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In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many

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Question: In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people like only cats?

Options:

  1. 15
  2. 20
  3. 10
  4. 5

Correct Answer: 15

Solution: 

The number of people who like only cats is |Cats| - |Both| = 25 - 10 = 15.

In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many

Practice Questions

Q1
In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people like only cats?
  1. 15
  2. 20
  3. 10
  4. 5

Questions & Step-by-Step Solutions

In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people like only cats?
  • Step 1: Identify the total number of people who like cats, which is 25.
  • Step 2: Identify the number of people who like both dogs and cats, which is 10.
  • Step 3: To find the number of people who like only cats, subtract the number of people who like both from the total number of cat lovers: 25 - 10.
  • Step 4: Calculate the result: 25 - 10 = 15.
  • Step 5: Therefore, the number of people who like only cats is 15.
  • Set Theory – Understanding the relationships between different groups and how to calculate the number of elements in overlapping sets.
  • Venn Diagrams – Visualizing the problem using Venn diagrams can help clarify the relationships between those who like dogs, cats, and both.
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