University administrator: Any proposal for a new department will not

Question

University administrator: Any proposal for a new department will not be funded if there are fewer than 50 people per year available for hire in that field and the proposed department would duplicate more than 25 percent of the material covered in one of our existing departments. The proposed Area Studies Department will duplicate more than 25 percent of the material covered in our existing Anthropology Department. However, we will fund the new department.

Which one of the following statements follows logically from the university administrator’s statements?

(A) The field of Area Studies has at least 50 people per year available for hire.
(B) The proposed Area Studies Department would not duplicate more than 25 percent of the material covered in any existing department other than Anthropology.
(C) If the proposed Area Studies Department did not duplicate more than 25 percent of the material covered in Anthropology, then the new department would not be funded.
(D) The Anthropology Department duplicates more than 25 percent of the material covered in the proposed Area Studies Department.
(E) The field of Area Studies has fewer than 50 people per year available for hire.

KarishmaB · Accepted Answer

This is the admin's argument: 
Any new dept will NOT be funded if A AND B.
A - fewer than 50 people for hire
B - Duplicate more than 25% stuff of existing dept

A new dept will not be funded if BOTH A and B are satisfied.

Area studies satisfies B. However, we will fund Area Studies. (Since it duplicates more than 25% stuff of another dept, one might expect the admin to not fund the new dept. But the university is funding the new dept. Hence the use of "however")

What does this imply? That A is NOT satisfied. If both A and B had been satisfied, Area studies would not have been funded. 
If A is not satisfied, it means there're at least 50 people for hire.

Answer (A)

vanam52923 · Answer

Though the solution is straight forward ,i didnot understand the question itself.
What does it mean?
 The proposed Area Studies Department will duplicate more than 25 percent of the material covered in our existing Anthropology Department. However, we will fund the new department.

What is the role of however.
Does it mean in spite of fulfilling one condition only (25 percent copy) we will allow Area studies dept?
should not however be hence then
or does it mean inspite of filling this condition,we will not allow Area study department and will allow some other new department?
Why did they use the word new department instead of Area search dept?
Plz explain 
 daagh 
 VeritasKarishma

gvij2017 · Answer

Here I would like to raise my hand.

If A  and   B both are satisfied, no fund to new department. 
Means fund will issued only when condition A and Condition B are met.

Given:
Condition B satisfied, but fund still sanctioned.
It will tear apart the premise. 
And how can we say that one condition is met and other is not met, but fund was sanctioned for new department.

If this "and" were replaced with "or", argument could be more clear, isn't it?

AKY13 · Answer

Hi Karishma,
 
We have  AND  condition not  OR  condition. 
We are asked what can be logically followed.

If the admin can deviate condition B(<25% duplicate), it may be having power & authority to deviate condition A(>50% hire) also. Hence we can't logically follow statement A. 
Had A been phrased as new deptt. having potential of more than 90% hire, it could have been stronger but still not the best since no limit of deviation is mentioned in the argument.

I see statement D can be logically followed. We can't eliminate D just because it is too simple to logically followed.

Am I missing something.

HoneyLemon · Answer

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

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 ) AND (> 25%.) --> ~ PF

In taking the contrapositive of a conditional statement containing two sufficient conditions, “and” becomes “or” and vice versa:

PF --> ≥ 50P or ≤ 25%

Note also that instead of simply negating each of the sufficient conditions, we automatically translated them into their functional meaning (for example, “not less than 50 people” becomes “at least 50 people” or “50 or more people” when negated).

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.

jim441 · Answer

This is the admin's argument:
Any new dept will NOT be funded if A AND B.
A - fewer than 50 people for hire
B - Duplicate more than 25% stuff of existing dept

As per question B was satisfied, so how can they fund the department coz it's an "and" which means both A & B should be satisfied in order to be correct. So even if there are more than 50 people available for hire, still they shouln't fund the department coz cleearly B has been satisfied and hence doesn't qualify

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University administrator: Any proposal for a new department will not

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