Read the following information carefully and answer the questions given below:
Six executives—P, Q, R, S, T, and U—occupy individual floors of a six-storey office building, numbered 1 (ground floor) through 6 (topmost floor). Each executive decorates their workspace with a different theme: Minimalist, Vintage, Rustic, Modern, Industrial, and Bohemian.
T resides on an odd-numbered floor above floor 1, but does not use the Minimalist or Bohemian themes. Exactly two people live between T and the person whose office is decorated in a Vintage style. The person with the Modern office lives on a floor immediately above the one with the Vintage office. Q lives on a floor higher than the person with the Modern office, but Q's office is not Rustic. The number of floors below S is equal to the number of floors above R. P lives on an even-numbered floor below R. The executive with the Bohemian theme lives on a floor above the one with the Industrial theme, but below U. S does not have a Rustic or Minimalist theme.
Correct Answer :
Modern
Solution :
The correct answer is Modern.
Let me break down the step-by-step logical reasoning to determine the floor positions and decoration themes of each executive:
Step 1: Determine the floors for T, Vintage, and Modern themes
1. The building consists of 6 floors numbered 1 (ground floor) through 6 (topmost floor).
2. Executive T resides on an odd-numbered floor above floor 1, which means T can be on floor 3 or floor 5.
3. Exactly two people live between T and the person whose office is decorated in a Vintage style.
- If T were on floor 3, Vintage would have to be on floor 6 (since 3 + 3 = 6). However, the Modern office is immediately above Vintage, which would require floor 7 (invalid, as there are only 6 floors).
- Therefore, T must be on floor 5.
4. With T on floor 5, placing two people between T and Vintage puts the Vintage theme on floor 2 (floors 3 and 4 are between them).
5. The Modern theme is immediately above the Vintage theme, so the Modern theme is located on floor 3.
Step 2: Determine the positions of S, R, and P
1. We are given that the number of floors below S equals the number of floors above R.
Let represent the floor number of S and represent the floor number of R.
Floors below S =
Floors above R =
2. "P lives on an even-numbered floor below R."
Since P must live on an even-numbered floor lower than R:
- If R is on floor 3, P must be on floor 2 (the only even floor below floor 3).
- Using , if R is on floor 3, then S is on floor 4.
Checking this: there are 3 floors below S (floors 1, 2, 3) and 3 floors above R (floors 4, 5, 6), which satisfies the rule perfectly.
Step 3: Identify the theme for R
From Step 1, floor 3 is decorated with the Modern theme.
From Step 2, executive R occupies floor 3.
Therefore, executive R selects the Modern theme for their office.
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