects (30). This gives us 150 - 40 - 50 - 30 = 30 students who study only Physics.

• Chemistry: 110 students study Chemistry. We subtract the students who study Chemistry and Math (25), the students who study Chemistry and Physics (50), and the students who study all three subjects (30). This gives us 110 - 25 - 50 - 30 = 5 students who study only Chemistry.

Next, we add up the number of students who study each subject individually, the number of students who study two subjects, and the number of students who study all three subjects. This gives us 25 (only Math) + 30 (only Physics) + 5 (only Chemistry) + 40 (Math and Physics) + 50 (Physics and Chemistry) + 25 (Math and Chemistry) + 30 (all three subjects) = 205 students.

Finally, we subtract this from the total number of students (210) to find the number of students who do not study any of the subjects. This gives us 210 - 205 = 5 students.

So, the answer is 5.