My Learning Cart
?
Categories
Account

In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like bo

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like both. How many people like neither genre?

Options:

  1. 30
  2. 60
  3. 90
  4. 120

Correct Answer: 30

Solution: 

Using inclusion-exclusion, the number of people who like at least one genre is 90 + 60 - 30 = 120. Therefore, those who like neither is 150 - 120 = 30.

In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like bo

Practice Questions

Q1
In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like both. How many people like neither genre?
  1. 30
  2. 60
  3. 90
  4. 120

Questions & Step-by-Step Solutions

In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like both. How many people like neither genre?
  • Step 1: Identify the total number of people surveyed, which is 150.
  • Step 2: Identify how many people like rock music, which is 90.
  • Step 3: Identify how many people like pop music, which is 60.
  • Step 4: Identify how many people like both rock and pop music, which is 30.
  • Step 5: Use the inclusion-exclusion principle to find the number of people who like at least one genre: Add the number of rock and pop music lovers, then subtract those who like both. This is calculated as 90 (rock) + 60 (pop) - 30 (both) = 120.
  • Step 6: To find the number of people who like neither genre, subtract the number of people who like at least one genre from the total number of people surveyed: 150 (total) - 120 (like at least one) = 30.
  • Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by accounting for overlaps.
  • Set Theory – The study of collections of objects, which in this case are people who like different music genres.
  • Basic Arithmetic – The fundamental operations of addition and subtraction used to derive the final answer.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks