Finding sets of consecutive integers whose sum equals their product
Question
The sum of three consecutive integers is equal to their product. How many such possibilities are there?
Options
Only one
Only two
Only three
No such possibility is there
Explanation
Define three consecutive integers as (x-1), x, (x+1) to simplify the algebra.
Set up the algebraic equality: Sum = Product. (x-1) + x + (x+1) = (x-1)(x)(x+1) 3x = x(x² - 1)
Factor out the variable to expose all roots: x(x² - 1) - 3x = 0 x(x² - 1 - 3) = 0 x(x² - 4) = 0
This polynomial yields three distinct mathematical solutions for x:
There are exactly three such possibilities.
Answer: (c).
Question details
Year
2022
Paper
CSAT
Question
Q78
Section
Numerical Ability
Sub-topic
Number Puzzles
Type
Factual single
Difficulty
Medium
Source hint
Sum of three consecutive integers equal to product
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