Group Size Deduction
Group Size Deduction problems require finding the number of people in a group based on age constraints, sums, or averages. These problems test your ability to work with total sum and average relationships.
What You'll Learn
Introduction to Group Size Deduction
Group Size Deduction problems require finding the number of people in a group based on age constraints, sums, or averages. These problems test your ability to work with total sum and average relationships.
Prerequisites
How to Solve Group Size Deduction Problems
Step 1: Identify what is given (sum, average, or both)
Step 2: Use the formula: Count = Sum ÷ Average
Step 3: If sum is given without average, look for additional constraints
Step 4: Count must be a positive integer
Step 5: Sometimes sum and average are given indirectly
Step 6: Use age constraints to narrow down possible counts
Step 7: Verify that calculated count yields reasonable ages
Example Problem
Example: The average age of a group of people is 25 years. The total sum of their ages is 125 years. How many people are in the group? Solution: Step 1: Average = 25, Sum = 125 Step 2: Count = Sum ÷ Average = 125 ÷ 25 = 5 Answer: 5 people Example 2: The sum of ages of a family is 120 years. The average age is between 20 and 30. How many members could be there? Solution: Count = 120/Average. For average 20, count=6; avg 24, count=5; avg 30, count=4. Possible counts: 4, 5, 6.
Pro Tips & Tricks
- Count must be an integer
- Average = Sum/Count
- Sum = Average × Count
- If sum and average don't divide evenly, check if ages can be fractional
- Typical family sizes range from 2 to 10
- Use age reasonableness to eliminate extreme counts
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Group Size Deduction. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Group Size Deduction is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Group Size Deduction?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: