Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is
years. How many years older than Bella is Anna?
3
The eighth grade class at Lincoln Middle School has students. Each student takes a math class or a foreign language class or both. There are
eighth graders taking a math class, and there are
eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
39
A bus takes minutes to drive from one stop to the next, and waits
minute at each stop to let passengers board. Zia takes
minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus
stops behind. After how many minutes will Zia board the bus?
17
Carrie has a rectangular garden that measures feet by
feet. She plants the entire garden with strawberry plants. Carrie is able to plant
strawberry plants per square foot, and she harvests an average of
strawberries per plant. How many strawberries can she expect to harvest?
1920
How many positive integers can fill the blank in the sentence below?
“One positive integer is _____ more than twice another, and the sum of the two numbers is .”
9
A game board consists of squares that alternate in color between black and white. The figure below shows square
in the bottom row and square
in the top row. A marker is placed at
A step consists of moving the marker onto one of the adjoining white squares in the row above. How many
-step paths are there from
to
(The figure shows a sample path.)
28
Luka is making lemonade to sell at a school fundraiser. His recipe requires times as much water as sugar and twice as much sugar as lemon juice. He uses
cups of lemon juice. How many cups of water does he need?
24
How many positive integer factors of have more than
factors? (As an example,
has
factors, namely
and
)
7
Each square in a grid is randomly filled with one of the
gray and white tiles shown below on the right.
What is the probability that the tiling will contain a large gray diamond in one of the smaller
grids? Below is an example of such tiling.
1/64
Zara has a collection of marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?
12
Suppose of
equals
of
What percentage of
is
75
What is the area of the triangle formed by the lines ,
, and
?
16
Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculationwhere temperature is measured in degrees Fahrenheit
and the wind speed is measured in miles per hour (mph). Suppose the air temperature is
and the wind speed is
mph. Which of the following is closest to the approximate wind chill?
23
A scientist walking through a forest recorded as integers the heights of trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
24.2
Rectangles and
and squares
and
shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of
in units?
651