In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed iv A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between

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Q: 72 (IAS/2009)
In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed iv A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,4,4,4,0,0

keywords: 

{'examination': [0, 0, 1, 1], 'whole examination': [0, 0, 0, 1], 'students': [0, 1, 1, 1], 'subject': [2, 1, 6, 6], 'total number': [0, 0, 3, 0]}

The question refers to a situation where students must pass all three subjects to pass the whole examination. So, the lower limit of the total passing percentage would be equal to 100% minus the highest individual subject fail rate (22%, subject B). So, 100% - 22% = 78%. This means that at most 78% of students could have passed.

For the upper limit, it`s the case where all students who failed did so in multiple subjects and no student failed in only one subject - in other words, the fail percentages of all three subjects count the same students. To determine this scenario, you need to subtract all failure rates from 100%, like this: 100% - 20% (subject A) - 22% (subject B) - 16% (subject C) = 42%. This means that at least 42% of students could have passed.

So, the percentage of students passing the whole examination lies between 42% and 78%, which is option 1.

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