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14 Jun 2026, 04:39
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C
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In a school in Kettering, there are 100 students. Of these, 70 students passed Physics, 62 passed Mathematics, 84 passed English, and 82 passed Chemistry. Additionally, 37 students passed all four subjects. What is the maximum number of students who could have failed all four subjects?
A. 10
B. 12
C. 13
D. 15
E. 17
A. 10
B. 12
C. 13
D. 15
E. 17
14 Jun 2026, 06:11
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In a school in Kettering, there are 100 students. Of these, 70 students passed Physics, 62 passed Mathematics, 84 passed English, and 82 passed Chemistry. Additionally, 37 students passed all four subjects. What is the maximum number of students who could have failed all four subjects?
A. 10
B. 12
C. 13
D. 15
E. 17
To maximize the number of students who failed all four subjects, we need to minimize the number of students who passed at least one subject.
Think of each passed subject as one “pass.” For example, if one student passed Physics, Math, and English, that student contributes 3 passes.
Total passes in all subjects:
70 + 62 + 84 + 82 = 298
Now, 37 students passed all four subjects. These students contribute:
37 * 4 = 148 passes
So the remaining passes are:
298 - 148 = 150
These 150 remaining passes must be accounted for by students other than the 37 who passed all four. Since none of these other students can have passed all four subjects, each can account for at most 3 passes.
We want as many students as possible to have failed all four, so we want as few other passing students as possible. To do that, we give each such student the maximum possible number of passes, which is 3.
150/3 = 50
So, besides the 37 students who passed all four, we need at least 50 more students to account for the remaining passes.
Thus, the minimum number of students who passed at least one subject is:
37 + 50 = 87
Therefore, the maximum number of students who failed all four subjects is:
100 - 87 = 13
Answer: C.
A. 10
B. 12
C. 13
D. 15
E. 17
To maximize the number of students who failed all four subjects, we need to minimize the number of students who passed at least one subject.
Think of each passed subject as one “pass.” For example, if one student passed Physics, Math, and English, that student contributes 3 passes.
Total passes in all subjects:
70 + 62 + 84 + 82 = 298
Now, 37 students passed all four subjects. These students contribute:
37 * 4 = 148 passes
So the remaining passes are:
298 - 148 = 150
These 150 remaining passes must be accounted for by students other than the 37 who passed all four. Since none of these other students can have passed all four subjects, each can account for at most 3 passes.
We want as many students as possible to have failed all four, so we want as few other passing students as possible. To do that, we give each such student the maximum possible number of passes, which is 3.
150/3 = 50
So, besides the 37 students who passed all four, we need at least 50 more students to account for the remaining passes.
Thus, the minimum number of students who passed at least one subject is:
37 + 50 = 87
Therefore, the maximum number of students who failed all four subjects is:
100 - 87 = 13
Answer: C.
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