Question

The product of three consecutive positive integers is 2184. Then the sum of the three positive numbers is

• A. 39
• B. 49
• C. 29
• D. 59

Hint:

To solve problems involving consecutive integers, express the numbers algebraically and test plausible values to satisfy given conditions.

Answer 1

The Correct Option is A

Step 1: Understanding Consecutive Integers
Consecutive positive integers are numbers that follow each other in order, increasing by 1 each time, such as 3, 4, 5 or 10, 11, 12.
Step 2: Defining the Integers
Let the three consecutive positive integers be: \[ n, \quad n+1, \quad n+2, \] where \( n \) is a positive integer.
Step 3: Writing the Product Equation
Given their product is 2184, we write: \[ n \times (n+1) \times (n+2) = 2184. \]
Step 4: Solving the Equation by Trial
Since \( n \) is positive and the product is relatively large, try values around the cube root of 2184, which is about 13.
Check \( n=12 \): \[ 12 \times 13 \times 14 = 12 \times 182 = 2184, \] which satisfies the condition.
Step 5: Finding the Sum
Now, find the sum of these integers: \[ 12 + 13 + 14 = 39. \]
Step 6: Conclusion
Thus, the sum of the three consecutive positive integers whose product is 2184 is 39.