College Bowl questions

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1
Northern Arizona University
Department of Mathematics and
Statistics
2010 Math High School Day
College Bowl Competition
Students, start your brain cells!
2
Evaluate:
1 9
[2]
3
If one box of Froot Nootles will
feed three adults, or two teenagers,
or five children, how many boxes
would be needed to feed a crowd
of 30 adults,
30 children and 30 teenagers?
[31]
4
What number is three
more than half of itself?
[6]
5
If x$y stands for (x-1)y,
what is (5$3)$2?
[22]
6
Sam is two years older than
his brother Jim. The sum of
their ages is 30. When will
the sum of their ages be 40?
[2015]
7
What number is three
less than half of itself?
[-6]
8
How many ways are there to travel
from S to F along roads, never
visiting the same town twice?
S
F
[4]
9
Simplify:
2
1
1
3
4
[30/13]
10
How many distinct
arrangements of the
letters MATH are there?
[24]
11
What is 20% of 20
plus 30% of 30?
[13]
12
How many ways are there to travel
from S to F along roads, never
visiting the same town twice?
S
F
[9]
13
If a is 2 and b is 3, what is
b
a
a –b ?
[-1]
14
Evaluate: 25  81
[4]
15
Compare the two numbers
using <, =, or >.
7

5
-1.35
[<]
16
Solve:
x 1  5
[x = 24]
17
If half of it is 5 more
than a third of it, how
much is all of it?
[30]
18
What number is 12 more
than its square root?
[16]
19
How many distinct
arrangements of the
letters MATT are there?
[12]
20
What number is 12
more than twice itself?
[-12]
21
Two numbers differ by 3 and
their squares differ by 45.
What is their sum?
[15]
22
Calculate:
1
10 
2
3
2
2
[3]
23
The small circle has radius 1 and
passes through the center of the
big circle. What is the area of the
shaded region?
[3π]
24
25  16 
[3]
25
4 5 7
7 8 10
11 12 ??
[14]
26
x
If [email protected] is
,
y 1
what is ([email protected]) – ([email protected])?
[-1]
27
7 1

2
5 1
2
[2]
28
How long is side h of this
right triangle?
7
h
5
[√24 or 2√6]
29
If I drive at 30 mph for
20 minutes, then 60 mph
for 10 minutes, what is
my average speed?
[40 mph]
30
Which of these consists of a figure
4 and a reflection of it?
A
C
B
E
D
[D]
31
In a class of 30 students, 8 are
blonds, 10 have red hair, and 12
have black hair. If one student is
chosen at random, what is the
probability that his/her hair is black?
[2/5]
32
What is the next number
in the sequence below?
192, 96, 48, 24, 12, . . .
[6]
33
Ya wanna sandwich? What kinda
bread: white, wheat, rye, or
pumpernickel? Meat? We got ham,
roast beef and chicken. Cheese? Yeah,
Swiss, American, or Muenster.
How many different sandwiches can
you order?
[36]
34
What is the area of a
circle with radius π?
3
[π ]
35
10 is 20% of what number?
[50]
36
Simplify:
3
4 4
2
37
The square is 8 inches on a side,
the diagonals meet the sides at
midpoints. What is the area of
the
white
band?
8
4
[32 in2]
38
Two numbers differ by
9 and their sum is 7.
What are they?
[8 and -1]
39
The equation below has exactly
two solutions. Both of them can
be found without any solving.
What are they?
(x-1)(x-2)(x-3)(x-4) = 24
[0,5]
40
If x is the first number and y is
the second, how do you write the
statement “the first number is 5
more than twice the second”?
[x = 2y+5]
41
abc bca cab
bcd cdb dbc
cde dec ??
[ecd]
42
The radius OD is 5, the segment
OC has length 3 and is
perpendicular to the chord AB.
How long is AB?
A
C
B
3
O
[8]
5
D
43
The sum of a number and its
reciprocal is smaller than the
number. How can that be?
[The number
must be negative]
44
George tells you that the
average of 4 consecutive
numbers (i.e. positive integers)
is 120. What do you deduce?
[That George is a liar]
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