ABACUS International Math Challenge
for
5th and 6th graders
December, 2005
B.513. They wrote the following interesting
things about a man who was born after 100 AC. "Both the first and last
day of his life were the first days of palindrome years. During his life
he lived in 11 palindrome years. Even if he lived a long life, he did not
get to celebrate his 100th birthday." When was he born and when did
he die?
B.514. 8 volumes of a series of books was
published in 8 consecutive years. The sum of those 8 numbers is 15716. Which
year was the first volume published?
B.515. What is worth more money: 5 kg of
dimes or 10 kg of nickels? (The mass of a dime is 2.3 grams and it is worth
10 cents, the mass of a nickel is 5.1 grams and it is worth 5 cents.)
B.516. Both the sum and the product of
a few positive whole numbers are 91. What are these numbers?
B.517. Yesterday Lucy bought 9 bagels,
6 rolls, 12 eggs (for 15 cents each), and she also needed milk, so she decided
to buy 3 one-liter containers of milk. Good thing she did that, because
when she wanted to pay, the cashier asked for $8.65 . How did Lucy know
that the cashier was wrong even if Lucy did not know the unit prices of
the other items?
B.518. On the rectangle, covered by a square
grid below, the area of the black part is 192 sq.cm. Every curved line is
a quarter circle. How long is the side of a little square?
B.519. Tim took the train home and he fell
asleep half way home. When he woke up he realized that he will still have
to travel half of the time he just spent sleeping. What part of his whole
trip home did he sleep through? (The train was traveling with a uniform
speed for the whole trip home.)
B.520. How many different size rectangular
base columns can you build using 24 identical cubes?