UPSC Prelims 2021 · CSAT
Question 30: Basic Numeracy
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks ?
AnswerUPSC’s answer is (b).
Let the marks be 5k, 6k, 7k, 8k, 9k and 10k out of a common maximum M. They total 45k, and 60% of the total maximum 6M is 3.6M, so 45k = 3.6M and M = 12.5k. Sixty per cent of M is 7.5k. Papers scoring below 7.5k are the 5k, 6k and 7k papers: three papers. Remember: treat proportions as multiples of one unit and express the maximum in the same unit.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 2 would leave out the 7k paper, but 7k is below 7.5k.
- (b) Right: the 5k, 6k and 7k papers are below 60% of the 12.5k maximum, which is 7.5k.
- (c) 4 would include the 8k paper, which is above 7.5k.
- (d) 5 would include papers scoring 8k and 9k, both above 7.5k.
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.