UPSC Prelims 2023 · CSAT
Question 45: Basic Numeracy
How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers ?
AnswerUPSC’s answer is (d).
If 1186 leaves remainder 31 on division by n, then n divides 1186 - 31 = 1155, and n must exceed the remainder, 31. 1155 = 3 x 5 x 7 x 11, which has 16 divisors: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155. Those above 31 are 33, 35, 55, 77, 105, 165, 231, 385 and 1155: nine numbers.
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: nine divisors of 1155 exceed 31.
- (b) Wrong: nine divisors of 1155 exceed 31.
- (c) Wrong: nine divisors of 1155 exceed 31.
- (d) Right: 33, 35, 55, 77, 105, 165, 231, 385, 1155.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.