Bluegrass Conference - Math
9 rounds of 35 multiple-choice questions
2013
Copyright © 2013 Academic Hallmarks
Bluegrass Conference - Math Round 1 Page 1
1.
Yes We Have No Bananas
6.
Cubed Numbers
A door-to-door banana salesman sells B bananas at C
cents each day. He takes in D dollars during P days.
D equals ...
A. 100B/CP
B. BCP/100
C. 100/BCP
D. 100C/BP
E. BP/100C
What is the cube of 1.01?
A. 1.020201
B. 1.030301
C. 1.040401
D. 1.050401
E. 1.060401
2.
7.
Tree Distributions
Linear Equations
480 pine seedlings are distributed among three
tree-huggers in the ratio of 2 to 4 to 6. The one
getting the smallest share will have ...
A. 40
B. 50
C. 60
D. 70
E. 80
What is the value of y if -2 = 22 - 4y?
A. -8
B. -3
C. 2
D. 4
E. 6
3.
8.
Lines
GCFs
An oblique line is ...
A. thick
B. curved
C. slanting
D. parallel to another line
E. perpendicular to another line
The greatest common factor of 18 and 84 is ...
A. 2
B. 4
C. 6
D. 8
E. 12
4.
9.
Geologic Time
Linear Equations
The age of the Earth is estimated to be about 4.6
billion years. In scientific notation, that is 4.6 times
10 to the ---- power years.
A. 6th
B. 7th
C. 8th
D. 9th
E. 10th
The sum of three integers is one hundred seventy-five.
The second is ten more than twice the first. The third
is three times the second. The smallest number is ...
A. 10
B. 15
C. 20
D. 25
E. 30
5.
10.
Trial Problems
Four out of five people failed the trial by fire ordeal
during the Inquisition. If twenty people failed the
ordeal, how many passed it?
A. 2
B. 3
C. 4
D. 5
E. 6
Gift Wrapping
You need at least how many square feet of wrapping
paper to completely cover a box, all the edges of
which are four feet in length?
A. 90
B. 92
C. 94
D. 96
E. 98
Bluegrass Conference - Math Round 1 Page 2
11.
High Probability
16.
Grading Corrections
An event certain to occur has a probability of ...
A. 0
B. 1
C. 10
D. 100
E. 1000
A professor figured his class of 25 averaged 70% on a
test. But he incorrectly recorded Mo's score as 32
when it should have been 82. The correct average for
the exam is ...
A. 71
B. 72
C. 73
D. 74
E. 75
12.
17.
Gear Trains
Mass
You have a 20-toothed gear meshed with a 40-toothed
gear meshed with a 10-toothed gear which is finally
meshed with a 5-toothed gear. How many times does
the 5-toothed gear rotate when the 20-tooth gear
rotates once?
A. 2
B. 4
C. 6
D. 8
E. 10
Given the density of water is 1000 kg per cubic meter,
the mass of the water in a tank with interior measures
of .6 by 1.3 meters filled to a depth of .3 meter is ---kilograms.
A. 117
B. 234
C. 362
D. 468
E. 525
13.
18.
Prime Probability
Crate Volume
What is the probability of randomly selecting a prime
number from the whole numbers 20 to 40 inclusive?
A. 1 in 3
B. 2 in 7
C. 3 in 7
D. 4 in 21
E. 5 in 21
The area of one side of a crate is 120 square inches.
The area of its other side is 72 square inches. Its top
is 60 square inches. The crate's volume is ---- cubic
inches.
A. 600
B. 720
C. 864
D. 926
E. 1020
14.
19.
Sumerian Math
Sets
The Sumerians stated large numbers in 60s. For
example, they stated 120 as two 60s and 180 as three
60s. What did they divide into six 60s?
A. circles
B. triangles
C. hexagons
D. heptagons
E. pentagons
What is the intersection of these sets?
{squares of whole numbers from 2 to 9}
and {all even numbers}
A. {2, 4, 6, 8}
B. {3, 5, 7, 9}
C. {9, 25, 49, 81}
D. {4, 16, 36, 64}
E. {22, 44, 66, 88}
15.
20.
Population Explosions
The time for the human population to double is
estimated by dividing 70 by the annual growth rate.
At a 2% rate, man's population of 6.5 billion in 2005
will be 13 billion in ...
A. 2030
B. 2035
C. 2040
D. 2045
E. 2050
Venn Diagrams
Of the 29 doggies in the window, 17 had waggly tails
and 21 had floppy ears. How many had both
characteristics?
A. 1
B. 3
C. 5
D. 7
E. 9
Bluegrass Conference - Math Round 1 Page 3
21.
Numbers
26.
Algebraic Transformations
Which number is not a perfect square?
A. 25
B. 49
C. 81
D. 102
E. 121
What is W given that P = 2(L+W)?
A. 2/LP
B. PL -2
C. (L-2)/P
D. 2P - 2L
E. (P-2L)/2
22.
27.
Algebraic Expressions
Mathematical Sets
x/6 could not mean ...
A. x divided by 6
B. one-sixth of x
C. the ratio of x to 6
D. the product of 6 and x
E. the quotient of x and 6
The set of all even numbers illustrates a(n) ---- set.
A. null
B. empty
C. infinite
D. disjoint
E. overlapping
23.
28.
Late for Work
Card Probability
The guy who hit his snooze alarm every five minutes,
864 times in a row, went to work how many days late?
A. 1
B. 2
C. 3
D. 4
E. 5
If you randomly pull one card from a standard deck,
what are the chances that it is either a black queen or a
red seven?
A. 1 in 11
B. 1 in 13
C. 1 in 18
D. 1 in 22
E. 1 in 26
24.
29.
Sets
GCFs
Which is a disjoint set in relation to this set?
(kangaroo, opossum, lemur, aardvark, wapiti)
A. (hare, lemur, coyote)
B. (seal, whale, opossum)
C. (wallaby, mink, leopard)
D. (wolf, pronghorn, aardvark)
E. (opossum, wapiti, kangaroo)
The greatest common factor of 24 and 60 is ...
A. 2
B. 4
C. 6
D. 8
E. 12
25.
30.
Auto Averages
Nell's odometer said 86,350 miles when she began a
trip at 3:20 p.m. At 4:50 p.m., it read 86,437 miles.
Her average speed was ---- mph.
A. 50
B. 52
C. 54
D. 56
E. 58
Mechanical Drawing
The scale on a drawing says 3 inches equal 1 foot.
The drawing is what fraction of the size of the actual
object?
A. 1/8
B. 1/6
C. 1/4
D. 1/3
E. 1/2
Bluegrass Conference - Math Round 1 Page 4
31.
Area Plotting
You draw a line 5' north, 6' east, 4' north, 4' east, 9'
south, and 10' west. The area of the enclosed figure is
---- square feet.
A. 33
B. 44
C. 55
D. 66
E. 77
32.
Binary Biology
Using the binary system, which creature is not
correctly paired with its number of legs?
A. primate - 10
B. insect - 110
C. canine - 100
D. spider - 1100
E. octopus - 1000
33.
Sets
Which is a subset of this set?
{papayas, kiwis, figs, mangoes, chokecherries)
A. {mangoes, kiwis}
B. {figs, tangerines}
C. {papayas, guavas}
D. {pineapples, pomegranates}
E. {huckleberries, loganberries}
34.
Clock Angles
A minute hand initially pointing at 12 will point to
what number on the clock after rotating through 180
degrees?
A. 3
B. 6
C. 8
D. 9
E. 12
35.
Rhinoceros Washing
Tom can wash a rhinoceros in four hours while Jenny
can wash the same rhino in two hours. It will take
them ---- minutes to wash a rhino if they work
together.
A. 50
B. 80
C. 105
D. 120
E. 140
Bluegrass Conference - Math Round 1 - Answers
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Bluegrass Conference - Math Round 2 Page 1
1.
Number Problems
6.
Integer Relationships
Three times the sum of two consecutive odd numbers
is 132. What is the smaller number?
A. 21
B. 19
C. 23
D. 25
E. 27
What can be said about these numbers?
5211 2466 9423 3330 9531
A. They are primes.
B. They are multiples of 9.
C. Their reciprocals are odd.
D. They are evenly divisible by 11.
E. The sums of their digits are even.
2.
7.
Birthday Calculations
Marine Soup
What birthday will be celebrated in 2016 by someone
born in 1947?
A. 63rd
B. 65th
C. 67th
D. 69th
E. 71st
If the number of clams is five times greater than the
number of oysters, how many clams are in this soup
containing 360 mollusks?
A. 260
B. 280
C. 300
D. 320
E. 340
3.
