Out of 120 applicants for a post, 70 are males and 80 have driving licenses.…
2023
Out of 120 applicants for a post, 70 are males and 80 have driving licenses. What is the ratio of the minimum to the maximum possible number of males having driving licenses?
Answer: D. 3 : 7 — ConceptFor two groups A and B within a universe of N people, the smallest possible intersection is max(0, |A| + |B| - N). The largest possible intersection is…
- A.
1 : 2
- B.
2 : 3
- C.
5 : 7
- D.
3 : 7
Attempted by 11 students.
Show answer & explanation
Correct answer: D
Concept
For two groups A and B within a universe of N people, the smallest possible intersection is max(0, |A| + |B| - N).
The largest possible intersection is min(|A|, |B|), because an intersection cannot exceed the size of either group.
Application
Let A be the 70 male applicants, B be the 80 license holders, and N = 120.
Minimum male license holders = max(0, 70 + 80 - 120) = max(0, 30) = 30.
Maximum male license holders = min(70, 80) = 70.
Required ratio = minimum : maximum = 30 : 70 = 3 : 7.
Cross-check
At the minimum, all 50 non-males can hold licenses, so the remaining 30 license holders are males. At the maximum, all 70 males can hold licenses, which is possible within the total of 80 license holders.
Therefore, the required ratio is 3 : 7.