1. Triangle ABC is an obtuse, isosceles triangle. Angle A measures
20 degrees. What is the measure of the
largest interior angle of triangle ABC?
degrees
1. ________________
2. Quentin spent $480 to purchase 30 books. Using the same
average price per book, how much will 45 books cost?
$
2. ________________
3. In Clara county, 25% of households earn less than $30,000 per
year, and 65% of households earn less than $80,000 per year.
What is the largest possible percent of households that could
earn between $30,000 and $80,000 per year?
percent
3. ________________
4. For what value of x is the following equation true:
3000 + x  2000 = 1500 + 1000?
4. ________________
5. How many cubic feet are in one cubic yard? One yard is equal
to three feet.
cu feet
5. ________________
1 cu ft
1 cu yd
6. Forty-eight congruent parallelograms with sides of length
62 feet and 20 feet are placed in a chevron pattern forming
hexagon ABCDEF, as shown. What is the perimeter of hexagon
ABCDEF?
A
B
F
E
feet
6. ________________
C
D
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Sprint Round
7. The mean of four distinct positive integers is 5. If the largest
integer is 13, what is the smallest integer?
7. ________________
8. Congruent segments are used to form equilateral triangles in
this sequence so that each figure contains one more triangle
than the preceding figure. Figure 3 of the sequence is made
with seven congruent segments. How many congruent
segments must be used to make Figure 25 of the sequence?
segments
8. ________________
Figure 1
Figure 2
Figure 3
Figure 4
9. What is the sum of the odd integers from 11 through 39,
inclusive?
9. ________________
10. The average amount of money spent by a person who attended
a local sporting event in 2000 was $8.00, of which 75% was
the ticket price. In 2005, the average amount of money spent
by a person who attended a local sporting event increased
by 50%, but the ticket price did not increase. By how many
dollars did the non-ticket costs of 2000 increase to become the
non-ticket costs of 2005?
$
10. ________________
11. The I-Pick-Up messenger service delivers packages using the
following rate structure: $1 per ounce of the packages’ weight
plus $5 for each distinct drop-off site. Then a 4% service fee
per order is added to the subtotal of the weight and drop-off
site charges. Chen Li places the order below. How much
should I-Pick-Up charge for Chen Li’s order? (There are
16 ounces in one pound.)
1 four-ounce package to Imatrin
1 two-pound package to Imatrin
1 eight-pound package to Storyville
$
11. ________________
12. A line contains the points (1, 6), (6, k) and (20, 3). What is
the value of k?
12. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Sprint Round
13. A particular convex polygon with seven sides has exactly
one right angle. How many diagonals does this seven-sided
polygon have?
diagonals
13. ________________
14. The product of three consecutive odd integers is 1287. What is
the sum of the three integers?
14. ________________
15. In square ABCD, point M is the midpoint of side AB and point
N is the midpoint of side BC. What is the ratio of the area
of triangle AMN to the area of square ABCD? Express your
answer as a common fraction.
15. ________________
16. How many non-congruent triangles are there with sides of
integer length having at least one side of length five units and
having no side longer than five units?
triangles
16. ________________
17. What is the value of the following expression:
17. ________________
1 1 1 1
1
? Express your
3 9 27 81 243
answer as a common fraction.
18. A customer ordered 15 pieces of gourmet chocolate. The order
can be packaged in small boxes that contain 1, 2 or 4 pieces
of chocolate. Any box that is used must be full. How many
different combinations of boxes can be used for the customer’s
15 chocolate pieces? One such combination to be included is
to use seven 2-piece boxes and one 1-piece box.
combinations
18. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Sprint Round
19. The value of [x] is the greatest integer less than or equal to x.
What is the arithmetic mean of the 10 members of the set
[;P=, ; =, ;0=, ; =, ;0.689=, ¨ª
1
2
1
2
P
4
19. ________________
·¹, ¨ª P3 ·¹, ;2=, ¨ª 5 ·¹ , ;P=]?
Express your answer as a common fraction.
20. The summary of a survey of 100 students listed the following
totals:
59 students did math homework
49 students did English homework
42 students did science homework
20 students did English and science homework
29 students did science and math homework
31 students did math and English homework
12 students did math, science and English homework
How many students did no math, no English and no science
homework?
students
20. ________________
21. Given that 6x + y = 15, the value of 3x can be written in terms of y
as ay + b for some numbers a and b. What is the simplified value
of a + b?
21. ________________
22. Suelyn counts up from 1 to 9, and then immediately counts down
again to 1, and then back up to 9, and so on, alternately counting
up and down (1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,2,3,4,...). What is
the 1000th integer in her list?
22. ________________
23. The positive three-digit integer N yields a perfect square when
divided by 5. When N is divided by 4, the result is a perfect cube.
What is the value of N?
23. ________________
24. Grady rides his bike 60% faster than his little brother Noah. If
Grady rides 12 miles further than Noah in two hours, how fast
does Noah ride?
miles per hour
24. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Sprint Round
25. The length of a diagonal of a square is 2 3 units. What is
the area of the square? Express your answer in simplest
a
a
form as c , where is a common fraction and c has no
b
b
perfect square factors other than 1 .
sq units
25. ________________
26. Either increasing the radius or the height of a cylinder by six
inches will result in the same volume. The original height of
the cylinder is two inches. What is the original radius?
inches
26. ________________
27. Consider this pattern where
the positive, odd integers
are arranged in a triangular
formation. The 1st through
4th rows are shown; each row
has one more entry than the
previous row. What is the sum
of the integers in the 15th row?
