Determining which answer is an assumption on which the argument depends - LSAT Logical Reasoning

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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?

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Answer

To answer this question, it is necessary to recognize that while appointment criteria are set forth for the board of directors, they are applied to the position of Treasurer. We are never told that a Treasurer is a member of the board of directors. Thus, the conclusion is only warranted if eligibility for appointment to the board is a necessary condition for appointment to the position of Treasurer.

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