Product of Ages
Product of Ages problems involve the product (multiplication) of ages rather than sum or difference. These problems often appear as puzzles where the product gives clues about possible age combinations.
What You'll Learn
Introduction to Product of Ages
Product of Ages problems involve the product (multiplication) of ages rather than sum or difference. These problems often appear as puzzles where the product gives clues about possible age combinations.
Prerequisites
How to Solve Product of Ages Problems
Step 1: Write the product equation (e.g., A × B × C = P)
Step 2: Factorize the product into prime factors
Step 3: List all possible factor combinations that give the product
Step 4: Apply age constraints (reasonable ages, usually integers)
Step 5: Use additional conditions (sum, difference, relationships) to narrow possibilities
Step 6: Select the combination that satisfies all conditions
Example Problem
Example: The product of ages of three children is 36. The sum of their ages is the number of the house across the street. The oldest child has red hair. Find the ages. Solution: Step 1: All factor triples of 36 with ages reasonable: (1,1,36) sum=38, (1,2,18) sum=21, (1,3,12) sum=16, (1,4,9) sum=14, (1,6,6) sum=13, (2,2,9) sum=13, (2,3,6) sum=11, (3,3,4) sum=10 Step 2: The sum is the house number. Since the person needed more info (oldest child exists), there must be ambiguity: two triples with same sum: (1,6,6) and (2,2,9) both sum to 13. Step 3: 'Oldest child' means a unique oldest exists, so (1,6,6) has two oldest (twins) while (2,2,9) has unique oldest (9). Answer: Ages are 2, 2, and 9
Pro Tips & Tricks
- Age products are typically for children or young adults
- Reasonable ages are usually under 100
- Prime factorization is essential for systematic listing
- The 'oldest' or 'youngest' clues help resolve ambiguities
- Products often come with sum information for puzzle logic
- Consider that ages are usually positive integers
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Product of Ages. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Product of Ages is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Product of Ages?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: