ABACUS International Math Challenge
for
5th and 6th graders
September, 2007
B.585. How many triangles with different
shapes and sizes can you draw so that its vertexes are on the dots of the
following diagram? (Two triangles of the same shape but different sizes
are considered to be different.)
B.586. Helga has two candles with different
thicknesses and different lengths. One of them, the 10-cm long candle, burns
down in 5 hours, the other in 6 hours. She lights them up at the same time
and in 2 hours they are the same length. How long was the other candles
originally?
B.587. Tom bought notebooks for 1/3 of
his money, then he bought chocolate for 1/3 of the rest of his money, and
then he bought a present for his brother for 1/3 of the rest of his money.
He has $80 left after all the shopping. How much money did he spend on chocolate?
B.588. Out of the following statements
exactly one is false:
1) A is older than B.
2) C is younger than B.
3) The sum of the ages of B and C is twice the age of A.
4) C is older than A.
Who is the youngest of them all?
B.589. Alan, Ben, Conrad, Danny and Edward
are going horseback riding. Five horses are waiting for them at the stable:
Kansas, Leila, Mirza, Nina and Oliver. Alan can ride only Kansas; Leila
wants to carry only Ben or Conrad; Ben, Conrad and Danny are the only ones
who can ride Mirza. How many different ways can they horseback ride together?
B.590. If you increase one side of a square
by 2/5 of that side, and you reduce the neighboring side by the same amount,
will the area of this new rectangle be different?
B.591. Two positive whole numbers are called
competitors if the product of the digits of either one of them is
greater than the sum of the digits of the other number. 6a5 and 31a are
competitors. What is smallest value of a?
B.592. We erected a flag on top of a sand
castle by sticking its pole vertically half way into the sand. The top of
the flag pole is 76 cm above the ground. The bottom of the pole is 60 cm
from the ground level. How tall is the castle and how long is the flag pole?