In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?

To find out how many students opt for none of the three subjects, we need to determine the number of students who opt for each subject individually and then subtract that from the total number of students.

First, let's find out how many students opt for Physics. Since all even-numbered students opt for Physics, we can divide the total number of students by 2 to get the number of even-numbered students. In this case, 120 divided by 2 equals 60. Therefore, 60 students opt for Physics.

Next, let's determine how many students opt for Chemistry. We know that students whose numbers are divisible by 5 opt for Chemistry. To find out how many students meet this criteria, we divide the total number of students by 5. In this case, 120 divided by 5 equals 24. Therefore, 24 students opt for Chemistry.

Finally, let's calculate the number of students who opt for Math. Students whose numbers are divisible by 7 opt for Math. Dividing the total number of students by 7 gives us 17.14. Since we can't have a fraction of a student, we round down to the nearest whole number. Therefore, 17 students opt for Math.

Now, let's calculate the number of students who opt for none of the three subjects. To do this, we subtract the number of students who opt for Physics, Chemistry, and Math from the total number of students.

Total number of students = 120 Number of students who opt for Physics = 60 Number of students who opt for Chemistry = 24 Number of students who opt for Math = 17

To find the number of students who opt for none of the three subjects, we subtract the sum of the students who opt for Physics, Chemistry, and Math from the total number of students:

Number of students who opt for none of the three subjects = Total number of students - (Number of students who opt for Physics + Number of students who opt for Chemistry + Number of students who opt for Math) Number of students who opt for none of the three subjects = 120 - (60 + 24 + 17) Number of students who opt for none of the three subjects = 120 - 101 Number of students who opt for none of the three subjects = 19

Therefore, 19 students opt for none of the three subjects.