A team of five archaeologists—Q, R, S, T, U—are excavating five sites—Site 1, Site 2, Site 3, Site 4, Site 5. Each archaeologist is assigned to exactly one site, and each site has exactly one archaeologist. The following conditions apply: 1. Q is assigned to a site with a lower number than R. 2. S is assigned to Site 3. 3. T is assigned to a site immediately adjacent to Q's site. 4. U is assigned to a site with a higher number than T. Which of the following is a complete and accurate list of the sites to which Q could be assigned?
- ASite 1
- BSite 1, Site 2
- CSite 1, Site 2, Site 3
- DSite 1, Site 2, Site 4
Show answer & explanationAnswer & explanation
Correct answer: B. Site 1, Site 2
Archaeologists: Q, R, S, T, U Sites: 1, 2, 3, 4, 5 Fixed: S = Site 3 (Rule 2) Let's test possible sites for Q: * **Q = Site 1:** * Rule 3: T is immediately adjacent to Q's site. So T = Site 2. * Current: Q T S _ _ (1=Q, 2=T, 3=S, 4=?, 5=?) * Rule 1: Q < R. Since Q=1, R can be 4 or 5. * Rule 4: U > T. Since T=2, U can be 4 or 5. * So, R and U must be 4 and 5. This is possible. (e.g., R=4, U=5 or R=5, U=4). Both work. * Q can be Site 1. * **Q = Site 2:** * Rule 3: T is immediately adjacent to Q's site. T can be Site 1 or Site 3. * Case 1: T = Site 1. * Current: T Q S _ _ (1=T, 2=Q, 3=S, 4=?, 5=?) * Rule 1: Q < R. Since Q=2, R can be 4 or 5. * Rule 4: U > T. Since T=1, U can be 4 or 5. * So, R and U must be 4 and 5. This is possible. (e.g., R=4, U=5 or R=5, U=4). * Q can be Site 2 (with T=1). * Case 2: T = Site 3. This conflicts with S = Site 3 (Rule 2). So T cannot be Site 3. * Q can be Site 2. * **Q = Site 3:** * This directly conflicts with S = Site 3 (Rule 2). So Q cannot be Site 3. * **Q = Site 4:** * Rule 3: T is immediately adjacent to Q's site. T can be Site 3 or Site 5. * Case 1: T = Site 3. This conflicts with S = Site 3 (Rule 2). So T cannot be Site 3. * Case 2: T = Site 5. * Current: _ S _ Q T (1=?, 2=?, 3=S, 4=Q, 5=T) * Rule 1: Q < R. Since Q=4, R must be Site 5. But T is already in Site 5. This is a conflict. So R cannot be placed. * Q cannot be Site 4. * **Q = Site 5:** * Rule 1: Q < R. Since Q=5, there is no site with a higher number for R. This conflicts with Rule 1. So Q cannot be Site 5. Therefore, only Site 1 and Site 2 are possible assignments for Q. The complete and accurate list is Site 1, Site 2.
Why the other options are wrong
- A. This list is incomplete, as Q can also be assigned to Site 2.
- C. Incorrect, Q cannot be assigned to Site 3 because S is already there (Rule 2).
- D. Incorrect, Q cannot be assigned to Site 4 because it leads to a contradiction with R or T.
Exhaustive Possibility Listing
Determining all possible positions an element can occupy by systematically testing each potential position against all rules and eliminating those that lead to contradictions.
- Test each potential position one by one.
- Apply all rules for each test case.
- Eliminate positions that violate any rule or create an impossible scenario.
Memory trick: Try every door, only open the ones that don't trigger alarms.