Out of 120 applicants: 70 are males and 80 have a driver’s license. What is the ratio of the minimum to the maximum possible number of males having a driver’s license?

Introduction / Context: This is an inclusion–exclusion style bounds question. We must find the minimum and maximum possible number of males with licenses, given totals for males and total licensed applicants.

Given Data / Assumptions:

• Total applicants = 120.
• Males = 70 ⇒ Females = 50.
• Licensed applicants = 80.

Concept / Approach:

• Maximum males with licenses occurs when as many licenses as possible are assigned to males: min(males, licensed) = min(70, 80) = 70.
• Minimum males with licenses occurs when as many licenses as possible go to females: max(0, licensed − females) = 80 − 50 = 30.

Step-by-Step Solution: Minimum males with license = 30. Maximum males with license = 70. Required ratio (min : max) = 30 : 70 = 3 : 7.

Verification / Alternative check: Construct extreme cases: Case min: all 50 females licensed ⇒ remaining 30 licenses to males ⇒ 30 males licensed. Case max: all licenses to males until exhausted ⇒ 70 males licensed.

Why Other Options Are Wrong: 1 : 3, 2 : 3, 5 : 7, and 3 : 5 do not match the computed bounds.

Common Pitfalls: Forgetting to cap by the number of females (for license allocation) or by the number of males when maximizing.

Final Answer: 3 : 7