Question:

At an overpriced department store there are 112 customers. If 43 have purchased shirts, 57 have purchased pants, and 38 have purchased neither, how many purchased both shirts and pants?

Show Hint

Use the principle of inclusion and exclusion when dealing with overlapping sets.
Updated On: Sep 30, 2025
  • 74
  • 26
  • 38
  • 14
  • The answer cannot be determined.
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is D

Solution and Explanation

Step 1: Use the principle of inclusion and exclusion.
Let: - \( S = 43 \) (customers who purchased shirts),
- \( P = 57 \) (customers who purchased pants),
- \( N = 38 \) (customers who purchased neither).
The total number of customers is 112, so the number of customers who purchased either shirts or pants is: \[ 112 - 38 = 74. \] By the inclusion-exclusion principle:
\[ S + P - x = 74 \quad \Rightarrow \quad 43 + 57 - x = 74 \quad \Rightarrow \quad x = 26. \] Thus, 26 customers purchased both shirts and pants.
Was this answer helpful?
0
0

Top Questions on Set Theory

View More Questions

Questions Asked in GRE exam

View More Questions