1 Northern Arizona UniversityDepartment of Mathematics and

Statistics2010 Math High School DayCollege Bowl Competition

Students, start your brain cells!

22

Evaluate:

[2]

1+ 9

33

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]

44

What number is three more than half of itself?

[6]

55

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

[22]

66

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]

77

What number is three less than half of itself?

[-6]

88How many ways are there to

travel from S to F along roads, never visiting the same town

twice?

[4]

S F

99

Simplify:

[30/13]

2+1

3 + 14

1010

How many distinct arrangements of the

letters MATH are there?

[24]

1111

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

[13]

1212

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

[9]

S F

1313

If a is 2 and b is 3, what is ab – ba ?

[-1]

14

Evaluate:

[4]

25− 81

1515

Compare the two numbers using <, =, or >.

-1.35

[ < ]

5

7−

1616

Solve:

[x = 24]

x +1 =5

1717

If half of it is 5 more than a third of it, how

much is all of it?

[30]

1818

What number is 12 more than its square root?

[16]

1919

How many distinct arrangements of the

letters MATT are there?

[12]

2020

What number is 12 more than twice itself?

[-12]

2121

Two numbers differ by 3 and their squares differ by 45.

What is their sum?

[15]

2222

Calculate:

[3]

10 +12

32

+ 2

2323 The small circle has radius 1 and passes through the center of the

big circle. What is the area of the shaded region?

[3π]

2424

[3]

25 + 16 =

2525

[14]

4 5 7

7 8 10

11 12 ??

2626

If x@y is ,

what is (3@4) – (4@3)?

[-1]

xy −1

2727

[2]

72 −152 −1

=

2828

How long is side h of this right triangle?

[√24 or 2√6]

7

5

h

2929

If I drive at 30 mph for 20 minutes, then 60 mph for 10 minutes, what is

my average speed?

[40 mph]

3030

Which of these consists of a figure 4 and a reflection of it?

[D]

C

E

A

B

D

3131

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]

3232

What is the next number in the sequence below?

192, 96, 48, 24, 12, . . .

[6]

3333

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]

3434

What is the area of a circle with radius π?

[π3]

3535

10 is 20% of what number?

[50]

3636

Simplify:

2

3 44

3737The square is 8 inches on a side, the diagonals meet the sides at midpoints. What is the area of

the white band?

[32 in2]

8

4

3838

Two numbers differ by 9 and their sum is 7.

What are they?

[8 and -1]

3939 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]

4040 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]

4141

[ecd]

abc bca cab

bcd cdb dbc

cde dec ??

4242 The radius OD is 5, the segment OC has length 3 and is

perpendicular to the chord AB. How long is AB?

[8]

O

D

A BC

3

5

4343

The sum of a number and its reciprocal is smaller than the number. How can that be?

[The number must be negative]

4444

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]