8.
Probability
Time Angles
Jennifer's practice tennis ball bag contained 22 yellow
balls, 7 red balls, and 20 white balls. What is the
probability that the first ball she randomly pulled
from the bag was red?
A. 1 in 7
B. 2 in 7
C. 3 in 7
D. 4 in 7
E. 5 in 7
How many degrees does a minute hand move in 40
minutes?
A. 200
B. 210
C. 220
D. 230
E. 240
4.
9.
Speed
Quadrilateral Areas
A lanky left-legged lion loping along at eleven feet
per second after a little lovable lamb travels how many
feet in two minutes?
A. 1020
B. 1120
C. 1220
D. 1320
E. 1420
Which rectangle has the same area as a square 6 inches
on a side?
A. 4" x 6"
B. 3" x 9"
C. 5" x 8"
D. 2" x 18"
E. 1" x 24"
5.
10.
Arithmetic Summation
When using clock arithmetic, which is not a correct
sum?
A. 7 + 7 = 2
B. 8 + 7 = 3
C. 9 + 9 = 5
D. 10 + 3 = 1
E. 11 + 5 = 4
Polygons
What is the total number of edges on 2 pentagons, 3
hexagons, and 4 octagons?
A. 54
B. 56
C. 58
D. 60
E. 62
Bluegrass Conference - Math Round 2 Page 2
11.
Algebraic Expressions
16.
Percentages
Evaluate this expression given
that w = 3, x = 2, y = 1, and z = 5.
w(yz - xy)
A. 3
B. 6
C. 9
D. 12
E. 15
Which percentage is not paired with its decimal value?
A. 6%, .6
B. 3.5%, .035
C. 1/5%, .002
D. 1/10%, .001
E. 205%, 2.05%
12.
17.
Coordinate Geometry
Algebraic Evaluation
On a graph, what is the distance between (-3, 3)
and (-3, 11)?
A. 5
B. 6
C. 7
D. 8
E. 9
Evaluate -6 + 5p given that p = 3.
A. 5
B. 6
C. 7
D. 8
E. 9
13.
18.
Triangle Angles
Long Flights
If the angles of a triangle measure 2p, 3p, and 4p, the
measure of the largest angle is ---- degrees.
A. 20
B. 40
C. 60
D. 80
E. 100
In 1924, two U.S. Army planes completed the first
flight around the world. Since they took 175 days to
complete the 27,000-mile journey, how many miles
did they average daily?
A. 114
B. 134
C. 154
D. 174
E. 194
14.
19.
Teeter-totter Math
Pressure
Big Bob weighs 260 pounds and is on a teeter-totter 4
feet from the fulcrum while Little Linda Lou is
balancing him by sitting 16 feet from the fulcrum.
She weighs ---- pounds.
A. 65
B. 70
C. 75
D. 80
E. 85
A load exerting a pressure of 3744 pounds per square
foot exerts a pressure of how many pounds per square
inch?
A. 26
B. 34
C. 48
D. 60
E. 72
15.
20.
Sale Math
At the Frank's Fine Finnery, six carp and four
anchovies cost $33. Six carp and one anchovy cost
$28.50. How much does one carp cost?
A. $1.50
B. $2.50
C. $3.50
D. $4.50
E. $5.50
Population Density
Given that there are some 6.83 billion people on Earth
whose land area, excluding Antarctica, is 52 million
square miles, this planet's population density is about
---- people per square mile.
A. .131
B. 1.31
C. 13.1
D. 131
E. 1310
Bluegrass Conference - Math Round 2 Page 3
21.
Lots o' Ice
26.
Surface Area
The Antarctic Ice Sheet covers some 5 million square
miles, making it about how many times larger than the
Greenland Ice Sheet with its area of 670,000 square
miles?
A. 3
B. 5
C. 7
D. 9
E. 11
Which solid with a one-cubic-inch volume has the
least surface area?
A. cube
B. sphere
C. octahedron
D. tetrahedron
E. icosahedron
22.
27.
Inverse Proportions
Polygons
If it takes 4 killer tomatoes 40 minutes to wipe out a
neighborhood, it would take 10 killer tomatoes ---minutes to do the same job.
A. 10
B. 12
C. 14
D. 16
E. 18
What is the total number of sides of 3 pentagons, 4
hexagons, 5 heptagons, and 6 octagons?
A. 104
B. 110
C. 116
D. 122
E. 128
23.
28.
Pressure
Grids
A 200-pound cube with a volume of 125 cubic feet
exerts how many pounds per square foot on the
surface upon which it rests?
A. 2
B. 4
C. 6
D. 8
E. 10
Aukville is laid out on a grid with 31 avenues running
north to south and 23 streets running east to west. If
there is one traffic light at each intersection, how
many traffic lights are there?
A. 635
B. 661
C. 687
D. 713
E. 768
24.
29.
Grass Math
Timepiece Pace
Moe must mow a yard measuring 1440 by 4800 feet.
How many lengthwise round trips must he make with
his 24-inch mower to finish the job?
A. 180
B. 240
C. 360
D. 420
E. 550
In one hour and forty-five minutes, the minute hand
of a clock turns through how many degrees?
A. 500
B. 540
C. 600
D. 630
E. 720
25.
30.
Reciprocals
What is the sum of the reciprocals of 1/3 and 3/4?
A. 5/3
B. 7/3
C. 9/3
D. 11/3
E. 13/3
Force
At one end of a rope, two guys pull west with forces of
130 and 160 lbs. At the other end, four guys pull east
with forces of 40, 50, 70, and 90 lbs. The resulting
force is ---- pounds west.
A. 30
B. 40
C. 50
D. 60
E. 70
Bluegrass Conference - Math Round 2 Page 4
31.
Rotations
In 270 minutes, the hour hand of a watch turns
through an angle of how many degrees?
A. 115
B. 125
C. 135
D. 145
E. 155
32.
Fuel Usage
An airplane consumes fuel at the rate of 12 gallons
per hour. 54 gallons remain in the tank. The fuel
lasts ---- hours.
A. 3.6
B. 4.5
C. 5.2
D. 6.1
E. 7.8
33.
Numbers
Which is an ordinal number?
A. 92
B. 3 pi
C. 725th
D. 24 3/7
E. 8 squared
34.
Angles
In a Star of David, the angle at each of the points
equals how many degrees?
A. 15
B. 30
C. 45
D. 60
E. 90
35.
Rentals
Office space rents for $485 per month for 400 square
feet. What is the monthly rent for 320 square feet?
A. $362
B. $388
C. $400
D. $424
E. $436
Bluegrass Conference - Math Round 2 - Answers
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Bluegrass Conference - Math Round 3 Page 1
1.
Footsie Math
6.
Bacteria Everywhere
Of 16 people, 7 are wearing socks, 5 are wearing
shoes, and 4 are wearing both. How many are
barefooted?
A. 4
B. 5
C. 6
D. 7
E. 8
A single bacterium landed in Igor's nose where it
divided every 15 minutes. How many bacteria were in
his schnozzola after 2 1/2 hours?
A. 64
B. 128
C. 256
D. 512
E. 1024
2.
7.
Find the Number
Work Calculations
What one-digit number can you multiply by 3, add 8
to the product, divide the sum by 2, subtract 6 from
the quotient, and end up with the original number?
A. 1
B. 2
C. 3
D. 4
E. 5
Since work equals force times distance, moving 20
pounds 36 inches results in the same amount of work
as moving ...
A. 5 pounds 4 feet
B. 60 pounds 1 foot
C. 40 pounds 2 feet
D. 30 pounds 18 inches
E. 12 pounds 48 inches
3.
8.
LCM and GCF
Racing Statistics
What is x if two numbers, 16 and x, have a least
common multiple of 48 and a greatest common factor
of 8?
A. 12
B. 16
C. 18
D. 22
E. 24
In a bike race, Ned peddled 24 mph for the first 3
hours, 22 mph for the next 3 hours, 18 mph for the
next hour, and 16 mph for the final hour. His average
speed for the race was ---- mph.
A. 20.5
B. 21.5
C. 22.5
D. 23.5
E. 24.5
4.
9.
Mathematical Expressions
Protester Probability
5x/8 could not mean ...
A. 5x divided by 8
B. five-eighths of x
C. the ratio of 5x to 8
D. the product of 8x and 5
E. the quotient of 5x and 8
A group of protesters at the Seattle WTO conference
included 60 dockworkers, 40 tree huggers, 30
save-the-turtlers, and 10 aged hippies. What is the
probability that the first person arrested in this group
is a tree hugger?
