ABACUS International Math Challenge

for

5th and 6th graders

April, 1999

B.121. The sides of a rectangle are 18 cm and 24 cm. We changed one of its sides by twice as much as we changed the other side to get a square. What is the size of this square?

B.122. There are 30 students in a class, more boys than girls. One night they all went to the theater. In the first intermission every girl bought a cheesecake, and every boy bought a coke. (A cake and a coke each costs a whole number of dollars.) In the second intermission every girl bought a coke and every boy bought a cheesecake. The class spent $2 less in the second intermission than in the first one. How many boys and girls are there in this class?

B.123. There are several different locks on the safe of a bank.Their keys are distributed among the four clerks of the bank in such a way that at least 3 of the clerks always have to be present if they want to open all the locks on the safe with the keys those people present have. (More than one person may have a key to the same lock, and a clerk may have more than one key.) How many locks are there on the safe?

B.124. You had to answer 20 questions on a test. For every correct answer you get 5 points, but for every incorrect answers you lose 2 points. If you do not answer a question, you get 0 points for it. One of your classmates received 48 points on this test. How many correct answers did she give?

B.125. Which number is greater and why: 191919/999999, or 191919191919/999999999999?

B.126. Find the greatest whole number with all different digits in which the sum of any three digits is not divisible by 19.

B.127. In a math class the teacher wrote a number on the board. One of the students said: "It is divisible by 31." Another student said: "It is also divisible by 30." the third student said: "It is also divisible by 29." And so on, and finally the 30th student said: "It is also divisible by 2." Then the teacher said that out of all of these observations only two consecutive statements were incorrect. What were these two statements?

B.128. Fill in the blanks with numbers so that the statement in the box is true.

In this box the number of digit 0's is ____, the number of digit 1's is ____, the number of digit 2's is ____, the number of digit 3's is ____, the number of digit 4's is ____, the number of digit 5's is ____, the number of digit 6's is ____, the number of digit 7's is ____, the number of digit 8's is ____, and the number of digit 9's is ____.

Please, send your solutions to:

tdiveki@gcschool.org

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