In a group of 500 students, 150 are studying physics, 220 are studying biology, and 100 are studying chemistry. At least 25 students are studying more than one of these sciences. What is the greatest possible number of these students that might NOT be studying any of these sciences?
463
To find the greatest possible number of students that might not be studying any of these sciences, we need to consider the scenario where the number of students studying two or three sciences is minimized.
If we assume that all 25 students studying more than one science are studying only two sciences, then the maximum number of students studying two sciences would be 25. This means that the number of students studying physics and biology, physics and chemistry, or biology and chemistry would be 25 in each case.
Now, let's calculate the number of students studying only one science:
Number of students studying physics only = Total number of students studying physics - Number of students studying physics and biology - Number of students studying physics and chemistry = 150 - 25 - 25 = 100
Number of students studying biology only = Total number of students studying biology - Number of students studying physics and biology - Number of students studying biology and chemistry = 220 - 25 - 25 = 170
Number of students studying chemistry only = Total number of students studying chemistry - Number of students studying physics and chemistry - Number of students studying biology and chemistry = 100 - 25 - 25 = 50
Therefore, the number of students studying only one science is 100 + 170 + 50 = 320.
Finally, to find the maximum number of students not studying any of these sciences, we subtract the total number of students studying any science from the total number of students:
Total number of students not studying any of these sciences = Total number of students - (Number of students studying physics + Number of students studying biology + Number of students studying chemistry) = 500 - (150 + 220 + 100) = 500 - 470 = 30
Therefore, the greatest possible number of these students that might not be studying any of these sciences is 30.
To find the greatest possible number of students who might not be studying any of these sciences, we need to determine the maximum number of students who could be studying more than one science.
Let's start by adding the number of students studying each science: 150 (physics) + 220 (biology) + 100 (chemistry) = 470.
Now, we need to consider that at least 25 students are studying more than one science. Therefore, we subtract 25 from the total calculated above: 470 - 25 = 445.
Now, we can find the maximum number of students who might not be studying any of these sciences by subtracting the remaining number of students from the total number of students: 500 (total students) - 445 (students studying at least one science) = 55.
Therefore, the greatest possible number of students who might not be studying any of these sciences is 55.