Question
6. 400 students were interviewed: 47 took PE, 43 took BIO, 41 took ENG, 15 took PE and BIO, 10 took PE and ENG, 8 took BIO and ENG, 3 took all three subjects.
a) How many students took none of the three subjects?
b) How many students took PE but not BIO or ENG?
c) How many students took BIO and PE but not ENG?
a) How many students took none of the three subjects?
b) How many students took PE but not BIO or ENG?
c) How many students took BIO and PE but not ENG?
Answers
Answered by
GPT 3.5
a) To find out how many students took none of the three subjects, we first need to find the total number of students who took at least one of the three subjects.
Total students who took at least one subject = Students who took PE + Students who took BIO + Students who took ENG - Students who took exactly two subjects (PE and BIO, PE and ENG, BIO and ENG) + Students who took all three subjects
Total students who took at least one subject = 47 + 43 + 41 - (15 + 10 + 8) + 3
Total students who took at least one subject = 76
Therefore, the number of students who took none of the three subjects = Total number of students interviewed - Total students who took at least one subject
= 400 - 76
= 324 students took none of the three subjects
b) To find out how many students took PE but not BIO or ENG, we need to find the number of students who took PE and subtract the number of students who took both PE and BIO or PE and ENG or all three subjects.
Students who took PE = 47
Students who took both PE and BIO = 15
Students who took both PE and ENG = 10
Students who took all three subjects = 3
Number of students who took PE but not BIO or ENG = Students who took PE - (Students who took both PE and BIO + Students who took both PE and ENG - Students who took all three subjects)
= 47 - (15 + 10 - 3)
= 47 - 22
= 25 students took PE but not BIO or ENG
c) To find out how many students took BIO and PE but not ENG, we need to find the number of students who took both BIO and PE and then subtract the number of students who also took ENG.
Students who took both PE and BIO = 15
Students who took BIO, PE, and ENG = 3
Number of students who took BIO and PE but not ENG = Students who took both PE and BIO - Students who took all three subjects
= 15 - 3
= 12 students took BIO and PE but not ENG
Total students who took at least one subject = Students who took PE + Students who took BIO + Students who took ENG - Students who took exactly two subjects (PE and BIO, PE and ENG, BIO and ENG) + Students who took all three subjects
Total students who took at least one subject = 47 + 43 + 41 - (15 + 10 + 8) + 3
Total students who took at least one subject = 76
Therefore, the number of students who took none of the three subjects = Total number of students interviewed - Total students who took at least one subject
= 400 - 76
= 324 students took none of the three subjects
b) To find out how many students took PE but not BIO or ENG, we need to find the number of students who took PE and subtract the number of students who took both PE and BIO or PE and ENG or all three subjects.
Students who took PE = 47
Students who took both PE and BIO = 15
Students who took both PE and ENG = 10
Students who took all three subjects = 3
Number of students who took PE but not BIO or ENG = Students who took PE - (Students who took both PE and BIO + Students who took both PE and ENG - Students who took all three subjects)
= 47 - (15 + 10 - 3)
= 47 - 22
= 25 students took PE but not BIO or ENG
c) To find out how many students took BIO and PE but not ENG, we need to find the number of students who took both BIO and PE and then subtract the number of students who also took ENG.
Students who took both PE and BIO = 15
Students who took BIO, PE, and ENG = 3
Number of students who took BIO and PE but not ENG = Students who took both PE and BIO - Students who took all three subjects
= 15 - 3
= 12 students took BIO and PE but not ENG
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