UPSC Prelims 2020 · CSAT
Question 60: Basic Numeracy
How many different sums can be formed with the denominations ₹ 50, ₹ 100, ₹ 200, ₹ 500 and ₹ 2,000 taking at least three denominations at a time?
AnswerUPSC’s answer is (a).
Choose at least three of the five denominations: C(5,3) + C(5,4) + C(5,5) = 10 + 5 + 1 = 16 subsets. Check that no two give the same sum: the four smaller notes make 350, 650, 750 and 800 (three notes) and 850 (all four); adding 2,000 to two or more of them gives eleven sums above 2,100, all different. So there are 16 distinct sums.
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) Right: 10 + 5 + 1 = 16, and every sum is different.
- (b) 15 would drop one subset, but none repeats a sum.
- (c) 14 undercounts the choices.
- (d) 10 counts only the three-note choices.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.