1
3
7
13
27. ________________
5
9
15
11
17
19
28. Four couples are at a party. Four people of the eight are
randomly selected to win a prize. No person can win more
than one prize. What is the probability that both members
of at least one couple win a prize? Express your answer as a
common fraction.
28. ________________
29. The points of this 3-by-3 grid are equally spaced
horizontally and vertically. How many different
sets of three points of this grid can be the three
vertices of an isosceles triangle?
sets
29. ________________
30. In parallelogram ABCD, AB = 16 cm, DA = 3 2 cm, and
sides AB and DA form a 45-degree interior angle. In isosceles
trapezoid WXYZ with WX ≠ YZ, segment WX is the longer
parallel side and has length 16 cm, and two interior angles each
have a measure of 45 degrees. Trapezoid WXYZ has the same
area as parallelogram ABCD. What is the length of segment YZ?
centimeters
30. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Sprint Round
1. The symbols !, ", # and $ each represent a distinct digit that
has not been used already in the subtraction problem below.
Whenever a symbol appears more than once, it represents the
same digit each time. What is the digit that ! represents in the
following subtraction problem?
1. ________________
6 " #
!! 8 #
1 $ "
2. An 8-inch by 8-inch square is folded along a diagonal creating
a triangular region. This resulting triangular region is then
folded so that the right angle vertex just meets the midpoint of
the hypotenuse. What is the area of the resulting trapezoidal
figure?
sq inches
2. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Target Round
3. The distance between two cities on a map is 4 centimeters. If
the scale is 0.5 cm = 1 km, how far apart are the actual cities?
kilometers
3. ________________
4. Six years ago a vacant lot was turned into a park. At that time
46 trees were planted. Three years ago 50 trees were planted in
the park, and 60 trees were planted in the park today. Each tree
was planted as a seed. Assuming that all of these planted trees
survive and no other trees are added in the next 10 years, what
will be the average age of the trees in the park 10 years from
today? Express your answer to the nearest whole number.
years
4. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Target Round
5. In order to compute the area of a particular circle, Juan first
measures the length of its diameter. The actual diameter is
20 cm, but Juan’s measurement has an error of up to 20%.
What is the largest possible percent error in Juan’s computed
area of the circle?
percent
5. ________________
6. A quadrilateral in the plane has vertices at (1, 3), (1, 1), (2, 1)
and (2006, 2007). What is the area of the quadrilateral?
sq units
6. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Target Round
7. Six boys and six girls are seated randomly in a row of
12 chairs. What is the probability that no two boys are seated
next to one another and no two girls are seated next to one
another? Express your answer as a common fraction.
7. ________________
8. Dr. Lease leaves his house at exactly 7:20 a.m. every
morning. When he averages 45 miles per hour, he arrives at
his workplace five minutes late. When he averages 63 miles
per hour, he arrives five minutes early. What speed should Dr.
Lease average to arrive at his workplace precisely on time?
Express your answer as a decimal to the nearest tenth.
miles per
8. ________________
hour
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Target Round
1. The positive integer divisors of 175, except 1, are arranged
around a circle so that every pair of adjacent integers has a
common factor greater than 1. What is the sum of the two
integers adjacent to 7?
1. ________________
2. The square quilt block shown is used in a larger
quilt. The four small squares in the block are
congruent, and the four small vertical rectangles
in the block that are not squares are also
congruent. The total area of the shaded regions
is what fraction of the total area of the block?
Express your answer as a common fraction.
2. ________________
3. The ages of the 27 students signed up for the community
center’s Spanish I class are given below. In the stem and leaf
plot shown, 3 2 represents 32 years old. For this data, the
mean is x years, the median is y years, and the mode is z years.
What is the value of x(y  z)?
3. ________________
1
2
3
4
9
0
0
5
9
0 1 1 2 4 5 5 6 7 8 8
0 0 1 2 2 4 4 5 8 9
8
4. If 40♦ represents a three-digit positive integer with a ones digit
of ♦ and 1♦ is a two-digit positive integer with a ones digit of ♦,
what value of ♦ makes the equation 40♦ ÷ 27 = 1♦ true?
4. ________________
5. A particular right pyramid has a square base, and each edge
of the pyramid is four inches long. What is the volume of the
pyramid? Express your answer as a decimal to the nearest
hundredth.
cu inches
5. ________________
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Team Round
6. The diagram shown is the net of a regular dodecahedron. In
a regular dodecahedron, three edges come together at each
vertex. When the net of this
dodecahedron is put together, the
solid has x vertices and y edges.
What is the value of x + y?
6. ________________
7. On the first day, Barry Sotter used his magic wand to make an
object’s length increase by 12 ; on the second day he increased
the object’s longer length by 13 ; on the third day he increased
the object’s new length by 14 ; and so on. On the nth day of
performing this trick, Barry will make the object’s length
exactly 100 times its original length. What is the value of n?
7. ________________
8. A cube is sliced with one straight slice which passes through
two opposite edges. The result is two solids, as shown. The
area of the largest face on one of these two solids is
242 2 square units. What was the exact surface area of the
original cube? Express your answer in simplest form.
sq units
8. ________________
9. Using the digits 2, 3, 4, 7 and 8, Carlos will form five-digit
positive integers. Only the digit 2 can be used more than once
in any of Carlos’ five-digit integers. How many distinct fivedigit positive integers are possible?
integers
9. ________________
10. Bricklayer Ben places 42 bricks per hour. Bricklayer Bob
places 36 bricks per hour. Bricklayer Bob worked twice as
many hours as Bricklayer Ben, and the two of them placed a
total of 1254 bricks. How many bricks did Bricklayer Ben
place?
10. ________________
bricks
Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Team Round