Q. The sum of three consecutive integers is equal to their product- How many such possibilities are there?
a. Only one
b. Only two
c. Only three
d. No such possibility is there
Correct Answer: c. Only three
Question from UPSC Prelims 2022 CSAT Paper
Explanation :
Possibilities of three consecutive integers whose sum equals their product.
Let’s assume the three consecutive integers to be n-1, n, and n+1.
Their sum would be (n-1) + n + (n+1) = 3n
Their product would be (n-1)n(n+1) = n^3 – n
As per the question, their sum is equal to their product, so we can equate them:
3n = n^3 – n
Rearranging the equation:
n^3 – 4n = 0
n(n^2 – 4) = 0
n = 0 or n = ±2
