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#37542
Complete Question Explanation
Must Be True, SN. The correct answer choice is (A)
The stimulus contains a fact set. When analyzing it, you should notice the sufficient condition indicator “if” in the first sentence: you must meet both sufficient conditions in order to establish that the proposal will not be funded. Do not be distracted by order in which the conditions are presented—the necessary condition here appears before the two sufficient conditions, and this is a presentation trick often used by the test makers in order to test your understanding of how conditional relationships work.
The first sentence can be diagrammed as follows:
In taking the contrapositive of a conditional statement containing two sufficient conditions, “and” becomes “or” and vice versa:
In considering the contrapositive of the initial conditional statement, for the proposal to be funded, at least one of the two necessary conditions must be met: either at least 50 people must be available for hire, or else the department must duplicate no more than 25 percent of the material covered in other departments. According to the stimulus, the proposed Area Studies Department will receive funding, and the proposal duplicates more than 25 percent of the material covered in the Anthropology Department. Therefore, because the sufficient condition occurs and one of the two possible necessary conditions does not occur, the other necessary condition must occur and at least 50 people per year must be available for hire. This prephrase immediately reveals answer choice (A) to be correct.
Answer choice (A): This is the correct answer choice. If one of the necessary conditions cannot be met (the Area Studies Department duplicates more than 25 percent of the material covered in other departments), the other condition must be met, i.e. Area Studies must have at least 50 people per year available for hire. Otherwise, the department would not be funded.
Answer choice (B): Whether Area Studies duplicates more than 25 percent of the material covered in any existing department other than Anthropology is unknown. All we know is that it duplicates more than 25 percent of the material in the Anthropology department.
Answer choice (C): It is entirely plausible that Area Studies would have been funded even if it did not duplicate more than 25 percent of the material covered in Anthropology. In fact, one of the necessary conditions a department must meet in order to receive funding is to ensure that it does not duplicate more than 25 percent of the material in other departments. Although meeting this condition does not ensure funding (this would be a Mistaken Reversal), it certainly does not preclude it.
Answer choice (D): Just because Area Studies duplicates more than 25 percent of the material in Anthropology does not mean that the reverse is also true. We can only infer this if we knew that the two departments cover an identical amount of material. However, if Area Studies covers more material than Anthropology, it is possible that Anthropology duplicates a much smaller fraction of the Area Studies material, even though Area Studies duplicates 25 percent of the Anthropology material.
Take a simpler scenario: John has 4 apples and Mary has 10. If they share one apple in common, Mary shares 25% of John’s apples, whereas John shares only 10% of Mary’s apples.
Answer choice (E): This Opposite answer is the logical opposite of answer choice (A). If Area Studies meets neither one of the two necessary conditions for receiving funding—it duplicates 25 percent of the material covered in another department and has fewer than 50 people per year available for hire, it would not receive funding. This would contradict the final sentence in the stimulus, in which the administrator explicitly states that they will fund the new department.
Must Be True, SN. The correct answer choice is (A)
The stimulus contains a fact set. When analyzing it, you should notice the sufficient condition indicator “if” in the first sentence: you must meet both sufficient conditions in order to establish that the proposal will not be funded. Do not be distracted by order in which the conditions are presented—the necessary condition here appears before the two sufficient conditions, and this is a presentation trick often used by the test makers in order to test your understanding of how conditional relationships work.
The first sentence can be diagrammed as follows:
- 50P = 50 people per year available for hire
25% = duplicate 25% of the material covered in other departments
PF = proposal is funded
< 50P
+
PF
> 25%
In taking the contrapositive of a conditional statement containing two sufficient conditions, “and” becomes “or” and vice versa:
- ≥ 50P
PF or
≤ 25%
In considering the contrapositive of the initial conditional statement, for the proposal to be funded, at least one of the two necessary conditions must be met: either at least 50 people must be available for hire, or else the department must duplicate no more than 25 percent of the material covered in other departments. According to the stimulus, the proposed Area Studies Department will receive funding, and the proposal duplicates more than 25 percent of the material covered in the Anthropology Department. Therefore, because the sufficient condition occurs and one of the two possible necessary conditions does not occur, the other necessary condition must occur and at least 50 people per year must be available for hire. This prephrase immediately reveals answer choice (A) to be correct.
Answer choice (A): This is the correct answer choice. If one of the necessary conditions cannot be met (the Area Studies Department duplicates more than 25 percent of the material covered in other departments), the other condition must be met, i.e. Area Studies must have at least 50 people per year available for hire. Otherwise, the department would not be funded.
Answer choice (B): Whether Area Studies duplicates more than 25 percent of the material covered in any existing department other than Anthropology is unknown. All we know is that it duplicates more than 25 percent of the material in the Anthropology department.
Answer choice (C): It is entirely plausible that Area Studies would have been funded even if it did not duplicate more than 25 percent of the material covered in Anthropology. In fact, one of the necessary conditions a department must meet in order to receive funding is to ensure that it does not duplicate more than 25 percent of the material in other departments. Although meeting this condition does not ensure funding (this would be a Mistaken Reversal), it certainly does not preclude it.
Answer choice (D): Just because Area Studies duplicates more than 25 percent of the material in Anthropology does not mean that the reverse is also true. We can only infer this if we knew that the two departments cover an identical amount of material. However, if Area Studies covers more material than Anthropology, it is possible that Anthropology duplicates a much smaller fraction of the Area Studies material, even though Area Studies duplicates 25 percent of the Anthropology material.
Take a simpler scenario: John has 4 apples and Mary has 10. If they share one apple in common, Mary shares 25% of John’s apples, whereas John shares only 10% of Mary’s apples.
Answer choice (E): This Opposite answer is the logical opposite of answer choice (A). If Area Studies meets neither one of the two necessary conditions for receiving funding—it duplicates 25 percent of the material covered in another department and has fewer than 50 people per year available for hire, it would not receive funding. This would contradict the final sentence in the stimulus, in which the administrator explicitly states that they will fund the new department.