In a 30-day month beginning with a Sunday, a museum records an average of 720 visitors on Sundays, and the number of visitors on…

Question

In a 30-day month beginning with a Sunday, a museum records an average of 720 visitors on Sundays, and the number of visitors on each of the other days is half of that number.

What is the average number of visitors per day during the month?

1. A. 420 (Correct answer)
2. B. 408
3. C. 540
4. D. 520

Correct Answer

Option A — 420

Detailed Solution & Explanation

The correct answer is 420.

Key Points

• A 30-day month beginning on a Sunday has Sundays on the 1st, 8th, 15th, 22nd and 29th — 5 Sundays and 25 other days.
• Visitors on Sundays = 5 × 720 = 3,600.
• Visitors on other days = 25 × 360 = 9,000 (each other day being half of 720).
• Total = 12,600 over 30 days, so the average = 12,600 ÷ 30 = 420.

Additional Information

• The detail that the month *begins with a Sunday* is what fixes the count at 5 Sundays; a 30-day month starting on another weekday may contain only 4.
• The distractor 408 arises from assuming 4 Sundays: (4 × 720 + 26 × 360) ÷ 30 = 408.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*