SAT Math Multiple Choice Practice Question 44: Answer and Explanation

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Question: 44

22. Melvin, Chris, Enoch, Dave, Carey, Mike, Dan, and Peter are choosing dorm rooms for college. Each room holds four people. They have the following requirements:

I.Mike and Melvin refuse to live together.

II.Enoch will live with Chris or Carey (or possibly both).

III.If Dave and Dan live together, Peter will live with them.

When rooms are chosen, Melvin, Carey, and Dan live together. Which of the following groups must live in the other room?

A. Chris, Dave, and Mike
B. Chris, Mike, and Peter
C. Dave, Enoch, and Peter
D. Dave, Mike, and Peter
E. Enoch, Mike, and Peter

Correct Answer: A


A. Call the room shared by Melvin, Carey, and Dan room X, and the other room Y. Because Mike and Melvin won't live together, Mike must be in room Y. Now, if Dave and Dan live together, Peter will live with them, but you can't fit two more people into room X, so Dave and Dan must live apart, which puts Dave in room Y also. Similarly, because Enoch will live with Chris or Carey, Chris can't be in room X either, which puts Chris, Dave, and Mike in room Y.

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