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The following are sample problems from the Prince George's Community College Math Tournament held at the school's Largo campus April 18.

Answers are listed at the bottom.

1. In "PGCC," each distinct letter is replaced by a different digit 0 to 9. The difference between the largest and the smallest four-digit number so created is divisible by two prime numbers between 10 and 100. Find those prime numbers.

2. There are seven brothers in the Tryhard family. Any of the six older brothers can clean the house in 12 hours. The youngest brother, 2-year old Jack Tryhard, can on the other hand, mess up the house in three hours. How long does it take for the seven brothers "working" together to clean the house?

3. One of Prince George's branch libraries has between 2,500 and 3,500 books. 1/11 of them are math books, 1/19 of them are social science books and 20 percent of them are novels. How many books does the library have?

Answers:

1. 11 and 23

2. 6 hours

3. 3,135 books