A. 1 in 5
B. 2 in 7
C. 3 in 8
D. 4 in 9
E. 5 in 11
5.
10.
Tire Rotation Calculation
Mel got 5 new tires for a trip. To have equal wear on
all at the end of 5000 miles, he should use each for
how many miles?
A. 2500
B. 3000
C. 3500
D. 4000
E. 4500
Tournament Math
There are 25 entries in a handball tournament in
which two players at a time meet with the loser being
eliminated. How many matches must be played to
determine the final winner?
A. 11
B. 15
C. 17
D. 21
E. 24
Bluegrass Conference - Math Round 3 Page 2
11.
Reciprocals
16.
Quadrilaterals
0.0250 is the reciprocal of ...
A. 25
B. 40
C. 58
D. 65
E. 90
The perimeter of a rectangle with a width of 9 feet and
a length 2.5 times the width is ---- yards.
A. 21
B. 22
C. 23
D. 24
E. 25
12.
17.
Binary Math
Fund Figuring
The number of U.S. states is represented by which
binary number?
A. 110010
B. 101010
C. 111001
D. 101110
E. 110011
George has $24, Glenda has twice as much money as
George, and Goldie has four times as much as Glenda.
What is the average amount?
A. $80
B. $82
C. $84
D. $86
E. $88
13.
18.
Pressure
Cubes
A metallic cube 6 centimeters on an edge weighs 144
grams. In grams per square centimeter, how much
pressure does it exert?
A. 2
B. 4
C. 6
D. 8
E. 10
What is the length of any side of a cube with a total
surface area of 216 square inches?
A. 5
B. 6
C. 7
D. 8
E. 9
14.
19.
Stucco Math
Graphing
Rocco charges $14 per square yard for his work.
What would he charge to stucco both sides of a wall
10 feet high and 90 feet long?
A. $2700
B. $2800
C. $2900
D. $3000
E. $3100
A pie graph of Maukrosoft expenses shows 12 cents
of every dollar goes to research, 9 cents to advertising,
and 54 cents to anchovy snacks. The arc representing
the remaining expenses is subtended by an angle of
---- degrees.
A. 50
B. 60
C. 70
D. 80
E. 90
15.
20.
Drafting
If 1/4 inch represents 1 foot on a blueprint, how many
inches on the drawing represent 8 yards?
A. 3
B. 4
C. 5
D. 6
E. 7
Puppy Partitioning
A crowded humane society divided 800 puppies into
three pens. 270 of them went into pen 1. 150 more
were put into pen 2 than into pen 3. How many went
into pen 2?
A. 310
B. 320
C. 330
D. 340
E. 350
Bluegrass Conference - Math Round 3 Page 3
21.
Linear Equations
26.
Alien Averages
5.2 is the result when 8.8 is subtracted from twice the
value of what number?
A. 3
B. 4
C. 5
D. 6
E. 7
On a UFO, 3 aliens are 10 centuries old and 2 are 5
centuries old. Their average age is ---- centuries.
A. 4
B. 6
C. 8
D. 10
E. 12
22.
27.
Algebraic Geometry
Myth Math
Find the length of a rectangle whose perimeter is 40
inches and whose length is 2 inches greater than its
width.
A. 7
B. 9
C. 11
D. 13
E. 15
Express as a binary numeral the number of labors
demanded of Hercules by Hera.
A. 1001
B. 1010
C. 1011
D. 1100
E. 1101
23.
28.
Probability
Currency Calculations
The odds are highest of rolling which number with a
pair of dice?
A. 2
B. 5
C. 7
D. 10
E. 12
Since Marie has 61 euros, or 7 more than 3 times what
Joan has, how many does Joan have?
A. 9
B. 12
C. 15
D. 18
E. 21
24.
29.
Consecutive Integers
Compasses
Find the largest of three consecutive integers whose
sum is 48.
A. 15
B. 16
C. 17
D. 18
E. 19
The exact opposite of a compass heading of 90
degrees is ---- degrees.
A. 250
B. 260
C. 270
D. 280
E. 290
25.
30.
Pounds of Money
If five nickels weigh one ounce, what is the value of
40 pounds of them?
A. $150
B. $160
C. $170
D. $180
E. $190
Cube Constructions
If you had to paint the exposed sides of a stack of
cubes 8 cubes long and 5 cubes high, how many faces
of the cubes would have to be painted?
A. 90
B. 94
C. 96
D. 98
E. 100
Bluegrass Conference - Math Round 3 Page 4
31.
Squares
Which is not a perfect square?
A. 144
B. 169
C. 196
D. 225
E. 262
32.
Logic
Of 50 students, 13 are taking art and 27 are taking
music. If another 6 students are in both classes, how
many are in neither class?
A. 4
B. 5
C. 6
D. 7
E. 8
33.
Bad Songs
Catfish Bob writes 7 bad country and western songs
every 10 days. The number of bad songs he writes in
any given September is ...
A. 15
B. 17
C. 21
D. 23
E. 25
34.
Angles
Which choice does not guarantee equal angles?
A. vertical angles
B. adjacent angles in a rhombus
C. supplements of the same angle
D. opposite angles in parallelograms
E. base angles of an isosceles triangle
35.
Town Statistics
In a picturesque New England town with a population
of 22,000, there are 440 real estate agents. What is the
number of agents per capita?
A. .02
B. .04
C. .06
D. .08
E. .10
Bluegrass Conference - Math Round 3 - Answers
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E
D
E
D
D
E
B
B
B
E
B
A
B
B
D
A
E
B
E
D
E
C
C
C
B
C
D
D
C
D
E
A
C
B
A
Bluegrass Conference - Math Round 4 Page 1
1.
Ranch Ratios
6.
Mathematical Anagrams
On a ranch, the ratio of two-legged critters to
four-legged critters is 4 to 1. What fraction of the
critters in the group are four-legged?
A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/7
Which is an anagram for "eleven plus two"?
A. nine plus four
B. seven plus six
C. ten plus three
D. eight plus five
E. twelve plus one
2.
7.
Hunting Expenses
Volume
Bill went hunting. He spent $90 on a license, $15 on
shells, $60 on gas, $10 on a hat, and $5 on Gummy
Bears. He shot 4 quail. His cost per bird was ...
A. $35
B. $40
C. $45
D. $50
E. $55
The volume of a rectangular solid with a base of 13, a
height of 17, and a width of 12 feet is ---- cubic feet.
A. 886
B. 1094
C. 2652
D. 3428
E. 4068
3.
8.
Triangles
Rotations
If two sides of a triangle both measure 15, what could
be the measure of the third side?
A. 29
B. 31
C. 33
D. 35
E. 37
In 140 minutes, the second hand of a watch turns
through an angle of how many degrees?
A. 20,800
B. 30,200
C. 40,900
D. 50,400
E. 60,600
4.
9.
Marine Mammal Motion
Time and Speed Problems
A seal swimming along at 4 feet per second goes 2
miles in how many minutes?
A. 44
B. 46
C. 48
D. 50
E. 52
A plane that averages 500 mph leaves Seattle for
Boston at the same time a plane that averages 650
mph leaves Honolulu for Phoenix 3000 miles away.
They will meet in ---- hours.
A. 2.0
B. 2.2
C. 2.4
D. 2.6
E. 2.8
5.
10.
Perfect Squares
What is the sum of the perfect squares greater than 20
and less than 50?
A. 94
B. 98
C. 102
D. 106
E. 110
Counting Cubes
The surface of a solid cube measuring five inches on a
side was painted and then it was sliced into one-inch
cubes. How many of those little cubes were painted
on just one side?
A. 12
B. 24
C. 54
D. 62
E. 96
Bluegrass Conference - Math Round 4 Page 2
11.
Number Problems
16.
Pressure
One number is six times another and their sum is 56.
What is the larger number?
A. 40
B. 42
C. 44
D. 46
E. 48
In grams per square centimeter, how much pressure is
exerted by a cube weighing 324 grams with edges of
six centimeters?
A. 7
B. 9
C. 11
D. 13
E. 15
12.
17.
Farmer Statistics
Triangles
Al planted 20 acres Monday, 14 acres Tuesday, 24
acres Wednesday, and a total of 52 acres on Thursday
and Friday. What is the average number of acres he
planted each day?
A. 18
B. 22
C. 26
D. 30
E. 32
It is impossible to have a triangle with sides of ...
A. 1, 1, and 1
B. 1, 2, and 3
C. 3, 4, and 6
D. 2, 4, and 5
E. 3, 8, and 10
13.
18.
Numbers
Numbers
How many primes are there between 4 and 24?
