Q:
A university library budget committee must reduce exactly five of eight areas of expenditure—I, J, K, L, M, N, O and P—in accordance with the following conditions:
If both I and O are reduced, P is also reduced.
If L is reduced, neither N nor O is reduced.
If M is reduced, J is not reduced.
Of the three areas J, K, and N exactly two are reduced.
Question :
If both K and N are reduced, which one of the following is a pair of areas neither of which could be reduced?
Answer & Explanation
Answer: B) J, L
Explanation: This question concerns a committee’s decision about which five of eight areas of expenditure to reduce. The question requires you to suppose that K and N are among the areas that are to be reduced, and then to determine which pair of areas could not also be among the five areas that are reduced.
The fourth condition given in the passage on which this question is based requires that exactly two of K, N, and J are reduced. Since the question asks us to suppose that both K and N are reduced, we know that J must not be reduced:
Reduced :: K, N
Not reduced :: J
The second condition requires that if L is reduced, neither N nor O is reduced. So L and N cannot both be reduced. Here, since N is reduced, we know that L cannot be. Thus, adding this to what we’ve determined so far, we know that J and L are a pair of areas that cannot both be reduced if both K and N are reduced:
Reduced :: K, N
Not reduced :: J, L
Answer choice (B) is therefore the correct answer.
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