Seven college applicants – Michelle, North, Oscar, Pachai, Quinn, Raul, and Savannah – are admitted to three different colleges – X Y and Z. Two students are admitted to X, two students are admitted to Y, and three students are admitted to Z. The following conditions must apply:
1. Michelle is admitted to the same college as Savannah
2. Pachai is admitted to a different college than Quinn
3. If Oscar is admitted to college Y, then North is admitted to college Z
4. Pachai is admitted to Z
4. If Pachai gets accepted to the same college as Michelle, each of the following could be true EXCEPT:
A. North is accepted to college X
B. Raul is accepted to college X
C. Oscar is accepted to college Y
D. Quinn is accepted to college Y
E. North is accepted to college Y
Answer
CORRECT ANSWER: (C) – Oscar is accepted to college Y
EXPLANATION: If Pachai gets accepted to the same college as Michelle, that means they both must have been accepted to college Z since P is always in Z, per rule #4. We also know that wherever Michelle is accepted, Savannah must be accepted also per rule #1. So college Z is all filled up. Oscar, therefore, cannot be accepted to college Y, because if Oscar is accepted to Y, that means North must be accepted to college Z per rule #3, and there are no more spots open in college Z.
EXPLANATION: If Pachai gets accepted to the same college as Michelle, that means they both must have been accepted to college Z since P is always in Z, per rule #4. We also know that wherever Michelle is accepted, Savannah must be accepted also per rule #1. So college Z is all filled up. Oscar, therefore, cannot be accepted to college Y, because if Oscar is accepted to Y, that means North must be accepted to college Z per rule #3, and there are no more spots open in college Z.
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