UPSC Prelims 2001 · General Studies
Question 144: Basic Numeracy
In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what per cent of those surveyed owned a car or a mobile phone or both?
AnswerThe answer is (c).
Use the formula for the union of two sets: n(car or phone) = n(car) + n(phone) - n(both) = 80 + 60 - 55 = 85 per cent. Simply adding 80 and 60 would count the 55 per cent who own both twice, so it is subtracted once. Check: 25 per cent own only a car, 5 per cent only a phone, 55 per cent both, which is 85 per cent in all.
Why each option is right or wrong
- (a) 65 per cent is too low, as 80 per cent own a car alone.
- (b) 80 per cent counts only car owners and ignores phone-only owners.
- (c) Right: 85 per cent.
- (d) 97.5 per cent cannot be reached from these figures.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2001, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.