Sixth Grade Test - Excellence in Mathematics Contest - 2008
1.
The sum of two natural numbers is 80 and one is 24 larger than the other.
What is the product of these two numbers?
A. 1024
2.
B. 1456
B. 133
C. 134
B. 17
D. 135
E. 141
C. 18
D. 20
E. 23
Gabe was born on February 29th, 1952. So his first true ‘birthday’ was February 29th, 1956.
By today, how many ‘true’ birthdays has Gabe celebrated?
A. 13
5.
E. 6256
The 12 hours on a clock are written in Roman Numerals. How many I’s are used?
A. 15
4.
D. 4200
The sum of 16 consecutive natural numbers is 2008. What is the largest of these?
A. 132
3.
C. 2560
B. 14
C. 15
D. 16
E. 17
D. 96
E. 102
What is the sum of all positive factors of 42?
(Note: 1 and 42 do count as ‘positive factors’ of 42.)
A. 53
B. 79
C. 83
Use this number line, with ten points labeled with letters, to answer questions #6 and #7, below.
–1
p
6.
t
u
v
w
y
x
B. u
C. v
D. w
E. y
B. t
C. u
D. x
E. y
B. 30oF
C. 36oF
D. 38oF
E. 42oF
From an 8x8x8 cube, a 2x2x2 cube is removed from each corner.
What fraction of the 8x8x8 cube is removed?
A. 1/4
10.
s
On March 2, 2008, it was 42oF at 7 AM. From 7 AM to 4 PM, the temperature rose an average of 4oF
per hour. From 4 PM on March 2 to 8 AM on March 3, the temperature dropped an average of 3oF per
hour. What was the temperature at 8 AM on March 3?
A. 24oF
9.
r
2
Which of these points is closest to the sum v+p ?
A. s
8.
q
1
Which of these points is closest to the product ux?
A. t
7.
0
B.1/8
C.1/2
For how many natural numbers N is the fraction
A. 7
B. 8
C. 9
D. 3/32
E. 3/8
N
1
1
between and ?
3
2
55
D. 10
E. 11
Sixth Grade Test - Excellence in Mathematics Contest - 2008
11.
Assume that one gallon of water weighs 8.34 pounds and has a volume of 0.134 cubic feet. If a cube,
one foot on a side, is filled with water, how many pounds does the water weigh? Round to the nearest
tenth of a pound.
A. 0.9
12.
13.
A. 8
B. 10
D. 14
E. 16
17.
E. 62.2
C. 12
B. 0.288
C. 0.300
D. 0.320
E. 0.360
D. 16
E. 17
The sum of the first N positive square numbers is 55.
The sum of the first M positive integers is 55. What is M+N?
B. 14
C. 15
Given: 1 mile = 5280 feet = 8 furlongs.
A horse’s average speed in a 6 furlong race is 40 feet per second.
“Fur” () how long, in seconds, does the horse take to complete this race?
A. 94 sec
16.
D. 49.7
A baseball player’s ‘batting average’ equals his number of hits divided by his number of at-bats. In
April, Albert Pujols had a slow start. After 75 at-bats, his batting average was only 0.240 . If he then
follows with 18 hits in his next 50 at bats, what is his overall batting average?
A. 13
15.
C. 28.6
The first play of a game is to place this L-shape:
onto a 3x3 grid so that exactly 3 squares
are covered. How many different first
plays are possible?
Note: The following three first plays are considered different:
A. 0.280
14.
B. 1.1
B. 96 sec
C. 99 sec
D. 100 sec
In a magic square, the sum of the three numbers in each row, column, and
diagonal are equal. When you insert five numbers to complete this
magic square, what is the sum of the five numbers you used?
A. –7
B. –6
D. –4
E. –3
E. 132 sec
2
–1
C. –5
1
–4
A bicycle rider rides at a constant speed. By 10:00 AM, she has completed 3/8 of her ride; by 11:00
AM, she has completed 3/4 of her ride. How many minutes did the whole ride take?
A. 120
B. 150
C. 160
D. 175
E. 180
Sixth Grade Test - Excellence in Mathematics Contest - 2008
18.
The US Postal Service postage rate for Library Parcels is $2.02 for the first pound and $0.32 for each
additional pound. How much does a library save by combining two 7-pound parcels and one 16pound parcel all into one parcel?
A. $3.08
19.
B. $3.40
C. $3.72
D. $4.02
This sheet of paper is numbered from 1 through 16, as shown.
While lying on a table, this sheet of paper is folded
in half four times. After the following sequence of four folds,
in this order, the square with which number will be on top
(even if you can’t see the number)?
“Top half over Bottom half”
“Right half over Left half”
“Left half over Right half”
“Bottom half over Top half”
A. 6
20.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
D. 14
E. 15
B. 21.5oC
C. 27oC
D. 35oC
E. 40oC
B. 22.8%
C. 23.4%
D. 24.2%
E. 25%
A square magazine page, 12 cm by 12 cm, is to be filled with any
mix of ads that each measure 12x6, 6x12, or 6x6. How many
different designs are possible? Note: Being a magazine page,
these three sample designs are considered ‘distinct’.
A. 4
23.
2
A semi-circle with diameter 18 cm is inscribed in a rectangle.
Rounded to the nearest tenth, what per cent of the
rectangular region is shaded?
