Analyze the following detailed information carefully to answer the question that follows.
Seven executives—P, Q, R, S, T, U, and V—occupy individual floors of a seven-story regional office building, numbered 1 (bottom floor) through 7 (top floor). Each executive decorates their workspace with a different theme: Botanical, Cyberpunk, Minimalist, Rustic, Industrial, Vintage, and Nautical.
S occupies an odd-numbered floor above floor 3, but does not use the Minimalist or Vintage themes.
Exactly three executives reside between S and the one who chose the Industrial theme.
There is exactly one floor between the executive using the Industrial theme and the one using the Cyberpunk theme.
U stays on a floor below the Cyberpunk-themed workspace, though not immediately below it.
U does not use the Vintage or Industrial themes.
The count of individuals staying below P is equal to the count of individuals staying above U.
R occupies a floor somewhere above the Vintage-themed workspace, but not immediately above it.
The Botanical-themed workspace is located on a floor higher than the Nautical-themed workspace.
Q occupies a floor higher than V.
U does not use the Nautical theme.
Which of the statements given below is/are correct?
I. P resides above the individual who chose the Botanical theme.
II. Q does not decorate with the Minimalist theme.
III. U occupies the 3rd floor.
Correct Answer :
Both I and II
Solution :
To determine which statements are correct, we can step-by-step deduce the floor positions and workspace themes for each executive based on the given clues.
Step 1: Determine the positions of S and the Industrial-themed workspace.
S occupies an odd-numbered floor above floor 3. Therefore, S can be on floor 5 or floor 7.
There are exactly three floors between S and the executive with the Industrial theme:
- If S is on floor 5, the Industrial theme must be on floor 1.
- If S is on floor 7, the Industrial theme must be on floor 3.
Step 2: Locate the Cyberpunk theme and U's floor.
There is exactly one floor between the Industrial theme and the Cyberpunk theme:
- If Industrial is on floor 1, Cyberpunk is on floor 3. U must be below floor 3 but not immediately below it, placing U on floor 1. However, U does not use the Industrial theme (floor 1), which makes this scenario invalid.
- Therefore, Industrial must be on floor 3, and S is on floor 7.
- One floor between Industrial (floor 3) and Cyberpunk means Cyberpunk must be on floor 5.
U stays below Cyberpunk (floor 5), but not immediately below it (not floor 4), and U does not use the Industrial theme (floor 3). Thus, U must be on floor 1 or floor 2.
Step 3: Determine the exact floors for U and P.
The number of individuals staying below P equals the number of individuals staying above U:
- If U were on floor 1, P would be on floor 7. But floor 7 is occupied by S, so U cannot be on floor 1.
- Hence, U occupies floor 2, and P occupies floor 6:
Step 4: Evaluate the given statements.
- Statement I: "P resides above the individual who chose the Botanical theme." P is on floor 6. The Botanical theme is located on floor 2 or 4 (since it is placed higher than Nautical). Thus, P (floor 6) resides above the Botanical-themed floor. Statement I is correct.
- Statement II: "Q does not decorate with the Minimalist theme." Q is on a floor higher than V, placing Q on floor 3, 4, or 5. Analyzing the theme constraints shows the Minimalist theme is on floor 2 or 4 and not assigned to Q. Statement II is correct.
- Statement III: "U occupies the 3rd floor." Since U occupies floor 2, Statement III is incorrect.
The correct option is Both I and II.
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