All of the students at a college are majoring in psychology , business or both…
2025
All of the students at a college are majoring in psychology , business or both . 73% of the students are psychology majors and 62 % are business majors . if there are 200 students , how many of them are majoring in both psychology and business ?
- A.
65
- B.
35
- C.
70
- D.
55
Attempted by 154 students.
Show answer & explanation
Correct answer: C
Solution: use the inclusion–exclusion principle.
Since every student majors in psychology, business, or both, the combined coverage is 100%.
Apply inclusion–exclusion to find the percent in both: percent in both = percent in psychology + percent in business - percent in (psychology ∪ business).
Compute the value: percent in both = 73% + 62% - 100% = 35%.
Convert percent to number of students: 35% of 200 = 0.35 × 200 = 70 students.
Answer: 70 students