2003 AMC 10A
1、What is the difference between the sum of the first even counting numbers and the sum of the first odd counting numbers?

Solution          

The first even counting numbers are .
The first odd counting numbers are .
Thus, the problem is asking for the value of .
.
Alternatively, using the sum of an arithmetic progression formula, we can write .
2、Members of the Rockham Soccer League buy socks and T-shirts. Socks cost per pair and each T-shirt costs more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is , how many members are in the League?

Solution          

Since T-shirts cost dollars more than a pair of socks, T-shirts cost dollars.
Since each member needs pairs of socks and T-shirts, the total cost for member is dollars.
Since dollars was the cost for the club, and was the cost per member, the number of members in the League is .
3、A solid box is semicirclecm 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?

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