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What is the sum of the integers between
1 and 300 that are divisible by 11 or 13
(or both)?
Find three consecutive odd numbers such
that the sum of their squares is a four-digit
number with all four digits the same.
(
A stack of 100 nickels is 6.25 inches high.
To the nearest cent, how much would a
stack of nickels 8 feet high be worth?
Determine the largest prime divisor of
87! + 88!.
What is the ratio of the area of an equilateral triangle to that of a regular hexagon
inscribed in the same circle?
)
The sum of three numbers is 98. The first
number is 2/3 of the second, and the second is 5/8 of the third. What is the second
number?
*
Find the value in degrees of the sum of the
six angles indicated in the diagram.
B
C
D
E
A
B
C
D
A
E
+
A
,
F
Four congruent rectangles are arranged as
shown in the figure to form a large rectangle.
A
The area of the large rectangle is 768. What
is the area of a square that has the same
perimeter as the
large rectangle?
D
Solve for N if 6! • 7! = N!.
D
C
/
Find the measure of the angle z in the diagram here, given that the two horizontal
segments are parallel.
The number 2008 is a four-digit number
having two zeros and two even digits that
are not zeros. How many four-digit numC can also be described
bers besides 2008
this way?
B
0
145°
How many distinct triangles can be90°
conz
structed by choosing three vertices from
among the corners of a unit cube? 90°
1
2 3 z4
5 6 7 8 9
90°
10 11 12
13 14 15 16
135°
Among the triangles of problem 13, how
many distinct (noncongruent) triangles
exist?
90°
A
10
5
11
1
2
6
12
C3
4 D
7
8
9
X Y Z
13 14 15
Find the exact value of (111,111,111) .
B
C
D
A
E
F
((
Given a three-digit number, interchange
1
the units digit and the hundreds digit. The
2 3 4
product of 5the6original
and the
7 8 number
9
new number is 65,125. What is the smaller
10 11 12 13 14 15 16
three-digit1 factor?
145°
9
135°
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
()
If you continued the triangular array of
numbers shown in the figure, what number would be directly below 122?
B
.
2
('
135°
145°
F
B
(*
B
How long will it take a two-mile-long train
C
traveling 12 miles per hour to travel completely through a mile-long tunnel?
A
X
(+
Given theEdigits 1, 3, 6, and 9, find the
probability
that a four-digit number
D
formed
by using each of them only once is
Y Z
F
divisible by 7.
E
16
F
(In the sum of the expression 7 + 77 + 777 +
7777 + ... + 7,777,777,777,777,777,777,
what digit will be in the tens place?
O'
(.
The number 64 is divisible
O' by its units
digit (4). How many whole numbers less
than 64 are
A' divisible by their respective
units digit?
(/
The sum of the positive divisors of 480 is
1512. Find the sum of the reciprocals of
the positive divisors of 480.
(,
A
The five-square numerical puzzle below
requires the vertical column to be filled
with the digits from a three-digit integral
power of 5 and the horizontal row to be
filled with the digits
from a three-digit
integral power of 2.
A'
What digit will be
in the shaded
square?
O'
(0
B'
For the sequence 1, –2, 3, –4, 5, –6, 7, . . . ,
what is the difference between the mean
of the sequence’s first 400 terms and theA
mean of its first 200 terms?
B'
A'
B'
)'
Arrange the digits 1, 1, 2, 2, 3, and 3 to
form O
a six-digit number such that the
1s have one digitBbetween them, the 2s
have two digits between them, and the 3s
have three digits between them. What is
A
the sum of all possible six-digit numbers
formed under these conditions?
O
If [x] represents the greatest integer less
than or equal to x, solve for x: x • [x] = 40.
A
)+
B
Two students, Katelyn and Carly, are playing a game that uses ten different numbered
cards lying face down on a table. The faces
of the cards are labeled with one of the numbers from 1 to 10 (each card has a different
number).
If EKatelyn and Carly each turn
C
D
over a differentF card, what is the probability
that the sum of the two cards is even?
)/
)(
B
),
))
A group of friends went to dinner and
received a bill totaling $288. The group
decided to treat two people whose birthdays were that month and split the charges
equally among the rest of the group. This
resulted in each person having to pay
$4.80 more than each would have paid had
the bill been split equally among the entire
group. How many people were
in the dinner group?
)*
Determine the measure (in degrees) of an
angle whose complement is four-ninths its
supplement.
)-
Quadrilateral ABCD is a rhombus. Its
diagonals are 12 and 20 units in length.
Find the diameter of the circle inscribed
in rhombus ABCD. Round your answer
to the nearest
A
B
hundredth.
D
C
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).
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