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In a set of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many

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Question: In a set of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many people like only dogs?

Options:

  1. 70
  2. 50
  3. 80
  4. 100

Correct Answer: 70

Solution: 

The number of people who like only dogs is |Dogs| - |Both| = 120 - 50 = 70.

In a set of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many

Practice Questions

Q1
In a set of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many people like only dogs?
  1. 70
  2. 50
  3. 80
  4. 100

Questions & Step-by-Step Solutions

In a set of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many people like only dogs?
  • Step 1: Identify the total number of people who like dogs, which is 120.
  • Step 2: Identify the number of people who like both dogs and cats, which is 50.
  • Step 3: To find the number of people who like only dogs, subtract the number of people who like both from the total number of dog lovers: 120 - 50.
  • Step 4: Calculate the result: 120 - 50 = 70.
  • Step 5: The final answer is that 70 people like only dogs.
  • Set Theory – Understanding the relationships between different groups and how to calculate the number of elements in each subset.
  • Venn Diagrams – Using Venn diagrams to visualize the overlap between groups (dog lovers, cat lovers, and those who like both).
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