UPSC Prelims 2021 · CSAT
Question 46: Logical Reasoning and Mental Ability
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
AnswerUPSC’s answer is (b).
Use fractions of the villagers. Those under 25 are 4/5 and the literate are 1/3. If no literate villager were under 25, all of them would sit in the remaining 1/5, but 1/3 is more than 1/5. So at least 1/3 − 1/5 = 2/15 of all villagers are literate and under 25: some under-25 villagers are certainly literate. Home-owners (1/2) exceed the 1/5 aged 25 or more, ruling out (d), and 1/2 > 1/3 rules out (a). Paddy growers' literacy is not given, so (c) is not certain. Remember: if two groups together exceed the whole, they must overlap.
Why each option is right or wrong
- (a) Half own houses but only a third are literate, so not all home-owners can be literate.
- (b) Right: the literate (1/3) outnumber those aged 25 or more (1/5), so some under-25 villagers must be literate.
- (c) Paddy growers' literacy is not given; any share is possible.
- (d) Home-owners (1/2) outnumber those aged 25 or more (1/5), so some under-25 villagers own houses.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.