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SOURCE:COMPETITION Number of Problems: 11. FOR PRINT ::: (Book)
Each day, Jenny ate of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, remained. How many jellybeans were in the jar originally?
Since Jenny eats of her jelly beans per day, of her jelly beans remain after one day.
Let be the number of jelly beans in the jar originally.
A solid box is cm by cm by cm. A new solid is formed by removing a cube cm on a side from each corner of this box. What percent of the original volume is removed?
The volume of the original box is
The volume of each cube that is removed is
Since there are corners on the box, cubes are removed.
So the total volume removed is .
Therefore, the desired percentage is
A positive number has the property that of is . What is ?
At Euclid High School, the number of students taking the AMC 10 was in 2002, in 2003, in 2004, in 2005, and 2006, and is in 2007. Between what two consecutive years was there the largest percentage increase?
We compute the percentage increases:
The answer is .
In fact, the answer follows directly from examining the differences between each year. The largest differences are , and it is easy to see that due to the decreased starting number of students in 2002 that that will be our answer.
Last year Mr. Jon Q. Public received an inheritance. He paid in federal taxes on the inheritance, and paid of what he had left in state taxes. He paid a total of 10500 for both taxes. How many dollars was his inheritance?
After paying his taxes, he has of the inheritance left. Since is of the inheritance, the whole inheritance is .
In a certain year the price of gasoline rose by during January, fell by during February, rose by during March, and fell by during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is
Let be the price at the beginning of January. The price at the end of March was Because the price at the of April was , the price decreased by during April, and the percent decrease was So to the nearest integer is . The answer is .
Makarla attended two meetings during her -hour work day. The first meeting took minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
The percentage of her time spent in meetings is the total amount of time spent in meetings divided by the length of her workday.
The total time spent in meetings is
Therefore, the percentage is
In a collection of red, blue, and green marbles, there are more red marbles than blue marbles, and there are more green marbles than red marbles. Suppose that there are red marbles. What is the total number of marbles in the collection?
The number of blue marbles is , the number of green marbles is , and the number of red marbles is .
Thus, the total number of marbles is , and the answer is .
A carton contains milk that is % fat, an amount that is % less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?
Rewording the question, basically we are being asked "2 is 40% less than what number?" If x represents the number we are looking for, then 40% less than the number would be represented by or . Thus ; solving for x, we get ,