A. 5
B. 6
C. 7
D. 8
E. 9
Which choice is not equal to the remainder when your
subtract XIII from XXI?
A. 128/16
B. 2 cubed
C. square root of 64
D. absolute value of -16
E. .008 times 10 to the third power
14.
19.
Pressure
Tackle Box Quandaries
A load exerting a pressure of 1296 pounds per square
foot exerts a pressure of how many pounds per square
inch?
A. 7
B. 9
C. 11
D. 13
E. 15
A box holds 6 black, 6 chartreuse, 6 silver, 6 purple,
and 6 red jigs, but it is dark. To be certain of getting
a pair of matching jigs, you need to grab how many?
A. 5
B. 6
C. 7
D. 8
E. 9
15.
20.
Divisors
The square root of 152 is between ...
A. 9 and 10
B. 10 and 11
C. 11 and 12
D. 12 and 13
E. 13 and 14
Snake River Statistics
The Snake River begins in Yellowstone National Park
at an altitude of 9500 feet. Where it joins the
Columbia River 1036 miles downstream, its altitude is
340 feet. About how many feet does it drop per mile?
A. 6
B. 9
C. 12
D. 15
E. 18
Bluegrass Conference - Math Round 4 Page 3
21.
Binary Ages
26.
Fishy Averages
How old is the guy in this limerick?
There was a scientist from Verdun / Who with
binary digits had fun. / When asked his age, /
Replied this fine sage, / "I'm 100011."
A. 29
B. 33
C. 35
D. 37
E. 39
Dan caught 3 fish, Bud caught 2, Dean caught 4, and
Ron got skunked. How many fish will Diana have to
catch for each to go home with 10 fish?
A. 41
B. 43
C. 45
D. 47
E. 49
22.
27.
Square Roots
Pizza Portions
Which square root is not correct?
A. 1 = square root of 2
B. 4 = square root of 16
C. 8 = square root of 64
D. 11 = square root of 121
E. 15 = square root of 225
Al, Bo, Clara, Della, and Ed weigh 60, 80, 90, 100, and
120 pounds respectively. If they partition a pizza
according to their weights, the central angle of Clara's
piece should be ---- degrees.
A. 46
B. 50
C. 64
D. 72
E. 88
23.
28.
Sets
Gum Problems
Which is the least well-defined set?
A. counties of Nebraska
B. nuclear warheads in Russia
C. violent television programs
D. living female heads of state
E. letters of the English alphabet
If your chewing gum loses half its flavor on the
bedpost every night, what fraction of its flavor remains
after six nights?
A. 1/8
B. 1/16
C. 1/32
D. 1/64
E. 1/128
24.
29.
Speed Conversions
Algebraic Substitution
If you travel 3.6 miles in 18 minutes, what is your
speed in miles per hour?
A. 10
B. 12
C. 14
D. 16
E. 18
Since x = 6 and 3x + 2y = 32, what is y?
A. 4
B. 5
C. 6
D. 7
E. 8
25.
30.
Travel Problems
A bus leaves Hereville for Thereville traveling at 60
miles per hour. Simultaneously, another bus leaves
Thereville heading to Hereville at 50 miles per hour.
If it is 605 miles between the towns, how many hours
will it be until the buses meet?
A. 5
B. 5.5
C. 6
D. 6.5
E. 7
Binary Math
Express in binary the number of Wonders of the
Ancient World.
A. 11
B. 101
C. 110
D. 111
E. 1001
Bluegrass Conference - Math Round 4 Page 4
31.
Ballistics
A missile traveling at 3100 feet per second goes about
how many miles in 12 seconds?
A. 6
B. 7
C. 8
D. 9
E. 10
32.
Fish Averages
One morning, Ike caught fish weighing 9, 14, 22, 18,
and 6 ounces. The next fish must weigh ---- ounces
for all of them to average 16 ounces.
A. 21
B. 23
C. 25
D. 27
E. 29
33.
Wheels
If every pair of spokes on a bicycle wheel forms an
angle of 18 degrees, how many spokes are there?
A. 14
B. 16
C. 18
D. 20
E. 22
34.
Continued Ratios
As a continued ratio, express 1/4 day to 4 hours to 30
minutes.
A. 4 to 2 to 1
B. 6 to 2 to 1
C. 8 to 4 to 1
D. 10 to 6 to 1
E. 12 to 8 to 1
35.
Leaping Math
A jaguar chases an ostrich that has a 150 yard head
start. It leaps nine yards each time the ostrich leaps
seven yards. In how many leaps will the jaguar catch
his prey?
A. 45
B. 55
C. 65
D. 75
E. 85
Bluegrass Conference - Math Round 4 - Answers
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B
B
D
B
B
C
A
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B
B
A
D
D
D
D
B
D
D
E
D
Bluegrass Conference - Math Round 5 Page 1
1.
Contest Averages
6.
Window Framing
Bullwinkle needs an average score of 86 to win the
moose beauty contest. To exactly reach this mark,
what must his sixth score be if his first five scores were
84, 96, 82, 92, and 88?
A. 74
B. 76
C. 78
D. 80
E. 82
Molding costs $.40 per linear foot. How much does it
cost to put this molding around a square window that
has an area of 64 square feet?
A. $9.50
B. $10.40
C. $11.20
D. $12.80
E. $13.60
2.
7.
Number Sleuthing
Martian Math
One number is four more than another. 28 results
from adding twice the smaller to the larger. What are
the numbers?
A. 6, 10
B. 7, 11
C. 8, 12
D. 9, 13
E. 10, 14
On Mars, there are 3 auuks in 6 bauuks. 12 bauuks
equal 1 dauuk. How many auuks are there in 6
dauuks?
A. 36
B. 48
C. 64
D. 72
E. 96
3.
8.
Employment
Combinations
Gertrude works in a llama supercharging shop from
half past 8 a.m. to 5 p.m. with a 45 minute unpaid
lunch break. In a 5-day week at $8 per hour, she
earns ...
A. $240
B. $260
C. $280
D. $310
E. $360
If you have 4 rods and 5 reels and 7 lures, how many
different combinations of rods, reels, and lures could
you make?
A. 16
B. 32
C. 90
D. 140
E. 210
4.
9.
Geometric Journeys
Prisms
You go 10 miles N, 10 miles W, 8 miles N, 20 miles E,
18 miles S, and W to your starting point. The area of
the enclosed figure is ---- square miles.
A. 180
B. 220
C. 260
D. 300
E. 340
Consider a rectangular prism with a square base 6
centimeters on a side. If it has a volume of 324 cubic
centimeters, its height is ---- centimeters.
A. 6
B. 7
C. 8
D. 9
E. 10
5.
10.
Vacation Combinations
Jill wants to go snorkeling, water-skiing, or sailing in
the Caribbean, Baja, Tahiti, or the Azores. How many
possibilities does she have?
A. 7
B. 12
C. 18
D. 24
E. 49
Composite Numbers
What is the sum of all the composite numbers between
3 and 11?
A. 35
B. 37
C. 39
D. 41
E. 43
Bluegrass Conference - Math Round 5 Page 2
11.
Lofty Leapers
16.
Geometric Formulas
Larry can leap higher than Lanny. Len can leap
higher than Leland. Lucy can leap higher than Larry.
Lanny can leap higher than Len. Who can leap
highest?
A. Len
B. Lucy
C. Larry
D. Lanny
E. Leland
The formula, A = bh, finds the area of a ...
A. circle
B. triangle
C. pentagon
D. trapezoid
E. parallelogram
12.
17.
Number Palindromes
Arcs
You can make a number palindrome by starting with
any number, adding the reverse of the number, and
then adding the reverse of the sum to the sum, and so
on. If you start with 76, what palindrome number do
you come to?
A. 121
B. 484
C. 606
D. 1111
E. 1221
An arc that is three-sixteenths the circumference of a
circle contains ---- degrees.
A. 67.5
B. 69.5
C. 71.5
D. 73.5
E. 75.5
13.
18.
Negative Exponents
Election Math
Which number has the same value as 10 to the
negative 5th power?
A. 0.10000
B. 0.00001
C. 0.000001
D. -0.00001
E. -0.000001
Roy Bean was elected county judge with a majority of
nine votes. If 11,665 votes were cast, how many did
Mr. Bean get?
A. 5834
B. 5835
C. 5836
D. 5837
E. 5838
14.
19.
Waves
Deduction
The speed of waves 5 meters in length that pass
beneath an anchored buoy every 1.25 seconds is ---meters per second.
A. 1.25
B. 2.5
C. 3.75
D. 4
E. 5
If all fraps are forps and no fumps are forps, then we
know that ...
