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A group of friends consists of 12 people who like either football or basketball.

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Question: A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?

Options:

  1. 5
  2. 2
  3. 3
  4. 4

Correct Answer: 2

Solution: 

Let B be the number of basketball players. Total = Football + Basketball - Both. 12 = 7 + B - 5. Thus, B = 10, and only basketball = 10 - 5 = 5.

A group of friends consists of 12 people who like either football or basketball.

Practice Questions

Q1
A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?
  1. 5
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?
  • Step 1: Identify the total number of friends, which is 12.
  • Step 2: Identify how many like football, which is 7.
  • Step 3: Identify how many like both football and basketball, which is 5.
  • Step 4: Use the formula: Total = Football + Basketball - Both.
  • Step 5: Substitute the known values into the formula: 12 = 7 + B - 5.
  • Step 6: Simplify the equation: 12 = 7 + B - 5 becomes 12 = 2 + B.
  • Step 7: Solve for B (the number of basketball players): B = 12 - 2, so B = 10.
  • Step 8: To find how many like only basketball, subtract those who like both from the total basketball players: Only Basketball = B - Both = 10 - 5.
  • Step 9: Calculate: Only Basketball = 5.
  • Set Theory – Understanding the relationships between different groups and how to calculate the number of elements in overlapping sets.
  • Venn Diagrams – Using visual representations to solve problems involving overlapping groups.
  • Basic Algebra – Applying algebraic manipulation to solve for unknowns in equations.
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