Question
23. A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white? (A) 1 (B) 6 (C) 8 (D) 12 (E) 13
Ask by Coles Martinez. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
13 applicants wore neither blue nor white.
Solution
To determine the number of applicants who wore neither blue nor white, we can use the principle of inclusion-exclusion.
1. **Total number of applicants:** 21
2. **Applicants who wore blue (B):** 7
3. **Applicants who wore white (W):** 6
4. **Applicants who wore both blue and white (B ∩ W):** 5
First, calculate the number of applicants who wore either blue or white (or both):
\[
|B \cup W| = |B| + |W| - |B \cap W| = 7 + 6 - 5 = 8
\]
Now, subtract this from the total number of applicants to find those who wore neither color:
\[
\text{Applicants who wore neither} = 21 - 8 = 13
\]
**Answer:**
(E) 13
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Simplify this solution The Deep Dive
To find the number of applicants who wore neither blue nor white, we can use the principle of inclusion-exclusion. Let’s denote: - Total applicants = 21 - Applicants wearing blue = 7 - Applicants wearing white = 6 - Applicants wearing both blue and white = 5 Using the formula: Number of applicants wearing either blue or white = (Applicants wearing blue) + (Applicants wearing white) - (Applicants wearing both) = 7 + 6 - 5 = 8. Now, subtract this from the total number of applicants to find those who wore neither: 21 - 8 = 13. So, the answer is (E) 13.