A. no forps are fraps
B. no fumps are fraps
C. all fumps are forps
D. some fumps are forps
E. some fraps are not forps
15.
20.
Inequalities
If -2y - 8 < -14, then y is greater than ...
A. 1
B. 2
C. 3
D. 4
E. 5
Speed Problems
A sailboat traveled 9 miles in 45 minutes. What was its
speed in miles per hour?
A. 9
B. 10
C. 11
D. 12
E. 13
Bluegrass Conference - Math Round 5 Page 3
21.
Salary Proportions
26.
Angles
Mustapha Malouff makes mines for Minnie's
Mineworks in Mosul. He earns 80 dinars per week.
How many dinars does he make in a year?
A. 3280
B. 4160
C. 5440
D. 6220
E. 7460
One angle equals 13 degrees and another equals 77
degrees. These are --- angles.
A. reflex
B. adjacent
C. spherical
D. supplementary
E. complementary
22.
27.
Rectangles
Primes
The perimeter of a rectangle is 72 cm and its length is
17 cm. Its width in centimeters is ...
A. 19
B. 21
C. 23
D. 25
E. 27
Which prime number with its digits reversed does not
form another prime number?
A. 13
B. 17
C. 19
D. 37
E. 79
23.
28.
Snake Speed
Plane Figures
A sidewinder slithered 490 yards in 3.5 hours. What
is its rate of speed in feet per hour?
A. 380
B. 420
C. 460
D. 500
E. 540
You have a 100' string with the ends tied together. If
you lay it out to form each figure below, which would
have the greatest area?
A. circle
B. square
C. triangle
D. hexagon
E. pentagon
24.
29.
Inequalities
Primes
For which value of p is this inequality true?
3p > - 12
A. -7
B. -6
C. -5
D. -4
E. -3
What is the product of the 4th and 6th prime
numbers?
A. 55
B. 65
C. 91
D. 119
E. 187
25.
30.
Silhouettes
The silhouette of a Mobius strip has the appearance of
...
A. a circle
B. a pyramid
C. the letter C
D. a question mark
E. the symbol for infinity
Bug Math
Doris sent Cher half her bugs. Cher sent Jen half of
the bugs she got from Doris. Jen kept eight of those
and gave the remaining ten to Dana. How many bugs
did Doris give Cher?
A. 24
B. 28
C. 32
D. 36
E. 40
Bluegrass Conference - Math Round 5 Page 4
31.
Doggone Averages
6 Dobermans were each 3 feet long, while each of 4
St. Bernards were 5 feet long and each of 6
Chihuahuas had 1 foot lengths. The average length of
these pooches was ---- feet.
A. 1.75
B. 2.25
C. 2.50
D. 2.75
E. 3.00
32.
Fishy Finance
Fred went fishing in Alaska. He spent $340 for a
plane ticket, $220 for lodging and meals, $180 for a
boat rental, and $60 for bait. He caught 5 flounders.
His cost per fish was ...
A. $140
B. $160
C. $180
D. $200
E. $220
33.
Variation
Which is an example of inverse variation?
A. travel time and speed
B. weekly pay and hours worked
C. cost per pound and number of pounds
D. gallons of paint and square feet to paint
E. cups of milk and cups of flour in a recipe
34.
Marble Dispensation
Don gave Ted half of his marbles. Ted gave Jim half
of the marbles he got from Don. Jim kept 8 of those
and gave the remaining 10 to Lennie. How many
marbles did Don give Ted?
A. 24
B. 30
C. 36
D. 42
E. 48
35.
Work Problems
It takes 20 men 36 days to do a task. How many days
will it take 24 men to complete it?
A. 18
B. 25
C. 30
D. 32
E. 41
Bluegrass Conference - Math Round 5 - Answers
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C
D
C
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D
A
D
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B
B
B
B
D
C
E
A
D
B
D
B
A
B
E
E
E
C
A
C
D
D
B
A
C
C
Bluegrass Conference - Math Round 6 Page 1
1.
Reptilian Ratios
6.
Polygon Diagonals
An ax was used to divide an anaconda 36 feet long
into 4 parts in the ratio of 3 to 4 to 5 to 6. The
longest part was how many feet long?
A. 10
B. 12
C. 14
D. 16
E. 18
How many different diagonal lines can be drawn in a
hexagon?
A. 6
B. 7
C. 8
D. 9
E. 10
2.
7.
Radioactivity
Ballot Casting
After two hours, 1/16 of the original radioactive
material remains undecayed. The half-life of this
substance is --- minutes.
A. 20
B. 30
C. 40
D. 50
E. 60
If 1996 was the first year that Dan could vote in a
federal election, he must have been born in ...
A. 1971 or 1972
B. 1974 or 1975
C. 1977 or 1978
D. 1981 or 1982
E. 1984 or 1985
3.
8.
Sets
Quadrilaterals
Which are overlapping sets?
A. {5, 7} and {4, 6, 8}
B. {6, 8, 10} and {7, 9, 11}
C. {2, 4, 6, 8} and {8, 6, 4, 2}
D. {1, 2, 3, 4, 5} and {8, 10, 12}
E. {3, 7, 9, 12, 15} and {1, 4, 8, 9, 12}
A rectangle, rhombus, and square all ...
A. are equilateral
B. are equiangular
C. have congruent diagonals
D. have perpendicular diagonals
E. have properties of parallelograms
4.
9.
Quadrilaterals
Longitude
Angle A in parallelogram ABCD is one-fourth as
large as angle B. How many degrees are in angle B?
A. 36
B. 48
C. 96
D. 112
E. 144
If the noon meridian sweeps over 360 degrees of
longitude daily, it travels how many degrees every
thirty minutes?
A. 5.5
B. 7.5
C. 10
D. 12.5
E. 15
5.
10.
Consecutive Integers
What is the sum of two consecutive odd integers if
their product is 143?
A. 22
B. 24
C. 26
D. 28
E. 30
Alien Ratios
A trained blue-collar Neptunian can make 300
urldobs per hour. So how many minutes does he
require to make 40 urldobs?
A. 2
B. 4
C. 6
D. 8
E. 10
Bluegrass Conference - Math Round 6 Page 2
11.
Collectible Computations
16.
Coin Problems
Lou has three times as many kachinas as Kim. Kim
has two-thirds as many kachinas as Meg. Meg has 27
kachinas. How many does Lou have?
A. 50
B. 52
C. 54
D. 56
E. 58
Groucho and Harpo each has 10 coins that are either
quarters or dimes. If Groucho has 5 quarters and
Harpo has 60 cents more than Groucho, how many
quarters does Harpo have?
A. 5
B. 6
C. 7
D. 8
E. 9
12.
17.
Averages
Cubes
Each of 6 pheasants weighed 5 pounds. Two turkeys
weighed 20 pounds each. Two condors weighed 25
pounds each. The birds' average weight was ---pounds.
A. 8
B. 10
C. 12
D. 14
E. 16
A cube 20 inches on a side can be divided into how
many cubes 5 inches on a side?
A. 64
B. 66
C. 68
D. 70
E. 72
13.
18.
Mathematical Properties
Tennis, Anyone?
What mathematical property is illustrated in this
equation?
n(q+r) = nq + nr
A. reflexive
B. symmetric
C. associative
D. distributive
E. commutative
In a tennis match there are five players, each of whom
must play one set with every other player. How many
sets must be played?
A. 8
B. 10
C. 12
D. 14
E. 16
14.
19.
Age Problems
Rail Lines
Gomer Garbanzo will be 78 years old in 9 years if he
was ---- years ago.
A. 45 years old 16
B. 46 years old 17
C. 47 years old 18
D. 48 years old 19
E. 49 years old 20
The rails of a railroad track are ...
A. infinite
B. parallel
C. dihedral
D. concentric
E. perpendicular
15.
20.
Feline Frolicking
A lion loping along at 5 feet per second will cover 5
miles in how many minutes?
A. 55
B. 66
C. 77
D. 88
E. 99
Exponents
Which statement is not true?
A. 1 to the 9th power = 1
B. 2 to the 6th power = 64
C. 3 to the 4th power = 71
D. 7 to the 2nd power = 49
E. 8 to the 3rd power = 512
Bluegrass Conference - Math Round 6 Page 3
21.
Electric Charges
26.
Perimeters
You have a 150-watt light on for 1 hour every day for
a year. At 9 cents per kilowatt-hour, what does the
power to run this light cost?
A. $2.57
B. $3.86
C. $4.93
D. $5.51
E. $6.13
The length of the perimeter of a square five
centimeters on a side is the same as the perimeter of a
rectangle with sides of ---- centimeters.
