# College Bowl questions ```1
Northern Arizona University
Department of Mathematics and
Statistics
2010 Math High School Day
College Bowl Competition
2
Evaluate:
1 9

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
30 children and 30 teenagers?

4
What number is three
more than half of itself?

5
If x\$y stands for (x-1)y,
what is (5\$3)\$2?

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?

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

9
Simplify:
2
1
1
3
4
[30/13]
10
How many distinct
arrangements of the
letters MATH are there?

11
What is 20% of 20
plus 30% of 30?

12
How many ways are there to travel
from S to F along roads, never
visiting the same town twice?
S
F

13
If a is 2 and b is 3, what is
b
a
a –b ?
[-1]
14
Evaluate: 25  81

15
Compare the two numbers
using &lt;, =, or &gt;.
7

5
-1.35
[&lt;]
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?

18
What number is 12 more
than its square root?

19
How many distinct
arrangements of the
letters MATT are there?

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?

22
Calculate:
1
10 
2
3
2
2

23
The small circle has radius 1 and
passes through the center of the
big circle. What is the area of the
[3π]
24
25  16 

25
4 5 7
7 8 10
11 12 ??

26
x
If x@y is
,
y 1
what is (3@4) – (4@3)?
[-1]
27
7 1

2
5 1
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, . . .

33
Ya wanna sandwich? What kinda
pumpernickel? Meat? We got ham,
roast beef and chicken. Cheese? Yeah,
Swiss, American, or Muenster.
How many different sandwiches can
you order?

34
What is the area of a
3
[π ]
35
10 is 20% of what number?

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

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]
```