A. 21.5%
22.
C. 13
1
For every 3oC rise in temperature, the volume of a certain gas increases by 4 cubic centimeters.
50 cubic centimeters of this gas at –8oC is heated until there are 86 cubic centimeters of gas.
What is the temperature of the gas now?
A. 19oC
21.
B. 10
E. $4.36
B. 6
C. 7
D. 8
E. 9
A circle with diameter 12 cm sits on top of a square with side 12 cm. Pulled tight, a piece
of tape is wrapped exactly once (without overlap) to hold the square and circle together,
as shown. To the nearest tenth of a centimeter, what is the length of the piece of tape?
A. 66.8
B. 73.7
C. 85.7
D. 104.5
E. 123
12 cm
Sixth Grade Test - Excellence in Mathematics Contest - 2008
24.
Beth Morin must build a fence around a square garden of area 1225 square feet. Fence posts, which
are needed every 5 feet, cost $38 each. The fencing itself costs $6.50 per foot.
What will be the total cost of Beth’s project?
A. $1284
25.
31.
C. 4
D. 5
E. 6
B. 540
C. 560
D. 600
E. 660
B. 4
C. 5
D. 6
E. 8
B. 144
C. 156
D. 168
E. 180
Esky Middle School sends six 6th graders, eight 7th graders, and ten 8th graders to the Excellence in
Mathematics competition. This represents 2% of their 6th graders, 4% of their 7th graders, and
5% of their 8th graders. What is the total number of 6th, 7th, and 8th graders in Esky Middle School?
A. 700
30.
B. 3
If 2/5 of a cup of fish food can feed 24 goldfish, how many goldfish can be fed with 3 cups of fish
food?
A. 120
29.
E. $2126
A bag contains only blue marbles, green marbles, and 24 red marbles. If the probability of drawing a
blue marble is 1/2 and the probability of drawing a green marble is 1/8, how many green marbles are
in the bag?
A. 3
28.
D. $1974
A 3-digit natural number is divisible by 5 but not by 10.
The hundreds’ digit is odd and the tens’ digit is twice the hundreds’ digit.
What is the sum of all 3-digit numbers that meet all of these conditions?
A. 490
27.
C. $1936
You have 2 dimes, 8 pennies, and 4 nickels. In how many different ways can you make $0.26?
(Note: A solution such as “4 nickels and 6 pennies” counts only once even though you would have a
choice of which 6 of the 8 pennies to use.)
A. 2
26.
B. $1440
B. 720
C. 750
Eight identical sheets of paper were placed, one at a time,
overlapping as shown in the diagram.
Which sheet(s) of paper could have been the fifth one placed?
A. Only A
B. Only E
D. Only A or G
E. Only D or G
D. 780
E. 800
H
E
C. Only G
A
F
B
G
C
D
In the board game Careers, when Zan is sent to the Park Bench square she rolls two standard 6-sided
dice on each turn. She can leave the Park Bench square only if she rolls a sum of 7, a sum of 11, or
rolls the same number on each die.
What is the probability that she can leave Park Bench on her first turn there?
A. 7/18
B. 1/3
C. 1/2
D. 13/36
E. 2/9
Sixth Grade Test - Excellence in Mathematics Contest - 2008
32.
In a 6th grade basketball league, league rules state that in each game each player on a team must play
for the same number of minutes. Five players from each team play at a time. A game consists of four
8-minute periods. In one game, how many minutes does each of the players on an 8-person team play?
A. 16
33.
B. 25
B. 2
A. 1
E. 36
D. 8
E. 16
232,582,657  1 .
B. 3
What is its units’ digit?
C. 5
D. 7
E. 9
B. 271
C. 278
D. 280
E. 300
B. 1000
C. 1800
D. 2400
B. 20
C. 24
D. 30
E. 2800
22
26
28
E. 32
How many positive integers less than or equal to 200 are divisible by 3 or 5, but not by both 3 and 5?
A. 78
40.
C. 4
The six numbers on the faces of this cube are consecutive even numbers.
The sums of the two numbers on each pair of opposite faces are equal.
What number is on the face opposite 22?
A. 18
39.
D. 30
In a lake with 4000 fish, 90% are labeled ‘small’ which means that they are less than 5 cm long. How
many of these ‘small’ fish must be removed from the lake to reduce the percent of small fish in the
lake from 90% to 75%?
A. 600
38.
C. 27
In how many of the first 1000 natural numbers does the digit “7” occur at least once?
A. 270
37.
E. 28
In September, 2006, a team led by mathematicians from the University of Central Missouri found the
44th Mersenne Prime. It is:
36.
D. 25
The radius of one circle is twice as long as the diameter of a second circle.
What is the ratio of the area of the larger circle to the area of the smaller circle?
A. 1
35.
C. 24
The “digit-sum” of 744 is 7+4+4 = 15. How many even 3-digit numbers have a digit-sum of 18?
A. 22
34.
B. 20
B. 80
C. 93
D. 95
E. 96
2.487+4020.9+ 367.1+ 51.5 = 8455.6
This addition problem is incorrect because only one of the five decimal points is in the correct location
in its number. Move four of the 5 decimal points to make a correct sum.
Which number was not changed?
A. 2.487
B. 4020.9
C. 367.1
D. 51.5
E. 8455.6