A. 5 and 4
B. 6 and 3
C. 7 and 5
D. 8 and 2
E. 9 and 6
22.
27.
Algebraic Simplification
Canine Ages
Simplify this expression.
-3(x+y) - 2(2x-y)
A. 2x-y
B. x-2y
C. 7x-y
D. -x+y
E. -7x-y
At Priscilla's Puppy Parlor, a baby spaniel is 18 days
old and baby poodle is 3 days old. In how many days
will the spaniel be exactly twice as old as the poodle?
A. 6
B. 8
C. 10
D. 12
E. 14
23.
28.
Numbers
Fresco Finance
Which are not perfect squares?
A. 25 and 121
B. 34 and 132
C. 49 and 144
D. 64 and 169
E. 81 and 196
What would Mike Angelo charge to paint a fresco on
a square ceiling 50 feet on a side at $.20 a square
foot?
A. $400
B. $500
C. $600
D. $700
E. $800
24.
29.
Clock Math
A Really Cool Problem
If you draw a line on a clock face so that the sums of
the hours on each half were identical, the line would
go through ...
A. 1:30 and 7:30
B. 2:30 and 8:30
C. 3:30 and 9:30
D. 4:30 and 10:30
E. 5:30 and 11:30
The volume of the Ross Ice Shelf above sea level is
80,000 cubic miles. If its area is 200,000 square
miles, the average ice depth above sea level is ---- feet.
A. 880
B. 1056
C. 2112
D. 2428
E. 2640
25.
30.
Equations
Which equation is incorrect?
A. 6x + 3 = 15 when x = 2
B. 5x + x = 30 when x = 5
C. 4x + 1 = 17 when x = 4
D. 3x + 8 = 24 when x = 6
E. 2x + 10 = 16 when x = 3
Ratio
The ratio of the Vogons to Vulcans in a starship is 5
to 3. How many Vulcans are there if there are 200
Vogons?
A. 80
B. 100
C. 120
D. 140
E. 160
Bluegrass Conference - Math Round 6 Page 4
31.
Fishy Math
A water barrel contains 14 perch, 12 catfish, and 9
crappie. What is the probability that the first fish
caught from this barrel will be a perch?
A. 2/3
B. 1/2
C. 2/5
D. 1/6
E. 2/7
32.
Grocery Math
Jeannine paid $9.90 for a bag of Jerusalem artichokes
weighing 4 pounds 8 ounces. What was the cost per
pound?
A. $1.80
B. $1.90
C. $2.00
D. $2.10
E. $2.20
33.
Statistics
Each of 8 bunnies weighs 8 pounds while 8 javelina
weigh 60 pounds each. The mean weight of all these
animals is ---- pounds.
A. 30
B. 32
C. 34
D. 36
E. 38
34.
Storage
Two cubical storage bins whose edges are three and
five feet respectively enclose how many total cubic
feet?
A. 126
B. 132
C. 146
D. 152
E. 166
35.
Trinket Trading
Bonnie gave Beulah half of her baubles. Beulah gave
Barb half the baubles she got from Bonnie. Barb kept
8 of those baubles and gave the remaining 10 to her
brother, Bruce. How many baubles did Bonnie have
in the first place?
A. 56
B. 68
C. 72
D. 86
E. 94
Bluegrass Conference - Math Round 6 - Answers
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2.
3.
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B
B
E
E
B
D
C
E
B
D
C
C
D
E
D
E
A
B
B
C
C
E
B
C
D
D
D
B
C
C
C
E
C
D
C
Bluegrass Conference - Math Round 7 Page 1
1.
Military Time
6.
Area Formulas
A certain maneuver was supposed to begin at four
hours before midnight, but it was delayed by two
hours. In military time, when did it start?
A. 1400
B. 1600
C. 1800
D. 2000
E. 2200
This is a formula for the area of what figure?
A = 1/2 (a+b)h
A. circle
B. triangle
C. octagon
D. pentagon
E. trapezoid
2.
7.
Down for the Count
Factoring
If you count 100 numbers per minute, 24 hours per
day, it would take about 4 weeks to count to one
million, or about how many years to count to one
billion?
A. 20
B. 40
C. 60
D. 80
E. 100
The largest prime factor of 360 is ...
A. 2
B. 3
C. 5
D. 7
E. 11
3.
8.
Propeller Proportions
Duration Computation
The ratio of propeller rotation to that of an engine is 3
to 5. The engine is turning at 4000 rpm. The
propeller rate is ---- rpm.
A. 1800
B. 2000
C. 2200
D. 2400
E. 2600
Bernice is twice as old as Brunhilde and Brunhilde is
twice as old as Beulah. How old is Bernice if Beulah is
15 years old?
A. 30
B. 40
C. 50
D. 60
E. 70
4.
9.
Hairy Sets
Arcs
Given this collection of distinct elements, which choice
illustrates a disjoint set?
(fuzz, shag, mane, lock, braid)
A. (braid, lock, mane, shag)
B. (cowlick, tuft, wig, shag)
C. (beard, goatee, whisker, lock)
D. (sideburn, strand, crop, tuft)
E. (bun, fuzz, forelock, ponytail)
If its vertex is on the circle, how many degrees are in
an angle that subtends an arc of 48 degrees?
A. 12
B. 16
C. 24
D. 48
E. 96
5.
10.
Velocity
What is the velocity in feet per second of an object
that flies 45,000 feet in 5 minutes?
A. 50
B. 100
C. 150
D. 200
E. 250
Arcs
Major and minor arcs of the same circle could include
---- degrees.
A. 305 and 35
B. 315 and 45
C. 325 and 55
D. 335 and 15
E. 345 and 25
Bluegrass Conference - Math Round 7 Page 2
11.
Aging
16.
Equal Distances
How old will Olivia be in 7 years if she was 28 years
old 9 years ago?
A. 40
B. 42
C. 44
D. 46
E. 48
If you want to place four points at equal distances
from each other, place them ...
A. in a row
B. around a circle
C. along an ellipse
D. at the corners of a square
E. at the corners of a tetrahedron
12.
17.
Proportions
Distance Problems
If 200 photographs of Elvis sightings weigh 6.5
pounds, then how many such photos are in 52
pounds?
A. 1200
B. 1300
C. 1400
D. 1500
E. 1600
Two jets leave an airbase at the same time. One flies
west at 300 mph while the other flies east at 450 mph.
In how many hours will they be 2,250 miles apart?
A. 2
B. 3
C. 4
D. 5
E. 6
13.
18.
Large Numbers
Metric Conversions
When you multiply fifty thousand by two million, how
many zeroes are in the product?
A. 9
B. 10
C. 11
D. 12
E. 13
The 1980 eruption of Mount St. Helens lowered its
summit from 9500 feet to 8150 feet, a difference of
about how many meters?
A. 100
B. 200
C. 300
D. 400
E. 500
14.
19.
Ratios
Triangle Sides
3/8 is a simplified way of expressing the ratio of 42 to
...
A. 108
B. 112
C. 116
D. 120
E. 124
In triangle ABC, side AB is 18 and side AC is 7.
Therefore, side BC is less than ...
A. 17
B. 19
C. 21
D. 23
E. 25
15.
20.
Graphing
Find the distance between these points.
(-2, -6) and (-2, -21)
A. 9
B. 11
C. 13
D. 15
E. 17
Polling
There are 3200 octogenarians in a population of
30,000 people in town. How many must be included
in a poll of 150 to reflect the same proportion?
A. 14
B. 16
C. 18
D. 20
E. 22
Bluegrass Conference - Math Round 7 Page 3
21.
Angle Measures
26.
Mathematical Principles
If one of the exterior base angles of an isosceles
triangle is 115 degrees, how many degrees are in its
smallest interior angle?
A. 30
B. 35
C. 40
D. 45
E. 50
If p+r = q+r, we know that ...
A. p = r
B. p = q
C. p = r/q
D. q = r/p
E. pq = r/p
22.
27.
Baseball Statistics
Motion Problems
If Poison Ivy Macgruder got 42 hits in 210 times at
bat, what was her batting average?
A. .200
B. .210
C. .220
D. .230
E. .240
Jake rode 50 miles from 8:30 a.m. to 9:45 a.m. at an
average speed of ---- miles per hour.
A. 25
B. 30
C. 35
D. 40
E. 45
23.
28.
Setting Up Equations
Math Notation
If p fish cost q dollars, how many fish can be
purchased for $40?
A. p/40q
B. 40q/p
C. 40p/q
D. (p/40)q
E. (pq)/40
Vertical bars on either side of a number indicate ...
