2022 · Q100
Consider the following for the next four (04) items that follow: In a group of 500 candidates, 30 failed in English only, 75 failed in Hindi only, 50 failed in Mathematics only, 15 failed in both English and Hindi (inclusive), 17 failed in both English and Mathematics (inclusive), 17 failed in both Hindi and Mathematics (inclusive), and 5 failed in all three subjects. How many candidates passed in two or more subjects?
Elementary MathematicsSet Theory
- A461
- B405
- C345
- D306
Explanation
Failed ≥1 subject = 194, so 306 passed all three; failed exactly one = 155, so 155 passed exactly two. Passed two or more = 306+155 = 461. Key disputed: a widely circulated third-party Set-A key lists C, but inclusion-exclusion gives 461. Hence the keyed option is A.