To find the minimum overlap, assume the maximum number of males who do NOT have a license. If 70 are male and 80 have licenses, and 120 total applications, then the maximum number of males without licenses is 120 - 80 = 40. Since there are 70 males, at least 70 - 40 = 30 males must have licenses. For the maximum overlap, all 80 license holders could be male, provided there are at least 80 males (which there are, 70). Therefore, the maximum overlap is limited by the number of males, which is 70. The ratio of minimum to maximum is 30:70, which simplifies to 3:7. Wait, the correct answer is B, which implies 2:3. Let's re-evaluate. Maximum number of males is 70. Maximum number of license holders is 80. Minimum number of people with licenses OR males is 70 + 80 - 120 = 30. So, minimum number of males WITH licenses: Total males - (Total applications - License holders) = 70 - (120 - 80) = 70 - 40 = 30. Maximum number of males WITH licenses: Minimum of (Total males, Total license holders) = Minimum of (70, 80) = 70. The ratio is 30:70, which simplifies to 3:7. There must be an error in my understanding or the provided answer. Let's assume the question meant something else or there's a different interpretation. Given the answer is B (2:3), let's work backwards. If the ratio is 2:3, and the total is 120, the possible values for min/max could be derived from 2x and 3x. This doesn't directly map to the calculation. Let's re-read the problem carefully: 120 applications, 70 male, 80 driver's license. Min males with license: Total Males - (Total Applications - License Holders) = 70 - (120 - 80) = 70 - 40 = 30. Max males with license: min(Total Males, Total License Holders) = min(70, 80) = 70. Ratio min:max = 30:70 = 3:7. It appears the provided correct answer might be incorrect, as the calculation consistently yields 3:7. However, if we MUST reach 2:3, there might be a specific constraint or interpretation missed. Let's re-examine the maximum. If we assume the 40 people without licenses are ALL female, then all 70 males have licenses. This gives 70 as the max. For the minimum, we have 70 males and 80 license holders. Maximum number of females is 120 - 70 = 50. If all 50 females have licenses, then 80 - 50 = 30 males must have licenses. This confirms 30 as the minimum. The ratio 30:70 = 3:7. There seems to be a discrepancy with the provided answer 'B'. Let's assume there's a typo in the question or options. If the number of males was 80 and license holders 70, the calculation would be: Min = 80 - (120 - 70) = 80 - 50 = 30. Max = min(80, 70) = 70. Ratio 30:70 = 3:7. The calculation is robust. It's possible the question intends to check understanding of maximum and minimum intersection in sets, which is what was performed.