Multiple choice general knowledge math & puzzles

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

  1. 42% and 84%

  2. 42% and 78%

  3. 58% and 78%

  4. 58% and 84%
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B Correct answer
Explanation

Using set theory, maximum students passing all subjects occurs when failures don't overlap: 100-20=80% pass A, 100-22=78% pass B, 100-16=84% pass C, so max pass all = 78%. Minimum occurs when failures maximally overlap: minimum pass = 100-(20+22+16)=42%. This gives range 42% to 78%. Option C's lower bound of 58% is too high - it incorrectly assumes no overlap.

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