Problem 1
The median of the list
is
the mean?
Solution
. What is
Problem 2
A number is more than the product of its reciprocal and its additive inverse. In which interval does the number lie?
Solution
Problem 3
The sum of two numbers is . Suppose is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?
Solution
Problem 4
What is the maximum number for the possible points of intersection of a circle and a triangle?
Solution
Problem 5
How many of the twelve pentominoes pictured below have at least one line of symmetry?
Solution
Problem 6
Let
and
denote the product and the sum, respectively, of the digits of
and
. Suppose
is a
?
the integer . For example,
two-digit number such that . What is the units digit of
Solution
Problem 7
When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number?
Solution
Problem 8
Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their
schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab?
Solution
Problem 9
The state income tax where Kristin lives is levied at the rate of
of annual income plus
of any amount above
of the first
. Kristin of her
noticed that the state income tax she paid amounted to annual income. What was her annual income?
Solution
Problem 10
If ,
, and are positive with
is
,
, and
Solution
, then
Problem 11
Consider the dark square in an array of unit squares, part of which is shown. The ?rst ring of squares around this center square contains unit squares. The second ring contains unit squares. If we continue this process, the number of unit squares in the ring is
Solution
Problem 12
Suppose that is the product of three consecutive integers and that by . Which of the following is not necessarily a divisor of ?
is divisible
Solution
Problem 13
A telephone number has the form , where each letter represents a different digit. The digits in each part of the numbers are in decreasing order; that is, , , and . Furthermore, , , and are consecutive even digits; , , , and are consecutive odd digits; and . Find .
Solution
Problem 14
A charity sells benefit tickets for a total of . Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?
Solution
Problem 15
A street has parallel curbs feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is feet and each stripe is feet long. Find the distance, in feet, between the stripes?
Solution
Problem 16
The mean of three numbers is more than the least of the numbers and less than the greatest. The median of the three numbers is . What is their sum?
Solution
Problem 17
Which of the cones listed below can be formed from a radius by aligning the two straight sides?
sector of a circle of
Solution
Problem 18
The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to
Solution
Problem 19
Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?
Solution
Problem 20
A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length . What is the length of each side of the octagon?