ABACUS International Math Challenge
for
5th and 6th graders
October, 2003
B.385. We bought 5 cheese danish and 4
strawberry danish and paid a total of $4.45. Next time we bought 8 cheese
danish and 7 strawberry danish and paid a total of $7.45. How much would
we have to pay if we bought one of each danish.
B.386. The sum of two numbers is a 3-digit
number, which ends with 27. One of the numbers ends with zero, and if we
delete the digit zero from this number we get the other number. Find these
two numbers.
B.387. My friend and I both have an analog
watch. My watch is fast by one second every hour, but my friend's watch
is late by one and a half second every hour. Right now they show the same
time. When will this happen again for the first time?
B.388. We asked three people if they are
liars or they tell the truth. Those who are liars always lie, and those
who tell the truth they always tell the truth. We could not hear the answer
of the first person. The second person said: "He said he tells the
truth." Then the third person looked at the second person and said:
"You are a liar." Is the third person a liar or not?
B.389. On the escalator in a shopping mall
64 steps go down every minute. Julie can make 96 steps upwards on a regular
stairway in a minute. In the shopping mall there are 48 steps of a difference
between two consecutive floors. Julie wants to go up on the escalator that
is going downwards walking by her own regular speed of walking on the stairs.
How many minutes does it take her to go up one floor?
B.390. A man has less than 1000 apples
for sale. If he sold them in groups of 5, 6, 7, or 8, he would always have
one apple left over. How many apples does he have?
B.391. Mrs. Taylor had to wash the 30 meter
wide curtain in the theater. After washing this huge curtain, she wanted
to hang it with clips by clipping the two ends of the curtain onto the rod,
and then clips the middle of the curtain. Then she clips the middle of every
section onto the rod, and so on. How many clips does she need if she wants
the clips to be no more than 20 cm and no less than 10 cm apart?
B.392. Sarah and Lilly are traveling together
on the train from Washington to New York. During their conversation it turns
out that both of them made this trip several times before, and always by
train. One of them lives in Washington, and the other lives in New York.
Sarah took a train between these two cities 95 times including this trip,
while Lilly had only 86 trips. Where do these girls live?
Please, send your solutions to: