1 Northern Arizona UniversityDepartment of Mathematics and
Statistics2010 Math High School DayCollege Bowl Competition
Students, start your brain cells!
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]
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]
88How many ways are there to
travel from S to F along roads, never visiting the same town
twice?
[4]
S F
1212
How many ways are there to travel from S to F along roads, never visiting the same town twice?
[9]
S F
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]
2929
If I drive at 30 mph for 20 minutes, then 60 mph for 10 minutes, what is
my average speed?
[40 mph]
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]
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]
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
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]
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]
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