Sixth Grade Test - Excellence in Mathematics Contest – 2010
1. A restaurant has a total of thirty-six 3-legged stools and 4-legged chairs. They have three times as
many chairs as stools. What is the total number of legs on these stools and chairs?
A. 126
B. 128
C. 130
D. 132
E. 135
2. On this cube, point A is a “vertex”, segment AB is an “edge”, and square ABCD
is a “face”. On any cube, what is the sum of the total number of vertices, edges, and faces?
A
A. 18
B. 20
D. 24
E. 26
C. 22
D

3. The first five terms of an arithmetic sequence are: 7; 11; 15; 19; 23; …
What is the 20th term?
A. 80
B. 83
C. 85
D. 87
C
E. 89
4. In a card game, Matt’s scores on each of the first five hands are +13; –10; –20; +16; –10 . At
that time, the sum of the five scores of Paul is 25. How many points is Matt behind Paul?
A. 14
B. 31
C. 34
D. 36
E. 41
5. You complete 3/5 of a job in 45 minutes. Working at the same rate, how many more minutes will
it take you to complete the job?
A. 15
B. 18
C. 27
D. 30
E. 36
D. 60
E. 75
D. 4
E. 5
6. Which of these five numbers has the largest prime factor?
A. 42
B. 45
7. How many integers are between −
A. 1
B. 2
C. 48
𝟐𝟎
𝟕
and
𝟔
𝟓
?
C. 3
8. If Gabrielle multiplies her age by 2 and then adds 8 years, it equals her Uncle Wilhelm’s age.
If Uncle Wilhelm is 42 years old, her Uncle is how many years older than Gabrielle?
A. 17
B. 21
C. 25
D. 28
E. 29
D. 200
E. 210
9. What is the sum of the first 20 positive odd numbers?
A. 400
B. 800
C. 1600
10. In one day, the display on a 24-hour digital clock displays every minute as four digits
from 00:00 to 23:59. How many times in one day does this clock show times
including only the digits “0” and/or “3”?
A. 4
B. 8
C. 10
D. 12
E. 16
Sixth Grade Test - Excellence in Mathematics Contest – 2010
Use the following table of grades to answer Questions #11 and #12.
For a class of 30 students, the table shows their
grades on their first two mathematics tests. For
example, the shaded square shows that exactly 4
students scored a C on Test #1 and a B on Test #2.
Test #2
Test #1
A
B
C
D
F
A
3
2
1
0
0
B
1
3
4
0
0
C
2
1
3
1
1
D
0
1
0
2
1
F
0
0
1
1
2
11. How many students scored a B on one of the tests but not on both tests?
A. 7
B. 8
C. 9
D. 12
E. 15
12. How many students received a higher letter grade on Test #2 than on Test #1?
A. 7
B. 8
C. 10
D. 20
E. 23
13. An automobile gas tank which holds a maximum of 24 gallons is one-fourth full.
At $2.60 per gallon, how much does it cost to fill the gas tank?
A. $15.60
B. $28.40
C. $34.20
D. $46.80
E. $62.40
14. In the seven year period 2000-2006, approximately 1.5 billion live wild animals were imported
into the United States as pets and for other purposes. On the average, approximately how many
per day were brought into the United States?
A. 590
B. 140,000
C. 590,000
D. 4 million
E. 211 million
D. 208
E. 211
15. What is the sum of the prime factors of 2010?
A. 77
B. 79
C. 80
16. The marks on this number line are equally spaced. What is the value of N?
120
A. 360
N
B. 372
C. 400
𝐍
540
D. 420
E. 456
𝟓
17. N is a positive integer and
is a reduced fraction less than .
𝟐𝟒
𝟑
What is the number of possible values of N?
A. 13
B. 14
C. 15
D. 16
E. 17
18. Using any combination of nickels, dimes, and quarters, how many different ways are there to pay
exactly 40 cents for a bag of popcorn? (For example, three nickels and one quarter is one such
combination.)
A. 3
B. 4
C. 5
D. 6
E. 7
Sixth Grade Test - Excellence in Mathematics Contest – 2010
19. If 10% of a number is 60, what is 25% of the same number?
A. 1.5
B. 24
C. 150
D. 246
E. 2400
20. M and N are positive integers such that M2 + N3 = 360. What is M+N ?
A. 14
B. 15
C. 16
D. 17
E. 18
21. A train averaged 48 miles per hour for 80 minutes and then 72 miles per hour for 105 minutes.
How many miles were travelled?
A. 175
B. 180
C. 185
D. 190
E. 195
22. In a school of 860 students, 440 are girls. One fourth of the students travel to school by bus.
300 of the boys do not ride the bus. How many of the girls ride the bus?
A. 95
B. 96
C. 100
D. 105
E. 110
23. Of a $12,000 inheritance, Bianca invested 2/3 in a Certificate of Deposit paying 2.5% annual
interest and the rest in a Bond Mutual Fund paying 4% annual interest. How much interest does
she earn in one year?
