Question

A medical degree is necessary for appointment to the hospital's board of directors. Further, no one having more than a five-percent equity stake in a pharmaceutical company can be appointed to the board of directors. Consequently, Dell, a practicing physician with a PhD in bioethics, cannot be appointed the hospital's treasurer, since he owns fifteen percent of PillCo, a pharmaceutical company.
The argument's conclusion follows logically if which one of the following is assumed?

• A. PillCo is one of the hospital's pharmaceutical vendors.
• B. Anyone with a medical degree who does not hold more than a five-percent stake in any pharmaceutical company is eligible for appointment to the hospital's board of directors.
• C. If Dell sold his stake in PillCo, he would be appointed treasurer.
• D. A PhD is not necessary for appointment to the position of treasurer.
• E. Only those eligible for appointment to the hospital's board of directors can be appointed as the hospital's treasurer.

Hint:

In sufficient assumption questions, identify the "rogue" element in the conclusion—a term or concept that does not appear in the premises. The correct answer will almost always link this new element back to the terms and concepts in the premises. Here, "treasurer" is the rogue element.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This is a sufficient assumption question. We need to find the statement that, when added to the existing premises, makes the conclusion logically certain.

Step 2: Detailed Explanation:
Let's break down the argument's structure:
- Premise 1: To be on the Board of Directors (BoD), one needs a medical degree.
- Premise 2: Having $>$ 5% stake in a pharmaceutical company makes one ineligible for the BoD.
- Premise 3: Dell has a medical degree but owns 15% of PillCo.
- Intermediate Conclusion (unstated but implied): From Premises 2 and 3, Dell is ineligible for the BoD.
- Final Conclusion: Dell cannot be appointed as the hospital's treasurer.
There is a logical gap. The premises prove that Dell cannot be on the Board of Directors. The conclusion is about Dell not being able to be the treasurer. The argument is invalid unless there is a rule linking the two positions. We need an assumption that connects eligibility for the Board to eligibility for the treasurer position.
Option (E) provides this missing link: Treasurer \(\rightarrow\) Eligible for BoD. If being treasurer requires being eligible for the Board of Directors, and we already know Dell is ineligible for the Board, then it logically follows that he cannot be the treasurer.

Step 3: Final Answer:
The assumption that the treasurer must be someone who is eligible for the Board of Directors makes the conclusion logically valid.