ABACUS International Math Challenge
for
3rd and 4th graders
September, 2008
A.641. Olga noticed in a store that the
numbers on the price tags are such 3-digit numbers that are one less than
the numbers rounded to the nearest tens, and if you round the prices to
the nearest hundreds you always get 20 less than the number rounded to the
nearest tens. Find all these 3-digit numbers.
A.642. You can see 9 little cars in the
window of a toy store. From left to right every car (except for the first
one) costs $2 more than the previous one. You can buy the one in the middle
and the one on its left for the price of the last one all the way to the
right. What are the prices of the least and the most expensive cars if you
can buy all 9 of them for $90?
A.643. The Action Hero characters are very
popular at the toy store. This week on Monday people already bought half
of the inventory plus 4. By Wednesday 1/3 of the rest was sold, and only
46 of them were left on the inventory. How many Action Heroes were sold
in the 3 days (from Monday to Wednesday)?
A.644. The third and fourth graders are
going on a field trip to see a forest. On Monday the students went with
the hunters to fill up the animal feeders. The deer feeder was 480 meters
from the rabbit feeder, 60 meters farther than it is from the boar feeder.
How far could the rabbit feeder be from the boar feeder if they are as far
from each other as possible?
A.645. On Tuesday morning the students
had three options: they could either go on a bird watch or on an insect
watch tour, or they could stay back to do pottery. Three times as many (28
more) students chose to go on the bird watch than on the insect watch tour,
and 12 students stayed for pottery. How many students are there on the trip?
How many of them went on the bird watch and how many of them went on the
insect watch tour?
A.646. On Tuesday afternoon the students
played a game of "The War of the Numbered Kids." In this game
(3rd grade vs. 4th grade) each student places a card, with a 4-digit number
on it, on his/her forehead. (The 3rd graders use red numbers and the 4th
graders use blue numbers.) A student is out of the game if his/her number
and the color of his/her number is read properly by somebody from the other
team. The reader also has to describe the location of that student. Just
calling out numbers randomly disqualifies you from the game. Students could
pick a number below 2000, with a 1 or 7 on the tens place and an even digit
on the hundreds place. The digit in the ones place could not be less than
6. Each student on each team had to have a different number. How many students
could participate on each team?
A.647. On Wednesday afternoon the students
made bread. For one loaf of bread you need: 500 g of white flower, 500 g
of rye flower, 20 g of yeast, 100 g of margarine, 50 g of sugar, 10 g of
salt, 100 g of boiled potatoes, and 100 g of milk. The dough loses one tenth
of its mass during baking. How much is the mass of one loaf of bread?
A.648. On Thursday the Fourth Grade organized
a competition on an obstacle course in the forest. The 3-person teams left
the hunters' house every 8 minutes, and after a 40-minute tour they returned
back there. What time did the last (the 16th) team get back to the house
if the first team left at 8:45 am?
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