2013-14 Problems

5th and 6th graders

February, 2014

B.953. Sam transferred an ever-growing bean plant into his garden from the greenhouse. On the first day the plant grew a half of its original height. On the second day it grew 1/3 of its height at the beginning of that day. On the third day it grew 1/4 of its height at the beginning of that day, and so on. How many days did it take the plant to grow until it became as tall as 100 times its original height?

B.954. I have more than 2 animals at home. All of them are dogs, except for 2. All of them are cats, except for 2. All of them are hamsters, except for 2. What kinds of animals and how many of each animal do I have?
B.955. There are 5000 families living in the village of Neverfind. Every family has no more than 2 dogs. Most families have one dog, and half of the rest of the families have no dogs at all. How many dogs are there in Neverfind, if there are no homeless dogs?

B.956. Corina asked John: "How old are you?" John said: "2 days ago I was still 16 years old. Next year I will turn 19." What is John's birthday, and what day of the year did Corina ask him this question?

B.957. Alice and Bob are competing in The ABACUS International Math Competition. If Alice had half the points she has, and Bob had half more than what he has, then Alice had 1/3 of the points of Bob. Who is ahead of the other now in the competition?

B.958. John, Frank and Peter are competing in a league of the three of them. Everybody plays the same number of games with everybody. There is no tie, somebody always wins a game. Frank won twice against Peter and four times against John. John won four times against Peter and three times against Frank. Peter won 5 times against Frank and three times against John. How many games were there all together, and how many games did each player play?

B.959. Quadrilateral ABCD is a parallelogram. Its area is 24 area units. M and N are the midpoints of sides AD and BC. What is the area of triangle OQP?

B.960. Vera has a lucky 2-digit number. When she multiplies the two digits, she gets half of the number. What is her lucky number?

Please, send your solutions here 

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