Question

The product of three consecutive positive integers is 120. Then the sum of the three positive numbers is?

• A. 16
• B. 24
• C. 15
• D. 12

Hint:

For problems involving consecutive integers with a known product, try factoring small numbers or set the middle number as \( x \) to simplify.

Answer 1

The Correct Option is C

Let the three consecutive positive integers be: \( x - 1, x, x + 1 \).
Their product is: \( (x - 1)(x)(x + 1) = x(x^2 - 1) = x^3 - x \).
We are told this product equals 120:
\[ x^3 - x = 120 \] Try values of \( x \) that satisfy this: \[ x = 5 \Rightarrow 5^3 - 5 = 125 - 5 = 120 \Rightarrow \text{Valid!} \] So the three consecutive numbers are: \[ x - 1 = 4, \quad x = 5, \quad x + 1 = 6 \] Sum of these numbers: \( 4 + 5 + 6 = \boxed{15} \)