A. factorial
B. greater than
C. absolute value
D. irrational number
E. approximately equal to
24.
29.
Polygons
Algebraic Expressions
How many more degrees are in the interior angles of a
square than in a triangle?
A. 30
B. 45
C. 60
D. 90
E. 180
Mr. Wong has x aliens in a closet. 1/3 are
green-lipped while 1/4 of the remainder are toothy.
The rest are unusual. How many of the aliens are
unusual?
A. 1/2x
B. 3/5x
C. 2/3x
D. 1/4x
E. 5/6x
25.
30.
Ratios
Express this continued ratio in lowest terms.
4 tons to 1500 pounds to 50 pounds
A. 140 to 20 to 1
B. 160 to 30 to 1
C. 180 to 40 to 1
D. 200 to 50 to 1
E. 220 to 60 to 1
Scientific Notation
6.2 times 10 to the fourth power equals what decimal
numeral?
A. 62
B. 620
C. 6,200
D. 62,000
E. 620,000
Bluegrass Conference - Math Round 7 Page 4
31.
Plane Figures
The more sides a regular polygon has, the greater ...
A. its area
B. its perimeter
C. its number of midpoints
D. the length of its diagonals
E. the sum of its interior angles
32.
Clock Angles
In 40 minutes, the second hand of a watch sweeps
through an angle of how many degrees?
A. 3,600
B. 7,200
C. 10,800
D. 14,400
E. 16,000
33.
Moving Along
A truck travels 540 yards in 15 seconds at a constant
speed. How many feet does it travel in 1/3 second?
A. 18
B. 24
C. 30
D. 36
E. 42
34.
Time Angles
In three and 1/4 hours, the minute hand of a clock
rotates through an angle of how many degrees?
A. 965
B. 990
C. 1080
D. 1125
E. 1170
35.
Surface Area
In square centimeters, what is the surface area of a
rectangular prism with dimensions of 3 x 3 x 5
centimeters?
A. 78
B. 80
C. 82
D. 84
E. 86
Bluegrass Conference - Math Round 7 - Answers
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35.
E
D
D
D
C
E
C
D
C
B
C
E
C
B
D
E
B
D
E
B
E
A
C
E
B
B
D
C
A
D
E
D
D
E
A
Bluegrass Conference - Math Round 8 Page 1
1.
Baby Frog Problems
6.
Alien Probability
Ted has 5 more tadpoles than Tina. If Ted's tadpoles
are added to twice Tina's, the total is 65. How many
tadpoles does Tina have?
A. 10
B. 15
C. 20
D. 25
E. 30
Three out of four Neptunians are eight-legged and
two out of five have lavender lips. The probability
that their leader is a lavender-lipped eight-legged
being is ...
A. 1 in 2
B. 2 in 3
C. 3 in 4
D. 5 in 9
E. 3 in 10
2.
7.
Polynomials
Math Vocabulary
Simplify this algebraic expression.
-5x - 7y - 10z - (10x + 2y - 5z)
A. -5x - 5y - 15z
B. -15x + 9y + 15z
C. 5x - 5y - 5z
D. -15x - 9y - 5z
E. 15x - 9y - 15z
Because the sum of any number and zero is that
number, zero is called the additive ...
A. factor
B. inverse
C. identity
D. reciprocal
E. coefficient
3.
8.
Age Problems
Money Problems
Roy is 8 years older than 4 times Mindy's age. Roy's
daughter is half his age. If Mindy is 18 years old,
how old is Roy's daughter?
A. 32
B. 34
C. 36
D. 38
E. 40
If you and your little sister saved a total of $240, but
your savings were four times hers, how much did you
save?
A. $160
B. $178
C. $186
D. $192
E. $204
4.
9.
Quadrilaterals
Perimeters
Two consecutive angles in a parallelogram measure x
degrees and x plus 30 degrees. How many degrees
are in the larger angle?
A. 95
B. 105
C. 115
D. 125
E. 135
The perimeter of a square whose area is 225 square
inches is ---- inches.
A. 40
B. 60
C. 90
D. 100
E. 120
5.
10.
Algebra
What is t if 16 = 2(t+3)?
A. 2
B. 3
C. 4
D. 5
E. 6
Numbers
Which number is not a perfect square?
A. 121
B. 144
C. 169
D. 196
E. 220
Bluegrass Conference - Math Round 8 Page 2
11.
Probability
16.
Algebraic Evaluation
A bag contains 12 brass, 6 aluminum, and 8 steel
keys. What is the probability that the first key drawn
randomly will be steel?
A. 3 in 13
B. 4 in 13
C. 5 in 13
D. 6 in 13
E. 7 in 13
Given x = 3, d = 7, and m = 10, evaluate this.
3(x to the fourth power) + 5d - m
A. 184
B. 202
C. 226
D. 268
E. 284
12.
17.
Ratios and Proportions
Astounding Age Problems
Which statement is true?
A. 4/5 = 16/18
B. 3/5 = 6/10 so 3 x 6 = 5 x 10
C. 6 for 85 cents is better than 8 for 1 dollar.
D. If cross products are equal, the ratios are
equal.
E. If two triangles are similar, their respective
sides have the same lengths.
How old will Methuselah be in 156 years if he was
721 years old 34 years ago?
A. 507
B. 608
C. 709
D. 810
E. 911
13.
18.
Integers
Spokes
What is the greatest of five consecutive odd integers
whose sum is 175?
A. 35
B. 37
C. 39
D. 41
E. 43
How many spokes are on a wheel if every two adjacent
spokes form an angle of 24 degrees?
A. 12
B. 15
C. 18
D. 21
E. 24
14.
19.
Mathematical Statements
Volume Comparison
Which statement is not true?
A. 7 is a factor of 112.
B. 12.6 is a mixed number.
C. 32 is a composite number.
D. 3/9 and 9/3 are reciprocals.
E. 10 is a common multiple of 2 and 5.
If a hollow cube with sides of 2 inches is filled with
water four times and poured into another cube with
sides of 4 inches, what will be the height of the water
in the larger cube?
A. 1/2"
B. 1"
C. 2"
D. 3"
E. 4"
15.
20.
Square Root Estimation
The square root of 8911 falls between ...
A. 91 and 92
B. 92 and 93
C. 93 and 94
D. 94 and 95
E. 95 and 96
Radioactive Decay
How much of the original radioactive substance
remains after 8 hours if that substance has a half-life
of 2 hours?
A. 1/2
B. 1/4
C. 1/8
D. 1/16
E. 1/32
Bluegrass Conference - Math Round 8 Page 3
21.
Prime Numbers
26.
Blueprint Proportions
The seventh prime number is ...
A. 13
B. 17
C. 19
D. 23
E. 29
The width of a house is to be 100 feet. The scale on a
blueprint is 1/4 inch to 1 foot. A line of the blueprint
representing the width of the house is ...
A. 2' 1"
B. 1' 4"
C. 2' 6"
D. 1' 8"
E. 2' 10"
22.
27.
Triangles
An Odd Question
If one of the angles in a triangle equals 109 degrees,
the triangle is ...
A. right
B. acute
C. obtuse
D. equilateral
E. equiangular
Which is an odd number?
A. -98
B. 2,848,624
C. 39 squared
D. 6 to the 4th power
E. the square root of 36
23.
28.
Heavy Lifting
Decimals
You want to raise a 200-pound box on the end of a
10-foot lever. If the fulcrum is 2 feet from the box,
how many pounds of force are needed to lift it?
A. 10
B. 20
C. 30
D. 40
E. 50
What fraction is equivalent to the repeating decimal
0.58333333333...?
A. 3/12
B. 5/12
C. 7/12
D. 9/12
E. 11/12
24.
29.
Age Algebra
Linear Equations
Little Nell is 5 days old and Dudley is 25 days old. In
how many days will Dudley be three times as old as
Nell?
A. 5
B. 10
C. 15
D. 20
E. 25
What is x when 19 + 5x = 4?
A. -7
B. -3
C. -2
D. 4
E. 6
25.
30.
Geometric Solids
Add the number of faces on a cone, a cube, a
triangular pyramid, and a cylinder.
A. 11
B. 13
C. 15
D. 17
E. 19
Statistics
In which set of scores is the range not 100?
A. 0, 8, 63, 68, 82, 100
B. 25, 38, 49, 69, 99, 125
C. 88, 93, 107, 129, 163, 188
D. 53, 97, 164, 193, 228, 253
E. 664, 683, 726, 728, 752, 764
Bluegrass Conference - Math Round 8 Page 4
31.
Fraction Conversion
What fraction equals 62.5%?
