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In a class of 50 students, 70% students pass in QA, 90% pass in EU, 85% pass in DI and 60% pass in RC. What is the minimum percentage of students who pass in all the papers?
  • a)
    3%
  • b)
    4%
  • c)
    5%
  • d)
    8%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a class of 50 students, 70% students pass in QA, 90% pass in EU, 85...
This question is just the extension of the earlier question.
The minimum value of EU and (QA∩RC) = 90% + 30% - 100% = 20%
The minimum value of DI and EU and  (QA∩RC) = 20% +85% - 100% = 5%
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Most Upvoted Answer
In a class of 50 students, 70% students pass in QA, 90% pass in EU, 85...
Solution:

To find out the minimum percentage of students who pass in all the papers, we need to find out the intersection of all the percentages.

QA = 70%
EU = 90%
DI = 85%
RC = 60%

Step 1: Find out the percentage of students who passed in at least one subject.

Percentage of students who passed in at least one subject = QA + EU + DI + RC - (Sum of any two) - (Sum of three) + (All four)

= 70 + 90 + 85 + 60 - (70 + 90) - (70 + 85 + 90) + (70 + 85 + 90 + 60)

= 305%

Step 2: Find out the percentage of students who passed in all four subjects.

Let the percentage of students who passed in all four subjects be x%.

So, we have

x% + Percentage of students who passed in at least one subject = 100%

Or, x% + 305% = 100%

Or, x% = 100% - 305%

Or, x% = -205%

Since x% cannot be negative, we can conclude that the percentage of students who passed in all four subjects is 0% (or more than 0%, but less than the minimum passing percentage in any of the four subjects).

Step 3: Find out the minimum percentage of students who pass in all the papers.

As we know that the intersection of all the percentages cannot be less than 0%, we can conclude that the minimum percentage of students who pass in all the papers is greater than 0%.

The options are 3%, 4%, 5%, and 8%.

Out of these options, the minimum percentage of students who pass in all the papers is 5%, which is the correct answer.

Therefore, the correct answer is option (c) 5%.
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