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In a survey, 60% of respondents preferred coffee over tea. If 30% of those who p

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Question: In a survey, 60% of respondents preferred coffee over tea. If 30% of those who preferred coffee also liked tea, what percentage of respondents liked only coffee?

Options:

  1. 30%
  2. 60%
  3. 42%
  4. 18%

Correct Answer: 42%

Solution: 

If 60% preferred coffee and 30% of those liked tea, then 30% liked both, leaving 30% who liked only coffee.

In a survey, 60% of respondents preferred coffee over tea. If 30% of those who p

Practice Questions

Q1
In a survey, 60% of respondents preferred coffee over tea. If 30% of those who preferred coffee also liked tea, what percentage of respondents liked only coffee?
  1. 30%
  2. 60%
  3. 42%
  4. 18%

Questions & Step-by-Step Solutions

In a survey, 60% of respondents preferred coffee over tea. If 30% of those who preferred coffee also liked tea, what percentage of respondents liked only coffee?
  • Step 1: Understand that 60% of the respondents preferred coffee.
  • Step 2: Recognize that 30% of those who preferred coffee also liked tea.
  • Step 3: Calculate how many respondents liked both coffee and tea. This is 30% of the 60% who preferred coffee.
  • Step 4: Calculate 30% of 60%. This is 0.30 * 60 = 18%. So, 18% of all respondents liked both coffee and tea.
  • Step 5: To find out how many liked only coffee, subtract the percentage of those who liked both from the total percentage of coffee lovers. This is 60% - 18% = 42%.
  • Step 6: Therefore, 42% of the respondents liked only coffee.
  • Percentage Calculation – Understanding how to calculate percentages and their relationships in a survey context.
  • Set Theory – Applying basic set theory concepts to determine the overlap between two groups (coffee lovers and tea lovers).
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