1.

In how many diffcrcnt ways can changc bc matlc

for $10 if only quarters or dimes are used?
2. A bag contains 10 marbles numbered 1-10. A inarblc
is rcmovcd from tlio bag, and without replacing it,
a second marble is drawn. Wlzat ia the probabWtg
that both numbers arc oddr? Exprw your answer as
a collllnon fraction.
3. A ~ i r c l e is circumscribcd around an
8cm x 6 cm rectangle. What is the number of squarc
centimeters in the area of the circle? Express your
answer in terms of T .
4. John's house is the twclfth from one chd of tfic row
and the fifth from the other end. How inany lzouses
are in the row'?
5 . Sixty-four 1'' x 1" x 1" cubes arc stacked t~ create a,
larger cube. The faces of thc ncw eubc are painted
white. What is the total number of faces of the
original cubes that remain unpainted?
6. Given that g(x) = ?, what is the value
of g ( $ ) - g ( - $ ) ?
7. When Jennifer bought a ncw car, she bought
five tires, although the car had only four wheels.
The tires were rotated so that when the car had
bcen drivcn 50 000 milcs, cach tire 11ad equal mileagc
and wcar. For how nluny nlilcs was tach tirc uscd?
8. What is the units digit of the prime
'

number 244 - 1:1

9. What is thc lcasl; intcgcr valuc of x for
which (2e- 31 < lo'?
10. Calculate the following, and express your answer as
a cominon fraction:

11. For how many positive integers n is 2n + 7 < 23?

12. What is the number of square inches in thc area
of a circle that has a circumference of 12n inches?
Express your answer in terms of n.
I+;
13. Calculate: m.Express your answer as a common
4+?
fraction.

1098-99 School Cou~~tdown.Round

15. The sequence 0 , 1 , 2 , 2 , 3 , 3 , 0 , 1 , 2 , 2 , 3 , 3 .-.
, . rcpeats
ewry six terms. The first term is 0, What is thc
908th tcrm?
16. How many three-digit numbers greater than 600 can
be formed from the digits 1, 3, 4, 6, 7, 8 &ad9 if no
repetitions are allowed?

17. At the Doggie Brash, dogs and thcir owners ran a

two-mile race. Thcrc wcrc 330 h c d s and 1040 legs
in the racc. How many dogs were in thc racc?
18. The probability of rain is 20% on Friday, 40%
on Saturday, and 50% on Sunday. Expressed as a
percent, what is the probability that there is no rain
on any of these three days?

10. A packer sorts eggs by sizc. She finds 5f dozcn large

eggs in the first 24 dozen eggs that she sorts. At this
rate, how many large eggs can she expect to find in
60 dozen eggs?

20. Mrs. Turncr gives a, multiple-choice test where

each question has four choices. If the test contains
fivc questions and Mark randomly guesscs dl of
the answers, what is t l ~ cprobability that hc gcts
all five correct? Express your answer as a common
fraction.
21. Ilow many squarcs arc pictured?

22. An average person can walk a mile in 15 minutes. 22.

At this rate, it takes 18 minutes to walk around the
outside of the Pentagon in Washington, .DC. What is
the number of feet in the perimeter of the Pentagon?
23. The United Statcs Mint produced 13.5 billion pennies 23.
in 1005. If thc value of thcsc pcnnics is exchanged
for hhc ssmc amount in dimes, how many dilncs
would be needcd?

1998-99 School Conntdowl~Rolulld

24. When three timcs a ecrtain natural nui~lbcris addcd 24.
to thc squaw of that nurnbcr, thc result is ten timcs
the original nuillbcr. What is the original number?

25. AABC is isosceles with AC = BC. If 7nL C = 40°, 25.

what is the number of degrees in m,L cBD?

26. Juanita paid $18 for a book after a 10% discount.

What was the number of dollars in the original price
of the book?
27. What is the number of degrees in the m e a w e of an
exterior angle of a regular octagon?
28. What is the fewest number of colors needed to
paint the faces of a regular octahedron so that no
two adjacent faces are the same color?
29. What time in the evening will appear on a digital
clock 465 minutes after it shows 2:00 p.m.?
30. If the word REPETITION is repeatedly written until
there are 1000 letters, what percent of the letters
are E's?
31. What is the maximum number of intersection points
in a diagram with two circles of unequal diameter
and a straight line?

