ABACUS International Math Challenge
for
7th and 8th graders
October, 2000
C.201. Multiply all the positive divisors
of 90. How many zeros are there at the end of this number?
C.202. Find the fraction between 1/2000
and 1/2001 with the smallest numerator.
C.203. Find a 4-digit square number, such
that if you increase its every digit by one, you still have a square number.
C.204. The height of a symmetrical trapezoid
is 10 units. What is its area if its diagonals are perpendicular to each
other?
C.205. An airplane takes off from an airport
and flies South 100 km, then it turns East and flies 100 km, then it turns
North and flies 100 km, then it turns West and after flying 100 km it arrives
back to the same airport it started from. Where on Earth is this airport?
(Ignore the rotation of the Earth.)
C.206. Peter and Wendy live in a big skyscraper
building, with 10 apartments on every floor. The apartments are located
in this building on the first floor and above, and numbered continually
starting with one on the first floor. Peter's floor number is the same as
Wendy's apartment number. The sum of their apartment numbers is 239. What
are their apartment numbers?
C.207. Put the 4-digit numbers into two
groups based on whether they are the products of two 2-digit numbers or
not. Which group is greater?
C.208. A, B, C, D, E, and F participated
in a competition. After the first round the judge said: "3 competitors
got 10 points, the rest of you got 7 points. Everybody, write down who you
think got 10 points." The competitors gave in the following guesses:
A, B, D
A, C, E
A, D, E
B, C, E
B, D, E
C, D, E
Then the judge said that none of these guesses guessed all three of
them right, 3 people guessed 2 of them right, and 2 people guessed 1 right,
and one person guessed totally incorrectly.
Who got 10 points?
Please, send your solutions to: