UPSC Prelims 2022 · CSAT
Question 78: Basic Numeracy
The sum of three consecutive integers is equal to their product. How many such possibilities are there?
AnswerUPSC’s answer is (c).
Let the integers be n − 1, n and n + 1. Their sum is 3n and their product is n(n² − 1). Setting n(n² − 1) = 3n gives n = 0 or n² = 4, so n = 0, 2 or −2. The triples are (−1, 0, 1), (1, 2, 3) and (−3, −2, −1). Check: sum and product are 0, 6 and −6 respectively. That is three possibilities.
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) Only one counts just the triple 1, 2, 3.
- (b) Only two misses a triple of negative integers or zero.
- (c) Correct: n = 0, 2 and −2 give three triples.
- (d) Such triples exist, as the check shows.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.