32. What is the probability of rolling three number

cubes, each with digits 1-6, and getting the same
number on top of all three cubes? Express your
answer as a common fraction.
33. If 10 kids can mow 20 yards in 3 hours, how many
hours will it take 5 kids to mow 10 yards at the
same rate?
34. A softball team played 25 games and won 7 more
games than they lost. How many games did the
team win?

1998-99 School Countdown Round

-- -
 35. For what positive value of + does $ -
. 36. Marsha borrowed one mystery, one comedy and
&?

one adventure video from a friend. If the friend had

five mysteries, seven comedies, and six adventures
from which to choose, how many different sets of
tapes could Marsha have cA6seh?
37. A model of a square pyTamid k comtmctd ming 37.
tennis balls. There afe 16 balls in the bottom layer,
and 1 ball in the top layer. In all other layers, each
ball rests on 4 other balls. How many balls will be
needed to form this pyramid?
38. fn a bag, there are three red marbles, five white 38. -
marbles, and four blue marbles. What is thc fewest
number of marbles that must be pulled f r ~ mthe bag
to ensure that there is at least one of each color?
39. What number is one-fifth of one-fourth of one-third
of one-half of 1200?
40. Two sides of a triangle measure 4cm and 9cm.
What is the greatest integer number of centimeters
that could be the third side of this triangle?
41. One-fourth of a bridge's length l i e on the land t o
the east of a. river, and one-sixth of the bridge's
length lies on the land to thc w t sf the fiver. Tl1c
width of the span between the two sides of the river
is 840 feet. How many feet are in the total length of

3x-1 2
42. Solve for x: -- -
4%- 4 3'
43. What is thc grcatest integer less than q? 43.

44. Reggie rents a bicycle for a fee of $6 plus $5 for each 44.
hour or fraction of an hour. What is the maximum
number of hours for which he can rent the bicycle
for a total cost of $41?
1
45. Express (&)b a common fraction. 45.

46. The sum of three consecutive cvcn integers is 72. 46.

What is thc grcntcst of thcsc integers?
47. The hypotenuse of a right triangle measures 10 inchcs 47.
and one angle is 45". What is the number of square
inchcs in thc nrcn of thc trimglc?

I9!)8-99 School Countdown 12orrnd

 48. Arthur's scores on his first five tests were 86, 80, 85,
75 aild 84. What score must he get on the next test
so that his average will be exactly 85?
49. How many different committees of 9 people can be
chosen from a group of 12 pcoplc?
50. What is the number of cubic feet in the volume ~f a
cube that has a surface area sf 96 square feet?
51. What is the number of units in the length of the line
segment connecting (4,3) and ( = I 1=9) ?
52. .fenny walked of the way hornc from &li~@liii
21 minutes. If shc continues to w d k at I130 samc
rate, how many more minutes will it twko ,Jenny to
arrive hornc?
53. It takes 8.5 gallons of gasoline for a CNX ca.r to
travel 306 miles. What is the average numbcr of
miles per gallon for the trip?
1.
54. For what positive value of n: does - = 1?
12
3 2%

55. In Pat's first 30 foul shots at basketball practice, he

made 2 baskets for every 3 that he missed. How
many shots must he now make consecutively to bring
his percentage up to 50%?
56. A square measures 6 centimeters on each side. A
1.5-centimeter square is cut from each corner. The
sides are folded up to form a box. How many cubic
centimeters are in the volume of the box fbrmed?
Express your answer as a decimal to the nearest
tenth.
57. One diagonal of a rhombus is 8 inches long, and the 57.
other diagonal is G inches long. How many inches
are in the.perirnetcr of the rhombus?
1234
58. Compute: 58.
123s2 - (1234)(123G)'
I 50. What is the least whole number value of n for 59.
which is less than 0.2?
I

GO. A whole numbcr is said to bc "Q-hcavy" if the GO.

rcmaindcr whcn the numbcr is tlivitlccl by 9 is grcatcr
than 5. What is the least three-digit 9-heavy wl~olc
numbcr?

1008-00 School Countdown Round