Sixth Grade Test - Excellence in Mathematics Contest - 2006
1.
102 minutes after 10:00 am is how many minutes before noon?
A. 18
2.
B. 28
B. 527,000
B. 2
3 A 60


5 45 B
A. 27
7.
D. 10
E. 13
B. 29.97
C. 39.6
D. 90
E. 499.5
B. 8
C. 10
D. 12
E. 15
What does A  B equal?
B. 29
C. 45
D. 109
E. 127
B. 16
C. 18
D. 20
E. 24
B. $95,370
C. $953,700
D. $9,537,000
E. $57,222,000
Doug bought three T-shirts at $8.90 each and a pair of jeans for $18.50.
How much change does Doug get from a $50 bill?
A. $0
10.
C. 7
The United States debt is increasing at the rate of $12,716 per second. In the 75 minutes that you
have to take this math contest, how much will the US debt increase?
A. $57,222
9.
E. 31,536,000
91 is the product of two prime numbers. What is their sum?
A. 14
8.
D. 1,224,000
When every vertex of a regular pentagon is connected to every other vertex,
a smaller pentagon and N non-overlapping triangles are formed. What is N?
A. 5
6.
C. 824,200
Starting with 653.187, create a new number by switching the tens’ digit and the hundredths’
digit. How much greater is the larger number than the smaller number?
A. 19.998
5.
E. 58
The product of two whole numbers is 30 and their sum is 17.
What is the positive difference between these two numbers?
A. 1
4.
D. 42
Even the cast members of the musical Rent know that the number of minutes in the year 2006 is:
A. 525,600
3.
C. 32
B. $4.80
C. $5.20
D. $15.50
E. $22.60
Determine both the least common multiple of 6 and 9 and the greatest common factor of 6 and 9.
What is their sum?
A. 12
B. 21
C. 24
D. 51
E. 57
Sixth Grade Test - Excellence in Mathematics Contest - 2006
11.
Two pitchers, A and B, each contain 48 ounces of juice. Half of the juice in A is poured into B.
Then, half of the juice in B is poured into A. Once again, half of the juice in A is poured into B.
How many ounces of juice are now in pitcher A?
A. 24
12.
B. 30
C. 36
D. 42
E. 48
When you fold this pattern into a cube, which face is opposite face F?
A. A
B. B
D. D
E. E
F
C. C
A
B
C
D
E
13.
What is the median of these five numbers?
0.125
A. 0.125
14.
B. 900
B. 3
B. 12 cm2
D. 0.5
E. 0.076
C. 950
D. 1000
E. 1050
C. 5
D. 6
E. 7
C. 64 cm2
D. 96 cm2
E. 256 cm2
A number line from 0 to 5 is divided into 20 equal parts.
What is the sum of the numbers located at points A and B?
A
0
A. 6
18.
C. 0.01
0.076
The perimeter of a rectangle is 40 cm. Its width is 8 cm. What is the area of this rectangle?
A. 5 cm2
17.
B. 0.08
0.5
In the standard M/D/Y for month, day, and year, March 18, 2006 is written 3/18/06.
Note that 3*6 = 18. Including March 18, how many times in the year 2006 will M*Y = D?
A. 2
16.
0.01
What is the sum of all positive multiples of 5 less than 99?
A. 850
15.
0.08
B. 6.25
C. 6.5
B
D. 6.75
5
E. 7
A “perfect number” is a whole number such that the sum of all its divisors, not including itself,
equals itself. For example, 12 is not a perfect number because 1+2+3+4+6 = 16, does not equal
12. What is the sum of the two perfect numbers between 1 and 50? (Hint: There is a clue on the
front cover of this test!)
A. 32
B. 34
C. 36
D. 44
E. 52
Sixth Grade Test - Excellence in Mathematics Contest - 2006
19.
An “abundant number” is a whole number such that the sum of all its divisors, not including
itself, is greater than itself. For example, 12 is an abundant number because 1+2+3+4+6 = 16
which is greater than 12. Including 12, how many abundant numbers are there less than 29?
A. 1
20.
B. 2
C. 3
D. 4
E. 5
On the number line below marked with 1 cm units, an ant crawls at a constant speed of 4 cm per
minute. Starting at “5”, Aunt Antie walks left for 2 minutes; right for 6 minutes, and then left for
3 minutes. Where is Aunt Antie on the number line?
0
-5
A. -1
B. 1
5
C. 4
D. 5
E. 9
21.
City
1990
2006
A
12,500
18,500
B
8,100
11,300
C
84,600
115,000
D
32,200
39,900
E
54,000
78,000
The 1990 and 2006 populations of five cities are given in the table.
Which city had the largest percent increase in population during this time period?
A. A
22.