A. 5/6
B. 5/7
C. 5/8
D. 5/9
E. 5/11
32.
Chapeau Ratio
There are 500 hats on Bartholomew's head. 25 are
derbies and the rest are sombreros. What is the ratio
of derbies to sombreros?
A. 1 to 18
B. 1 to 19
C. 1 to 20
D. 1 to 21
E. 1 to 22
33.
Sail Area
The area of a triangular sail 22 feet long at its base
and 73 feet high is ---- square feet.
A. 763
B. 773
C. 783
D. 793
E. 803
34.
Number Problems
If the sum of two numbers is 41 and the larger is one
less than twice the smaller, the larger number is ...
A. 21
B. 23
C. 25
D. 27
E. 29
35.
Cubes
You have a 3x3x3 cube made from 27 smaller cubes.
If you paint the outside of the big cube and then
disassemble it, how many of the small cubes will have
exactly three painted faces?
A. 4
B. 6
C. 8
D. 12
E. 16
Bluegrass Conference - Math Round 8 - Answers
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2.
3.
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35.
C
D
E
B
D
E
C
D
B
E
B
D
C
B
D
D
E
B
C
D
B
C
E
A
C
A
C
C
B
D
C
B
E
D
C
Bluegrass Conference - Math Round 9 Page 1
1.
Square Comparisons
6.
Paper Piling
The side of one square is four times longer than the
side of a smaller square. How many times greater is
the area of the larger square in comparison to that of
the smaller one?
A. 4
B. 8
C. 12
D. 16
E. 20
A Great Auk poster .02 millimeters thick is cut in half
and one piece is placed on the other. This is repeated
9 more times, leaving a pile of poster pieces how
many centimeters high?
A. 1.024
B. 2.048
C. 3.072
D. 4.096
E. 5.120
2.
7.
Figuring Flooring
Circles
Karen Kabonski is carpeting her cabin in Kenai. Its
floor is 20 feet by 30 feet. Pad and carpet together
run $9 per square yard. The materials cost will be ...
A. $480
B. $550
C. $600
D. $740
E. $820
In a circle in which the longest possible chord is ten
inches, the radius is ---- inches.
A. 3
B. 4
C. 5
D. 6
E. 7
3.
8.
Binary Numeration
Arcs
In the binary system, there are 110100 ...
A. dozen in a gross
B. planets in our solar system
C. lives that a cat is said to have
D. playing cards in a standard deck
E. dalmatians in the Walt Disney movie
An arc 1/16 the circumference of a circle contains
how many degrees?
A. 16.5
B. 18.5
C. 20.5
D. 22.5
E. 24.5
4.
9.
Number Palindromes
Ballistics
Which choice does not produce a numeric
palindrome?
A. 11 squared
B. 22 squared
C. 26 squared
D. 33 squared
E. 101 squared
A missile traveling at 9600 feet per second goes about
how many miles in 15 seconds?
A. 21
B. 23
C. 25
D. 27
E. 29
5.
10.
Duck Word Problems
A flightless duck completed 4/5 of its migration after
waddling 220 miles. It still have to travel ---- miles.
A. 40
B. 45
C. 50
D. 55
E. 60
Population Reductions
There were 372 deer in Bigdog County in early 1996
and 238 in late 2000. The rate of change per year in
this population is ...
A. -24.2
B. -26.8
C. -28.4
D. -30.6
E. -32.0
Bluegrass Conference - Math Round 9 Page 2
11.
Cabin Guests
16.
LCMs
Zeke lives in a square cabin with 720 cockroaches.
The population density of the roaches is 20 per square
foot. What are the cabin's floor dimensions?
A. 4' x 4'
B. 5' x 5'
C. 6' x 6'
D. 7'x 7'
E. 8' x 8'
The least common multiple of 12 and 15 is ...
A. 30
B. 40
C. 50
D. 60
E. 70
12.
17.
Population Prediction
Reasoning
Today just 6 people live in Greenscum. But if the
population doubles every 10 years, how many people
will live in Greenscum 70 years from now?
A. 96
B. 192
C. 184
D. 768
E. 1536
Which statement is true?
A. 36 > 63
B. 12(2) = 12/2
C. 6 + 9 = 14 or 8 - 3 = 5
D. 8/4 = 2 and 12 + 2 = 16
E. If 18/2 = 9 then 18(2) = 34
13.
18.
Prevention Proverbs
Numbers
Since an ounce of prevention is worth a pound of
cure, how many pounds of prevention are worth 128
pounds of cure?
A. 4
B. 6
C. 8
D. 10
E. 12
What is the largest number divisible by all whole
numbers less than its square root?
A. 24
B. 35
C. 48
D. 63
E. 80
14.
19.
Ratios
Special Sequences
How many bedbugs are in a sleeping bag containing
400 insects if there are only bedbugs and fleas in the
bag in the ratio of 7 to 1?
A. 150
B. 200
C. 250
D. 300
E. 350
What is the next number in this sequence of binary
numerals?
110 111 1000 1001 1010
A. 1100
B. 1011
C. 1110
D. 1101
E. 1111
15.
20.
Sets
Which is a finite group?
A. multiples of 7
B. divisors of 100
C. fractions between 1 and 2
D. decimal numbers between 11 and 13
E. whole numbers between 1 and 1 trillion
Factoring
The prime factors of 222 are 2 and 3 and ...
A. 37
B. 39
C. 41
D. 43
E. 45
Bluegrass Conference - Math Round 9 Page 3
21.
Geometric Figures
26.
Quadrilateral Areas
Any two points on a ---- are equidistant from the
center.
A. line
B. circle
C. square
D. triangle
E. pentagon
The base of a regular quadrilateral is 20 inches and its
perimeter is 110 inches. Its area is ---- square inches.
A. 250
B. 400
C. 550
D. 700
E. 850
22.
27.
Numbers
Rotations
What is the sum of the composite numbers less than
10?
A. 27
B. 28
C. 29
D. 30
E. 31
A spindle that rotates through 1440 degrees in one
second makes how many revolutions per minute?
A. 160
B. 180
C. 200
D. 220
E. 240
23.
28.
Mathematical Relations
Population Math
Which equation defines the relationship between X
and Y in this table?
X 1, 2, 3, 4, 5, 6
Y 1, 4, 7, 10, 13, 16
A. Y = 2 - X
B. Y = 3X - 2
C. Y = 4 - 3X
D. Y = 3X + 1
E. Y = x squared -2
If farmers account for 800 million of China's total
population of 1.2 billion, what percentage of the total
population is not involved in farming?
A. 21%
B. 25%
C. 29%
D. 33%
E. 37%
24.
29.
Squares
Running Averages
Which is not a perfect square?
A. 256
B. 423
C. 625
D. 729
E. 900
On day 1, Fred ran a mile in 6 minutes. On each of
the following 6 days, he cut 10 seconds off the
previous day's speed. What was his average speed for
the mile at the end of the 7 days?
A. 5 min 10 sec
B. 5 min 20 sec
C. 5 min 30 sec
D. 5 min 40 sec
E. 5 min 50 sec
25.
30.
Integers
Which must be an odd integer if x is any integer?
A. x - 1
B. x + 1
C. x + 2
D. 2x + 1
E. 2x + 2
Pepper Plucking
In an afternoon, Pete Piper picked four peppers more
than three times the number of peppers he picked in
the morning. If he picked a total of 112, how many
did he pick that afternoon?
A. 85
B. 87
C. 89
D. 91
E. 93
Bluegrass Conference - Math Round 9 Page 4
31.
Coordinate Geometry
What is the diameter of a circle tangent to the x-axis
with its center at (-4,6)?
A. 6
B. 8
C. 10
D. 12
E. 14
32.
Numbers
Which is an ordinal number?
A. 8250
B. 41st
C. 14/7
D. .66666 ...
E. 30 degrees Celsius
33.
Sets
Which number is in the intersection of whole numbers
from 11 to 52 evenly divisible by 3 and whole
numbers between 1 and 100 evenly divisible by 4?
A. 28
B. 30
C. 32
D. 34
E. 36
34.
Averages
The fish on one stringer weigh 12, 15, 21, 35, and 142
pounds while those on another weigh 12, 15, 23, 32,
and 43 pounds. In pounds, what is the difference
between the means of the two stringers?
A. 14
B. 16
C. 18
D. 20
E. 22
35.
Grade Averages
What grade must Igor receive on his fourth test to
raise his average to 80 if his scores on his first three
tests were as follows?
69 81 74
A. 84
B. 88
C. 92
D. 96
E. 98
Bluegrass Conference - Math Round 9 - Answers
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