Division E
4A Time: 4 minutes
A digital clock shows 2:35. This is the first time after midnight when all three digits are different prime numbers. What is the last time before noon when all three digits on the clock are different prime numbers?
4B Time: 5 minutes
The only way that 10 can be written as the sum of 4 different counting numbers is 1 + 2 + 3 + 4. In how many different ways can 15 be written as the sum of 4 different counting numbers?
4C Time: 5 minutes
The tower shown is made of congruent cubes stacked on top of each other. Some of the cubes are not visible. How many cubes in all are used to form the tower?
4D Time: 6 minutes
Hannah gives clues about her six-digit secret number:
Clue 1: It is the same number if you read it from right to left.
Clue 2: The number is a multiple of 9.
Clue 3: Cross off the first and last digits. The only prime factor of the remaining four-digit number is 11.
What is Hannah’s six-digit number?
4E Time: 7 minutes
The L-shape pictured is formed from three squares, each 1 cm on a side. Five of these L-shapes are placed next to each other to form a figure. What is the least possible perimeter of the figure they form, in cm?
Division M
4A Time: 3 minutes
Find the sum of the integers from –2007 through +2009, inclusive.
4B Time: 5 minutes
The sum of the lengths of three sides of a rectangle is 55 cm. Each side is a whole number of cm in length. The length is 8 cm more than the width. Find the perimeter of the rectangle, in cm.
4C Time: 4 minutes
Jen travels from home on a straight road. After a rest she returns along the same route. The graph shows her distance from home at any given time. What was her average speed for the entire 4-hour trip, in miles per hour?
4D Time: 6 minutes
The pages of a book are consecutively numbered from 1 through 384. How many times does the digit 8 appear in this numbering?
4E Time: 6 minutes
The product of 180 and the positive integer N is a perfect cubic number. What is the least possible value of N?