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