Problem 1
A scout troop buys candy bars at a price of five for $. They sell all the candy bars at a price of two for $. What was the profit, in dollars?
Solution
Problem 2
A positive number has the property that
of is . What is ?
Solution
Problem 3
A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?
Solution
Problem 4
For real numbers
and , define
?
. What is the value of
Solution
Problem 5
Brianna is using part of the money she earned on her weekend job to buy several equally-priced CDs. She used one fifth of her money to buy one third of the CDs. What fraction of her money will she have left after she buys all the CDs?
Solution
Problem 6
At the beginning of the school year, Lisa's goal was to earn an A on at least of her quizzes for the year. She earned an A on of the first quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?
Solution
Problem 7
A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square?
Solution
Problem 8
An -foot by
-foot ?oor is tiled with square tiles of size foot by foot. Each
foot
tile has a pattern consisting of four white quarter circles of radius
centered at each corner of the tile. The remaining portion of the tile is shaded.
How many square feet of the ?oor are shaded?
Solution
Problem 9
One fair die has faces , , , , , and another has faces , , , , , . The dice are rolled and the numbers on the top faces are added. What is the probability that the sum will be odd?
Solution
Problem 10
In
on line
, we have such that
and
lies between and
. Suppose that is a point and . What is ?
Solution
Problem 11
The first term of a sequence is . Each succeeding term is the sum of the
cubes of the digits of the previous term. What is the term of the sequence?
Solution
Problem 12
Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime?
Solution
Problem 13
How many numbers between and ?
are integer multiples of or but not
Solution
Problem 14
Equilateral midpoint of
has side length , . What is the area of
is the midpoint of
?
, and
is the