Question

The product of three consecutive positive integers is 720. Then the sum of the three numbers is

• A. 27
• B. 29
• C. 28
• D. 32

Answer 1

The Correct Option is A

Let the three consecutive integers be \( n-1 \), \( n \), and \( n+1 \). Their product is: \[ (n-1) \times n \times (n+1) = 720 \] Solve this equation. First, estimate \( n \) by taking the cube root of 720: \[ \sqrt[3]{720} \approx 8.99 \] Thus, \( n = 9 \). The three numbers are \( 8 \), \( 9 \), and \( 10 \). The sum of the three numbers is: \[ 8 + 9 + 10 = 27 \] To solve for three consecutive numbers whose product is known, estimate the middle number by finding the cube root of the product.