In a 1050-room competitive set, Hotel A has 300 rooms. Hotel B has 350 rooms, and Hotel C has 400 rooms. During a recent 30-day period in which the entire competitive set sold 25,400 rooms, Hotel A sold 8,000 rooms. Which of the following statements is indisputably TRUE?

Question

BlackTom AI · Accepted Answer

Fair share is calculated as (hotel rooms / total rooms) × total rooms sold.

1) Relevant concepts
- Fair share = proportion of total rooms × total rooms sold.
- If one hotel exceeds its fair share, at least one other hotel must be below its fair share because the sum of actual rooms sold equals the sum of fair shares (the total sold).

2) Step-by-step reasoning and calculations
- Total rooms in competitive set = 300 + 350 + 400 = 1,050.
- Hotel A’s proportion = 300 / 1,050 = 2 / 7 ≈ 0.285714.
- Fair share for Hotel A = 0.285714 × 25,400.
  Intermediate: 25,400 × (2/7) = (25,400 / 7) × 2.
  25,400 / 7 = 3,628.57142857.
  Multiply by 2 → 7,257.14285714 rooms (A’s fair share).
- Actual rooms sold by Hotel A = 8,000.
- Difference = 8,000 − 7,257.142857 ≈ 742.857143 rooms above fair share.

3) Why the correct answer is correct
Hotel A sold about 8,000 rooms while its calculated fair share was about 7,257.14 rooms; therefore Hotel A exceeded its fair share by approximately 743 rooms. That makes statement c indisputably true.

4) Why other choices are incorrect
- a (Neither B nor C achieved fair share): Not indisputable. Because A exceeded its fair share, the combined remainder for B and C is reduced, but it is possible (though not both) that one of B or C still reached its individual fair share while the other fell short. So you cannot assert neither achieved fair share.
- b (Both B and C achieved fair shares): Impossible given A exceeded its fair share, because the total sold is fixed; if A is above its fair share, the sum of actual sales would exceed total if both B and C also met or exceeded theirs.
- d (Hotel A failed to achieve its fair share): Directly contradicted by the calculation showing A sold more than its fair share.

5) Conclusion
The correct and indisputably true statement is c. Hotel A exceeded its fair share (matches the provided answer).

In a 1050-room competitive set, Hotel A has 300 rooms. Hotel B has 350 rooms, and Hotel C has 400 rooms. During a recent 30-day period in which the entire competitive set sold 25,400 rooms, Hotel A sold 8,000 rooms. Which of the following statements is indisputably TRUE?Single choice

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