Question

In a group of 80 people: 50 like Coffee, 35 like Tea, and 20 like both Coffee and Tea. How many people like only one of the beverages?

• A. 35
• B. 45
• C. 50
• D. 55
• E.

Hint:

Drawing a Venn diagram can be very helpful for visualizing set theory problems. Draw two overlapping circles, one for Coffee and one for Tea. Fill in the intersection (20) first, then calculate the "only" parts by subtracting from the totals for each circle.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
This problem involves the principles of set theory. We are given the total number of people in a group, the number of people in two different sets (Coffee lovers, Tea lovers), and the number of people in the intersection of these two sets (those who like both). We need to find the number of people who belong to exactly one of the two sets.
Step 2: Key Formula or Approach
To find the number of people who like only one beverage, we can calculate those who like only Coffee and those who like only Tea, and then add them together.
Number of people who like only Coffee = (Total who like Coffee) - (Total who like both)
Number of people who like only Tea = (Total who like Tea) - (Total who like both)
Total who like only one = (Only Coffee) + (Only Tea)
Step 3: Detailed Explanation
Given data:
Total people = 80
Number who like Coffee, N(C) = 50
Number who like Tea, N(T) = 35
Number who like both Coffee and Tea, N(C \(\cap\) T) = 20
Calculate the number of people who like only Coffee:
\[ \text{N(Only Coffee)} = N(C) - N(C \cap T) = 50 - 20 = 30 \] Calculate the number of people who like only Tea:
\[ \text{N(Only Tea)} = N(T) - N(C \cap T) = 35 - 20 = 15 \] Calculate the total number of people who like only one beverage:
\[ \text{Total} = \text{N(Only Coffee)} + \text{N(Only Tea)} = 30 + 15 = 45 \] Step 4: Final Answer
There are 45 people who like only one of the beverages. This corresponds to option (B).