AMC10美国数学竞赛真题2003B卷

Problem 1

Which of the following is the same as

Solution

Problem 2

Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs more than a pink pill, and Al's pills cost a total of for the two weeks. How much does one green pill cost?

Solution

Problem 3

The sum of consecutive even integers is less than the sum of the first

consecutive odd counting numbers. What is the smallest of the even integers?

Solution

Problem 4

Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost each, begonias each, cannas each, dahlias each, and Easter lilies each. What is the least possible cost, in dollars, for her garden?

Solution

Problem 5

Moe uses a mower to cut his rectangular -foot by -foot lawn. The swath he cuts is inches wide, but he overlaps each cut by inches to make sure that no grass is missed. He walks at the rate of feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow the lawn?

Solution

Problem 6

Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is . The horizontal length of a \-inch\in inches, to which of the following?

Solution

Problem 7

The symbolism

and

denotes the largest integer not exceeding

. Compute

Solution

. For example,

Problem 8

The second and fourth terms of a geometric sequence are and . Which of the following is a possible first term?

Solution

Problem 9

Find the value of

that satisfies the equation

Solution

Problem 10

Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of the three letters followed by three digits. By how many times is the number of possible license plates increased?

Solution

Problem 11

A line with slope intersects a line with slope at point distance between the

-intercepts of these two lines?

Solution

. What is the

Problem 12

Al, Betty, and Clare split among them to be invested in different ways. Each begins with a different amount. At the end of one year, they have a total of

. Betty and Clare have both doubled their money, whereas Al has managed to lose . What was Al's original portion?

Solution

Problem 13

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