25.
D. D
E. E
B. 45
C. 45.5
D. 47
E. 49.5
On a Friday drive from St. Louis to Chicago, Aaron shares the driving with a friend. Before
lunch, Aaron drove 1/3 of the 180 miles covered. After lunch, Aaron drove 1/4 of the 120 miles
they had left. What fraction of the day’s trip did Aaron drive?
A. 3/10
24.
C. C
Jamaal reads an average of 32 pages per day from Monday through Friday and an average of 67
pages per day on the weekend. For each week, what is the average number of pages that Jamaal
reads per day?
A. 42
23.
B. B
B. 2/7
C. 7/12
D. 1/2
E. 2/5
Including small, medium, and large squares, what is the total
number of squares that can be traced in this diagram?
A. 10
B. 12
D. 15
E. 25
C. 13
60 cm
What is the maximum number of 4 cm by 10 cm
rectangles that can be cut from this 60 cm by 60 cm square?
A. 21
B. 36
D. 60
E. 90
C. 45
60 cm
Sixth Grade Test - Excellence in Mathematics Contest - 2006
26.
What is the maximum number of 4 inch by 4 inch by 2 inch blocks
that can be cut from a wooden cube one foot on a side?
A. 24
B. 36
D. 72
E. 108
1 foot
C. 54
1 foot
1 foot
27.
28.
What fraction of this rectangle is shaded?
A. 1/3
B. 3/8
D. 7/16
E. 9/16
C. 1/2
In a class of 20 students, these are their scores on a five-point quiz.
Quiz score
0
1
2
3
4
5
Number of students
2
0
1
5
9
3
What was the mean score on this quiz?
A. 2.5
29.
C. 2
D. 3
E. 4
B. 3/11
C. 1/4
D. 1/12
E. 3/8
B. 270o
C. 360o
D. 450o
E. 540o
B. 22.5o
C. 30o
D. 37.5o
E. 45o
For the team she coaches, Brenda buys sodas at $0.75 each and hamburgers at $1.20 each. If she
buys more hamburgers than sodas, buys at least one soda, and spends a total of $21.60 on sodas
and hamburgers, what is the total number of hamburgers and sodas she buys?
A. 21
34.
B. 1
From 10:00 am to 11:30 am, through how many degrees does the hour hand of a clock rotate?
A. 15o
33.
E. 4
From 10:00 am to 11:30 am, through how many degrees does the minute hand of a clock rotate?
A. 180o
32.
D. 3.4
Two standard 6-sided dice are rolled. What is the probability that the sum is 10, 11, or 12?
A. 1/6
31.
C. 3.2
In basketball, a player can score via 3-point shots, 2-point field goals, or 1-point free throws. If
Tonya makes seven 2-point field goals while scoring 34 points, what is the minimum number of
free throws that she has made?
A. 0
30.
B. 3
B. 22
C. 23
D. 24
E. 25
On a day in June, sunrise is 6:00 am and sunset is 9:00 pm. At what time of that day is the
number of hours past sunrise equal to twice the number of hours before sunset?
A. 11:00 am
B. 12:00 noon
C. 1:30 pm
D. 2:30 pm
E. 4:00 pm
Sixth Grade Test - Excellence in Mathematics Contest - 2006
35.
36.
You are given a cube, 10 cm on a side, and two
identical pyramids with square bases, 10-cm on a side.
You glue the two pyramids to opposite faces of
the cube so that the 10 cm squares line up.
How many edges does the solid have?
A. 8
B. 12
D. 20
E. 24
The product of three whole numbers is 48 (two of the numbers used could be the same).
What is the least possible sum of these three numbers?
A. 11
37.
39.
C. 13
D. 14
B. 80
C. 84
D. 92
Place the digits 2 through 7 in the 6 blank cells so that the sum of the
three numbers in the top row, in the bottom row, in the leftmost column,
and in the rightmost column each add to 12.
What digit is in the cell next to the cell with the “1”?
A. 2
B. 4
D. 6.
E. 7
E. 15
C. 5
E. 100
8
1
Emily, Sarah, and Andrea share a bowl of strawberries. First, Emily ate 1/3 of them. Then Sarah
ate 1/3 of the remaining strawberries. Andrea ate the last 8 strawberries. How many strawberries
did Emily eat?
A. 6
40.
B. 12
Unit squares (shown below) are used to build each pattern. The first three patterns are shown.
Not including the square hole, how many unit squares are needed to build the 10th pattern in this
sequence?
A. 76
38.
C. 16
B. 8
C. 12
D. 24
E. 48
In how many distinct ways can five 1 by 2 tiles be used to cover a 2 by 5 rectangle?
A. 5
B. 6
D. 9
E. 13
C. 8