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In a set of 150 students, 90 study English, 70 study History, and 30 study both.

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Question: In a set of 150 students, 90 study English, 70 study History, and 30 study both. How many students study only History?

Options:

  1. 40
  2. 30
  3. 50
  4. 60

Correct Answer: 40

Solution: 

The number of students who study only History is |History| - |Both| = 70 - 30 = 40.

In a set of 150 students, 90 study English, 70 study History, and 30 study both.

Practice Questions

Q1
In a set of 150 students, 90 study English, 70 study History, and 30 study both. How many students study only History?
  1. 40
  2. 30
  3. 50
  4. 60

Questions & Step-by-Step Solutions

In a set of 150 students, 90 study English, 70 study History, and 30 study both. How many students study only History?
  • Step 1: Identify the total number of students studying History, which is 70.
  • Step 2: Identify the number of students studying both English and History, which is 30.
  • Step 3: To find the number of students studying only History, subtract the number of students studying both from the total number studying History: 70 - 30.
  • Step 4: Calculate the result: 70 - 30 = 40.
  • Step 5: Conclude that 40 students study only History.
  • Set Theory – Understanding the relationships between different groups, specifically using Venn diagrams to visualize overlaps.
  • Subtraction in Set Operations – Calculating the number of elements in one set that do not belong to another set.
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