Mathcounts Chapter Competition Solutions Worksheet - Middle School - 2014 Page 2
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triangles. There are 4 of those.
Competition
Sprint Round
The total number of triangles is 8 + 4 + 4 =
1. (
+ 2)/3 = 5
+ 2 = 15
= 13 Ans.
16 Ans.
2. A shirt sells originally for $10. 30% off is
5. There are 4.5 inches of snow on the ground.
10 × 0.7 = 7
Snow is falling at an average rate of 1.5
Arturo pays $7 for the shirt. 50% more than
inches per hour for 9 more hours. At this rate,
$7 is 7 + (1/2 × 7) = 7 + 3.50 = 10.50 Ans.
an additional 9 × 1.5 = 13.5 inches of snow
will fall.
3. Sally needs a cleaning solution of 1 part
This makes a total of 4.5 + 13.5 = 18 inches
bleach to 8 parts water. That means she
that will have fallen. 18 Ans.
needs 1 quart of bleach for every 8 quarts of
water. Therefore, she needs 24/8 = 3 quarts
of bleach. 3 Ans.
6. Given xy = 100, find the positive difference
between the maximum and minimum possible
values of x + y, if x and y are positive.
4. A square is divided by its four lines of
Integer pairs with a product of 100 are:
symmetry. The four lines are symmetry are the
1 × 100
two diagonals and the horizontal and vertical
2 × 50
bisectors of the square.
4 × 25
5 × 20
10 × 10
So, x + y has minimum and maximum values
10 + 10 = 20 and 1 + 100 = 101,
respectively, and 101 – 20 = 81 Ans.
There are 8 triangles created by the bisectors.
7. A bat catches 560 bugs in 7 nights.
The bat catches the same number of bugs
each night.
Each night, the bat caught 560/7 = 80 bugs.
Therefore, the bat caught 80 bugs on the fifth
Let’s put together two adjacent triangles that
night. 80 Ans.
form a bigger triangle. There are 4 of those.
8. This problem basically asks us to find the
length of the diagonal of a square with side
length 20.
You may recognize that the diagonal of a
square also is the hypotenuse of a 4545-90
There’s no way to put three adjacent triangles
right triangle. Recall that a 4545-90 right
together but we can do four adjacent
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