In a university examination, it was found that 42% of the students passed in…
2015
In a university examination, it was found that 42% of the students passed in both English and Mathematics, 64% passed in Mathematics, and 52% passed in English. What is the percentage of students who failed in both the subjects?
Answer: C. 26% — For two overlapping groups expressed as percentages of the same population, the percentage belonging to at least one of the two groups equals the sum of the…
- A.
74%
- B.
36%
- C.
26%
- D.
20%
Attempted by 10 students.
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Correct answer: C
For two overlapping groups expressed as percentages of the same population, the percentage belonging to at least one of the two groups equals the sum of the two individual percentages minus the percentage common to both groups, since the common portion would otherwise be counted twice. The percentage belonging to neither group then equals 100% minus this combined figure.
Let M = percentage of students who passed in Mathematics = 64%, E = percentage of students who passed in English = 52%, and B = percentage of students who passed in both subjects = 42%.
The percentage of students who passed in at least one of the two subjects = M + E − B = 64% + 52% − 42% = 74%.
The percentage of students who failed in both subjects is the complement of this figure with respect to the whole student population: 100% − 74% = 26%.
As an independent check, partition the students into three mutually exclusive groups: those passing English only (52% − 42% = 10%), those passing Mathematics only (64% − 42% = 22%), and those passing both subjects (42%). These three groups add up to 10% + 22% + 42% = 74% of students passing at least one subject, matching the figure obtained above and confirming that 26% of the students failed in both subjects.