Download 1) Find the value of 12006 3

1. Find the value of 12006  3.
(A) 0 (B) 3 (C) -3 (D) 4
(E) 6018
2. Square ABCD is inscribed in circle O, with OD=10. E is the midpoint of AB and F is
the midpoint of BC. G is the midpoint of EF. Find the area of quadrilateral AEGD.
(A) 200 (B) 175 (C) 87.5 (D) 17.5 + 15 2 (E) 5+25 2
5
3. Find the x-coordinate of the x-intercept of the line y = -2x + .
2
5
5
(A) 0 (B)-2 (C)
(D)
(E) Does not exist
4
2
4. At Mathcounts nationals, a volunteer committee is selected from 8 people. However,
Klebian absolutely refuses to work with ehehheehee. Thus, ehehheehee and Klebian can
not both be on the committee. How many ways are there to do this?
(A) 56 (B) 50 (C) 28 (D) 336 (E) 300
5. Find the sum of the infinite series 4  2  1 
1 1 1
   ...
2 4 8
7
(B) 8 (C) 10 (D) 16 (E) 
8
6. Tommy is eight years old. His mother, Tammy, is twelve times older than one-half of
Tommy’s age two years ago. If the current year is 2006 and Tammy will die in 54 years,
how old will Tammy be when she dies?
(A) 2060 (B) 2070 (C) 36 (D) 90 (E) 100
(A) 7
7. How many distinct, non-congruent triangles can be drawn in a regular hexahedron?
(A) 3 (B) 4 (C) 20 (D) 56 (E) 0
8. Find the sum of all of the real roots of x2 + 2x + 8 = 0.
(A) 0 (B) 8 (C) -8 (D) -2 (E) 2
9. Quadrilateral ABCD has AB = 2, BC = 3, CD = 4, and DA = 5. mA = 460 and mC =
1340. Find the area of ABCD.
(A) 60 (B) 120 (C) 2 210 (D) 2 30 (E) Can’t tell
10. $10 is placed in a bank account at the beginning of every year. At a 6% annual
interest rate, how many dollars will there be at the end of the 10th year? Assume the
interest is compounded, and round to the nearest dollar.
(A) $100 (B) $133 (C) $16 (D) $18 (E) $140
11. Find the 20th term in the sequence 0, 11, 26, 45, 68, 95, …
(A) 209 (B) 810 (C) 893 (D) 980 (E) 1071
12. Treething has 9 pairs of gloves in a box. He has 4 identical pairs of black, 3 identical
pairs of brown, and 2 identical pairs of red. If he picks two gloves at random, what is the
probability that he picks a left glove and a right glove of the same color?
(A)
9
34
(B)
29
153
(C)
100
253
(D)
25
91
(E)
3
7
13. If daine increases her speed by 5 miles per hour, she will make the 780 mile trip in 1
hour less time. What is her original rate of speed, in miles per hour?
(A) 78
(B) 65
(C) 73
(D) 55
(E) 60
14. Cylinder A’s radius is 2/3 the measure of cylinder B’s radius, and cylinder B’s height
is 2/3 the measure of cylinder A’s height. Find the ratio of the volume of A to the volume
of B.
(A) 1:1 (B) 3:2 (C) 9:4 (D) 2:3 (E) 4:9
15. Senor Generosa has a total of $28 to give away to his class. He has 28 students in his
class. For each proper factor of 28, he gave away that much money to one of his students.
A student could not receive more than one prize. For example, he gave one person
exactly $4 as a prize, and that person did not receive any other prize. How many ways
could he have distributed the money?
(A) 11793600 (B) 98280 (C) 271252800 (D) 376740 (E) Not possible
16. A digital clock displays the hour and minutes of the day. From midnight to noon, how
many more minutes have at least one four appearing than minutes with at least one seven
appearing?
(A) 0 (B) 48 (C) 72 (D) 90 (E) 99
17. There are 500 students at Ignite168 Junior High. Let M be the set of 120 students who
participate in math contests and C be the 150 students who sing in the chorus. If M  C =
70, find the complement of M  C, where all of the students at Ignite168 Junior High is
the universe of discourse.
(A) 430 (B) 500 (C) 300 (D) 160 (E) 840
18. Weng-him has an average of exactly 85% on 5 tests. If 100% is the highest score, and
all of his test scores were distinct positive integers, what is the minimum score he could
have attained?
(A) 25 (B) 0 (C) 31 (D) 85 (E) 28
19. In the game of Backgammon, there is a cube with the numbers 2, 4, 8, 16, 32, and 64
on it. If this cube and a standard pair of dice are rolled together, what is the probability
that the sum of the numbers on these cubes is a prime number?
1
11
11
61
1
(A)
(B)
(C)
(D)
(E)
3
72
36
216
6
20. Jar A contains 2 red marbles and 1 blue marble. Jar B contains 1 red marble and 2
blue marbles. A marble is selected at random from jar A and placed in jar B, then a
marble is drawn at random from jar B. What is the probability that it is not blue?
1
3
1
5
7
(A)
(B)
(C)
(D)
(E)
4
4
2
12
12
21. A “triangular triple” is an ordered triplet of triangular numbers such that the sum of
the lesser two numbers is equal to the third. How many triangular triples (a, b, c) are that
a, b, c are all less than 70, when a, b, c are not necessarily distinct?
(A) 3 (B) 5 (C) 9 (D) 27 (E) 30
22. In chess, a knight can make 5 moves without crossing its path on a 4x4 board, as
shown below.
