ABACUS International Math Challenge
for
5th and 6th graders
February, 2006
B.529. A village wants to build a 1500
meter-pedestrian walk for which they have $62500. 1 meter of asphalt-covered
walkway costs $36, 1 meter tiled walkway costs $53. The village wants to
tile as much of the walkway as they can afford. How many meters will be
covered with tiles and how many meters with asphalt?
B.530. The length of the edge of a cube
in centimeters is a whole number. The volume of this cube is less than 1
cubic meter but not smaller than 1 cubic decimeter. How many such different
sized cubes are there?
B.531. There are two wheels on a bicycle
with circumferences 220 cm. The distance between the points of the wheels
touching the ground is 110 cm. With this bicycle we cross a 6 cm wide freshly
painted line in a direction perpendicular to the line. The wheels get paint
on them. After we crossed the line, and travel in a straight line, what
kind of marks do the wheels leave on the ground within the next 11 meters?
B.532. We put together 3 identical rectangles,
as shown on the diagram. The area of the big rectangle we get is 1350 square
centimeters. What is the perimeter of the big rectangle?
B.533. On a rainy day a store sold 55 umbrellas
in 5 different colors. They sold 5 times as many red as blue, 3 times as
many green as blue, 9 more black than blue, and 7 less purple than black
umbrellas. How many umbrellas did they sell from each color?
B.534. In a sports equipments store they
sell ping-pong balls in bags of 5 or 8 balls. Steve did not know that you
are not allowed to open the bags before paying for them, and asked for a
certain number of balls. The saleswoman said that she was sorry but she
could not give him that many, but if Steve asked for 1 or 2 or any other
number more balls then she could give them to him without having have to
open any of the bags. How many balls did Steve want to buy?
B.535. Find the smallest positive even
number that can be written as the sum of 2 prime numbers in four different
ways. (The order of the two primes is not important.)
B.536. Teri thought of a positive whole
number. She told me that it has 12 positive divisors, including 6 and 25.
What is Teri's number?