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 number of candidates who failed in at least one subject is
- A.
25
- B.
30
- C.
60
- D.
None of the above
Attempted by 49 students.
Show answer & explanation
Correct answer: C
Answer: 60
Explanation: Each number in the Venn diagram is a disjoint group of students (so adding them does not double count anyone). We must add all seven regions to find the number who failed in at least one subject.
English only = 13
Mathematics only = 9
Science only = 8
English and Mathematics only = 7
Mathematics and Science only = 10
English and Science only = 8
All three subjects = 5
Total failed = 13 + 9 + 8 + 7 + 10 + 8 + 5 = 60
Therefore, 60 candidates failed in at least one subject.