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Problem 1

Each morning of her five-day workweek, Jane bought either a 50-cent muffin or a 75-cent bagel. Her total cost for the week was a whole number of dollars, How many bagels did she buy?

Solution

Problem 2

Which of the following is equal to

?

Solution

Problem 3

Paula the painter had just enough paint for identically sized rooms.

Unfortunately, on the way to work, three cans of paint fell off her truck, so she had only enough paint for rooms. How many cans of paint did she use for the rooms?

Solution

Problem 4

A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths and meters. What fraction of the yard is occupied by the flower beds?

Solution

Problem 5

Twenty percent less than 60 is one-third more than what number?

Solution

Problem 6

Kiana has two older twin brothers. The product of their three ages is 128. What is the sum of their three ages?

Solution

Problem 7

By inserting parentheses, it is possible to give the expressionseveral values. How many different values can be obtained?

Solution

Problem 8

In a certain year the price of gasoline rose by during January, fell by during February, rose by during March, and fell by during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is ?

Solution

Problem 9

Segment and

and

intersect at

, as shown,

?

,

. What is the degree measure of

Solution

Problem 10

A flagpole is originally meters tall. A hurricane snaps the flagpole at a point meters above the ground so that the upper part, still attached to the stump, touches the ground meter away from the base. What is ?

Solution

Problem 11

How many -digit palindromes (numbers that read the same backward as forward) can be formed using the digits , , , , , , ?

Solution

Problem 12

Distinct points , , , and lie on a line, with . Points and lie on a second line, parallel to the first, with . A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?

Solution

Problem 13

As shown below, convex pentagon has sides , ,

, , and . The pentagon is originally positioned in the

plane with vertex at the origin and vertex on the positive -axis. The pentagon is then rolled clockwise to the right along the -axis. Which side will touch the point on the -axis?