Mathematical Olympiad + mean - practice problems
Number of problems found: 7
- Below-average 60271
In a given group of numbers, one number is equal to the average of all, the largest number is 7 larger than the average, the smallest is 7 smaller than the average, and most numbers in the group have below-average values. What is the smallest number of nu - Grandchildren 80639
The average age of the grandfather, grandmother, and their five grandchildren is 26 years. The average age of the grandchildren themselves is 7 years. Grandma is a year younger than grandpa. How old is grandma? - Christmas trees
The salesman sold Christmas trees: spruce for € 22, pine for € 25, and fir for € 33. In the morning, he had the same number of spruce, fir, and pine. In the evening, he had all the trees sold for € 3,600. How many trees does the day salesman sell? - Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, the average age was again equal to the number present. How many people were original to celebrate? - Squirrels
The squirrels discovered a bush with hazelnuts. The first squirrel plucked one nut, the second squirrel two nuts, and the third squirrel three nuts. Each new squirrel always tore one nut more than the previous squirrel. When they plucked all the nuts from - MO Z8–I–6 2018
The KLMN trapezium, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line. - Between two bus stops
Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that he would have arrived at the bus stop if he had run to one or the other. The average bus speed is 60 km/h. What is the average speed of Wanda r
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