UPSC Prelims 2019 · CSAT
Question 56: Basic Numeracy
Suppose you have sufficient amount of rupee currency in three denominations : ₹ 1, ₹ 10 and ₹ 50. In how many different ways can you pay a bill of ₹ 107 ?
AnswerUPSC’s answer is (c).
Count solutions of 50a + 10b + c = 107, where a, b and c are whole numbers and the ₹1 coins make up the rest. With no ₹50 note, b runs from 0 to 10: 11 ways. With one ₹50 note, 57 remains and b runs from 0 to 5: 6 ways. With two ₹50 notes, 7 remains and b = 0: 1 way. Total = 11 + 6 + 1 = 18.
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) Wrong: undercounts; 18 ways exist.
- (b) Wrong: undercounts by one.
- (c) Right: 11 + 6 + 1 = 18.
- (d) Wrong: overcounts by one.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.