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There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects
- a)is 12
- b)is 4
- c)is 2
- d)cannot be determined from given information
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
There are 100 students in a class. In an examination, 50 of them faile...
n(MUPUB) = n(M) + n(P) + n(B) -n(M ∩ P) - n(PMB) - n(B ∩ P) + n(M ∩ P ∩ B)
given n(M) = 50 , n (P) = 45, n(B) = 40;
n(M∩ P) + n(P∩ B) + n(B∩ M) - 3(M∩ P ∩ B) = 32
99 = 50 + 45 + 40 – (32 + 3 n (M ∩ P∩ B) )+ n(M ∩ P∩ B) ;
2 n(M ∩ P ∩ B) = 36 – 32;
n(M∩ P ∩ B) = 2
Most Upvoted Answer
There are 100 students in a class. In an examination, 50 of them faile...
Given Information:
- There are 100 students in a class.
- 50 students failed in Mathematics.
- 45 students failed in Physics.
- 40 students failed in Biology.
- 32 students failed in exactly two of the three subjects.
- Only one student passed in all the subjects.
To Find:
The number of students failing in all three subjects.
Solution:
Let's analyze the given information step by step.
Step 1: Total Number of Students
It is given that there are 100 students in the class.
Step 2: Number of Students Failed in Each Subject
- 50 students failed in Mathematics.
- 45 students failed in Physics.
- 40 students failed in Biology.
Step 3: Number of Students Failed in Exactly Two Subjects
It is given that 32 students failed in exactly two out of the three subjects.
Step 4: Number of Students Passed in All Subjects
It is given that only one student passed in all the subjects.
Step 5: Calculation
We need to find the number of students failing in all three subjects.
Let's assume the number of students failing in all three subjects is 'x'.
Using the given information, we can write the following equation:
Number of students failing in Mathematics + Number of students failing in Physics + Number of students failing in Biology - 2*(Number of students failed in exactly two subjects) - Number of students passed in all subjects = Total number of students
50 + 45 + 40 - 2*32 - 1 = 100
135 - 64 - 1 = 100
70 - 1 = 100
69 = 100
This is not possible, as the number of students cannot be greater than the total number of students in the class.
Therefore, it cannot be determined from the given information how many students failed in all three subjects.
Conclusion:
The correct answer is option 'D' - cannot be determined from the given information.
- There are 100 students in a class.
- 50 students failed in Mathematics.
- 45 students failed in Physics.
- 40 students failed in Biology.
- 32 students failed in exactly two of the three subjects.
- Only one student passed in all the subjects.
To Find:
The number of students failing in all three subjects.
Solution:
Let's analyze the given information step by step.
Step 1: Total Number of Students
It is given that there are 100 students in the class.
Step 2: Number of Students Failed in Each Subject
- 50 students failed in Mathematics.
- 45 students failed in Physics.
- 40 students failed in Biology.
Step 3: Number of Students Failed in Exactly Two Subjects
It is given that 32 students failed in exactly two out of the three subjects.
Step 4: Number of Students Passed in All Subjects
It is given that only one student passed in all the subjects.
Step 5: Calculation
We need to find the number of students failing in all three subjects.
Let's assume the number of students failing in all three subjects is 'x'.
Using the given information, we can write the following equation:
Number of students failing in Mathematics + Number of students failing in Physics + Number of students failing in Biology - 2*(Number of students failed in exactly two subjects) - Number of students passed in all subjects = Total number of students
50 + 45 + 40 - 2*32 - 1 = 100
135 - 64 - 1 = 100
70 - 1 = 100
69 = 100
This is not possible, as the number of students cannot be greater than the total number of students in the class.
Therefore, it cannot be determined from the given information how many students failed in all three subjects.
Conclusion:
The correct answer is option 'D' - cannot be determined from the given information.
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There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjectsa)is 12b)is 4c)is 2d)cannot be determined from given informationCorrect answer is option 'C'. Can you explain this answer?
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