What is the maximum number of moves a knight can make without crossing its path on a
5x5 board?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
23. Coach Bionunquieneist gave his twelve basketball players a passing drill. He put
them in a circle, so that the person with jersey number 0 was first, 1 was right next to him
going clockwise, then 2, all the way up to 11. He gave the ball to the person with jersey
#1 to pass 1 to the left then 2 to the left, etc. The passing went on for a long time. Find
the number of players who did not touch the ball.
(A) 0 (B) 1 (C) 2 (D) 3 (E) more than 3
24. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Find the number of n, from set A, that satisfy
the congruence n5  1(mod11).
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
25. Three congruent circles are externally tangent. The area of the region inside the
circles is 100 3 - 50  . Find the area of one of the circles.
(A) 10 (B) 20 (C) 10  (D) 25 
(E) 100 
26. Find the number of space diagonals in a regular icosahedron.
(A) 1140 (B) 100 (C) 72 (D) 36 (E) 6
27. Pentagon ABDEC is made up of equilateral triangle ABC on top of square BDEC.
8  4 3 . Find the area of ABCDE.
The length of AD is
(A) 4 +
3
(B) 10
(C) 5
(D) 6
(E) 16 + 4 3
28. How many ways are there to place 7 indistinguishable balls in 2 distinguishable
boxes?
(A) 21
(B) 256
(C) 8
(D) 4
(E) 128
29. Kyyuanmathcount is shooting targets. He has three columns of targets to choose
from. Two columns have 3 targets, 1 column has 2 targets. He begins by selecting a
column. Once he selects the column, he shoots the bottom target of that column. He never
misses. Find the number of ways he can shoot down all 8 targets.
(A) 28
(B) 56
(C) 560
(D) 6561
(E) 40320
30. A cylinder is inscribed in a cone such that the cylinder has the largest possible
volume. If the diameter of the cone is 10, the altitude of the cone is 12, and the height and
diameter of the cylinder are equal, find the radius of the cylinder.
(A)
8
3
(B)
30
11
(C) 3
(D)
25
8
(E)
7
2
31. Lotrgreengrapes has two pet rabbits, a male and a female. Both are newborn. Rabbits
can mate once they turn one month old, and mate forever, once a month. The rabbits are
immortal. When two rabbits mate, the female produces one rabbit. Assume there will be
enough male and female rabbits for mating. If Lotrgreengrapes got his rabbits in January
2006, in what month will he first have more than 800 rabbits? There is no gestation
period.
(A) April 2007
(B) May 2007
(C) June 2007
(D) July 2007
(E) August 2007
32. Ch1n353ch3s54a1l likes to play Chinese chess (surprising). He enters a double
elimination tournament consisting of 32 players (including himself- or herself, s/he didn’t
tell me his/her name). In double elimination, one is not eliminated until he or she loses
two games. Everything is best of 1. Once someone loses two games, he or she no longer
plays. Ch1n353ch3s54a1l wins the tournament, and he won his first game. Let A be the
maximum amount of games played in the tournament, B be the minimum number of
games played in the tournament, C be the maximum number of games that
Ch1n353ch3s54a1l played, and D be the minimum. Find (A + B) - (C + D).
(A) 136 (B) 112 (C) 52 (D) 55 (E) 63
33. Daniel Li deposited his $2000 from the masters round in a bank account that pays
4.8% interest annually, compounded monthly. Rounded to the nearest dollar, how much
interest is in the bank account after exactly 1 year? Do not do any intermediate rounding.
(A) $2096
(B) $2098
(C) $96
(D) $98
(E) $107
34. Pianoforte needed to multiply a number 2 more than a multiple of 7 by some other
number, n, to get 3 more than a multiple of 7. If Pianoforte only can use one of the
following numbers for n, what integer n does he multiply?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
35. A bagful of coins weighs 235 grams. If 1 penny weighs 3 grams, a nickel weighs 5
grams; a dime weighs 2 grams, and a quarter weighs 6 grams. If the bag can only have
these four coins, what is the maximum amount of money in the bag?
(A) $11.61 (B) $9.61 (C) $11.60 (D) $9.60 (E) $9.76
36. Allie, Billy, Casey and Davey are playing out in the snow. Each wears a hat and a
scarf. How many ways can they exchange hats and scarves such that each person has a
hat and a scarf that is not theirs and the hat and scarf that they get do not belong to the
same person?
(A) 576 (B) 36 (C) 24 (D) 12 (E) 6
37. In the picture below, ABCD is a rectangle and EFGH is a parallelogram. Vertices H
and F meet the short sides of the rectangle one third of the way up or down on their
respective edges of ABCD. Vertices E and G meet the rectangle one quarter of the way
from the left of right of their respective edges. What fraction of the area of the rectangle
is outside EFGH?
A
E
B
H
F
C
D
(A)
G
1
4
(B)
1
3
(C)
5
12
(D)
1
2
(E)
7
12
38. How many different lines contain exactly 3 points in the lattice grid bounded by the
lines x = 0, x = 4, y = 4, y = 0? (including the points on the lines)
(A) 2300
(B) 0
(C) 28
(D) 20
(E) 16
39. In the figure below, B is the center of the circle, A, C, and D are on the circle, the
measure of angle ACB is 65 degrees, and the measure of angle BCD is 14 degrees. Find
the measure of angle ADC.
C
A
B
D
(A) 14
(B) 25
(C) 65
(D) 30
(E) 50
40. A “comprimesite” number is the product of two primes. A “comprimesite
factorization is a way of expressing integers as the product of comprimesite and prime
numbers. The order never matters. One prime is allowed in a comprimesite factorization,
but all of the other numbers must be comprimesite. For example, 4 x 4 x 5 is a
comprimesite factorization of 80. How many distinct comprimesite factorizations are
there for 1800?
(A) 5
(B) 6
(C) 8
(D) 11
(E) 174