120 candidates appeared for examination in three subjects, namely, English…
2014
120 candidates appeared for examination in three subjects, namely, English (E), Mathematics (M) and Science (S). The number of candidates who failed in E, M and S are shown in the diagram given below:
The percentage of candidates who failed in at most two subjects is:
- A.
20.83
- B.
25
- C.
45.83
- D.
95.83
Attempted by 114 students.
Show answer & explanation
Correct answer: D
Key idea: "At most two subjects" means failing in zero, one, or two subjects (everyone except those who failed in all three).
Read the diagram's region counts and sum them:
Only English: 13
Only Mathematics: 9
Only Science: 8
English and Mathematics only: 7
English and Science only: 8
Mathematics and Science only: 10
All three subjects: 5
Sum of all regions = 13 + 9 + 8 + 7 + 8 + 10 + 5 = 60. These are the candidates who failed in at least one subject.
Number who failed in at most two subjects = total candidates − those who failed in all three = 120 − 5 = 115.
Percentage = (115/120) × 100 = 95.83%.
Common misunderstandings:
Counting only those who failed exactly two gives 25 candidates, which as a percentage is 20.83% (25/120 × 100). That is not what "at most two" asks for.
Counting only those who failed one or two subjects gives 55 candidates, which is 45.83% (55/120 × 100). This still excludes those who failed none and so is not the required answer.
Final answer: 95.83%.