A. $360
B. $390
C. $400
D. $520
E. $780
24. In this Magic Product Square, the numbers 1 through 9,
without repetition, are placed in the nine cells. The product
of the three numbers in each row and in each column is given.
What is the number in the cell marked N?
A. 1
B. 2
D. 4
E. 6
28
135
C. 3
N
42
96
54 160
25. How many even numbers are between 11 and 99?
A. 43
B. 44
C. 45
D. 88
E. 89
26. Three candy bars are to be shared equally among five people, including Gail and Fred. Gail and
Fred each get ½ of the first candy bar. If you use part of the second candy bar to complete Fred’s
fair share, what fraction of the second candy bar do you give Fred?
A. 1/10
B. 1/5
C. 1/6
D. 1/15
E. 3/5
27. The length of a rectangle is twice its width. The perimeter of the rectangle is 42 cm.
In square centimeters, what is the area of this rectangle?
A. 49
B. 72
C. 84
D. 98
E. 392
Sixth Grade Test - Excellence in Mathematics Contest – 2010
28. What is the 200th letter in the sequence: ABRACADABRAABRACADABRA…..?
(Note: The word “abracadabra” is being repeated.)
A. A
B. B
C. C
D. D
E. R
Use the following Rule for questions #29 and #30.


A sequence of numbers is generated by this pair of rules:
If a number N in the sequence is a multiple of 3, the next number is N/3
If a number N in the sequence is not a multiple of 3, the next number is N+7
30; 10; 17; 24; _____; _____; _____;_____; _____; _____
29. If the first four terms of a sequence are 30; 10; 17; 24;…, what is the 10th term?
A. 11
B. 12
C. 13
D. 14
E. 15
30. If the first four terms of a sequence are 30; 10; 17; 24;…, what is the 2010th term?
A. 1
B. 5
C. 8
D. 11
E. 15
31. The sum of the dates of the four Saturdays in December is 58.
What is the sum of the dates of the five Thursdays in the same month?
A. 75
B. 77
C. 78
32. A standard-sized 8.5-inch by 11-inch rectangular piece
of paper is cut into 8 squares as shown. What is the area
in square inches of one of the two smallest squares?
A. 0.25
B. 0.5
D. 2
E. 2.5
D. 80
E. 85
8.5
inches
C. 1
11 inches
33. The circumference of a circle is 20 cm. Rounded to the nearest tenth of a square centimeter, what
is the area of the circle?
A. 15.9
B. 18.8
C. 27.2
D. 31.8
E. 127.3
34. Among the fourteen members of a basketball team, ten have cell phones and four do not. For
Christmas, each person with a cell phone sends a text message to everyone else with a cell phone
and sends a card to the others. Each person without a cell phone sends a card to everyone (except
to himself or herself, of course). How many cards are sent?
A. 46
B. 52
C. 86
D. 92
E. 96
Sixth Grade Test - Excellence in Mathematics Contest – 2010
35. Chuck collects American paper money with 8-digit serial numbers with the pattern:
ABBAABBA where A and B are two different digits 0 through 9 inclusive.
For example: 68866886 and 07700770 fit this pattern but 55555555 does not.
How many different 8-digit serial numbers fit this pattern?
A. 90
B. 100
C. 256
D. 65,610,000
E. 100,000,000
10
–12
36. In this Magic Square, the sums of the four numbers in each row, in
each column, and in each long diagonal are all equal.
What is the sum of the eight numbers in the eight blank cells?
4
0
–10
–14
A. –66
B. –74
C. –84
D. –94
2
6
E. –100
37. Darryl has a large supply of two sizes of square tiles: 4 inches on a side and 8 inches on a side.
What is the least number of tiles needed to tile a 28 inch by 36 inch rectangle? (No tiles can be
broken; tiles cannot overlap; and no tiles can extend beyond the 28 inch by 36 inch rectangle.)
A. 16
B. 26
C. 27
D. 28
E. 30
38. The number pattern and the shading in the table below continues ‘forever’.
1
2
4
5
7
8
10
11
13
14
16
17
19
20
22
23
25
26
28
29
3
6
9
12
15
18
21
24
27
30
The cell with the number 444 will have the same shading
as which of the following cells: A, B, C, D, or E?
A
B
C
D
E
39. It is 6:00 PM Tuesday in San Francisco when it is 2:00 AM Wednesday in London. Zan at the
San Francisco Google office and Alec at the London Google office are scheduled to work together
on a project on their computers. Zan contacts Alec at 7:40 AM San Francisco time and they begin
working. They work together until Alec shuts down his computer at 7:15 PM London time. For
how many minutes did they work together?
A. 35
B. 95
C. 155
D. 215
E. 275
40. One-Pile Nim is a two-person game. Pattie and Malik take turns. There is one pile of chips. On
each turn, a player takes 1, 2, 3, 4, or 5 chips from the pile. The player to take the last chip wins.
At one point of the game, it is Pattie’s turn and there are 20 chips remaining in the pile. If both
players make their best plays, there is only one winning play for Pattie. What is it?
A. Take 1 chip
B. Take 2 chips
C. Take 3 chips
D. Take 4 chips
E. Take 5 chips