Sixth Grade Test - Excellence in Mathematics Contest – 2011
1. When you multiply one million times one million, the answer is a “1” followed by how many zeroes?
A. 6 B. 9 C. 12 D. 15 E. 18
2. Which is the largest of the following five numbers?
A. 0.6 B.
0.28 C. 0.0759 D. 0.064 E.
0.532
3. In the movie 127 Hours , the rock climber was trapped for 127 hours. If his ordeal began at 10
AM on Saturday, when did his ordeal end?
A. Wednesday, 5 PM
D. Thursday, 7 PM
B. Thursday, 5 PM C. Wednesday, 7 PM
E. None of These
4. I had eight quarters, four dimes, and four pennies in my pocket. Using these coins, I spent exactly
$1.37. How many coins did I still have?
A. 7 B. 8 C. 9 D. 10 E. 11
5. In basketball, a player can score by making 2-point shots, 3-point shots, and 1-point for each free throw made. In a game, Prince makes five of eight 2-point shots and three of twelve 3-point shots.
In addition, he attempted 20 free throws. If he scored a total of 28 points, how many free throws did Prince make?
A. 9 B. 10 C. 11 D. 12 E. 13
6. Stefan starts a job at 2:00 pm and by 3:00 pm he has finished 3/4 of the job. At that rate, what time will he finish the job?
A. 3:10 pm B. 3:12 pm C. 3:15 pm D. 3:20 pm E. 3:24 pm
7. B, C, and D are three different numbers from this set: { –5, –4, –3, –2, –1, 0, 1, 2, 3, 4 }.
What is the largest possible value of
?
A. 14 B. 20 C. 23 D. 24 E. None of These
8. On a 75 mile drive from her house to a friend’s house, Michelle averages 60 miles per hour. If she leaves her house at 3:20 PM, what time does she arrive at her friend’s house?
A. 4:35 PM B. 4:45 PM C. 4:50 PM D. 4:55 PM E. 5:00 PM
9. For a $15.20 bill at Omi’s Pizza, you give the waitress $19.00 and say, “Keep the change”.
What percent tip did you just leave?
A. 15% B. 18% C. 20% D. 25% E. 80%

Sixth Grade Test - Excellence in Mathematics Contest – 2011
0 1
Stick #2
2 3
Stick #1
Use the number line, above, to answer Questions #10 and #11.
10. How many units long is Stick #1?
A. 2.7 B. 2.75 C. 2.8
11. How many units longer is Stick #1 than Stick #2?
A.
1
4
B.
1
8
D. 2.875
C.
3
8
D. 1.2
E. 2.9
E. 1.4
4
12. 140 tickets were sold for a student play. Adults paid $12 each and children paid $4 each. If 86 adult tickets were sold and the rest were student tickets, what was the total amount of the ticket sales?
A. $1084 B. $1200 C. $1248 D. $1376 E. $1680
13. A driveway is 12 feet wide and 80 feet long. When 18 inches of snow fell last December, how many cubic feet of snow had to be removed from the driveway?
A. 187 ft 3 B. 276 ft 3 C. 1440 ft 3 D. 2880 ft 3 E. 17,280 ft 3
14. According to the movie Facebook , Eduardo’s share of the company was reduced from 34% to
0.03%. What is 0.03% of $25 billion dollars?
A. $7.5 million B. $7500 C. $750,000 D. $75 million E. $750 million
15. This is part of a Mother Goose rhyme:
What is the total number of wives, sacks, cats, and kits that this person met?
A. 154 B. 2400 C. 2408 D. 2800 E. 2801

Sixth Grade Test - Excellence in Mathematics Contest – 2011
16. My daughter Zan was born on the N th day of March.
From your age in years, you can calculate N and therefore know Zan’s birthday.
1.
Make a 6-digit number by writing your age three times. (For example, if your teacher is 28 years old, your teacher would write 282828.)
2.
Divide your 6-digit number by 1443.
3.
Add 133 to that answer.
4.
Divide that answer by 7.
5.
From that answer, subtract your age in years. Your final answer is N.
When is Zan’s birthday?
A. March 7 B. March 12 C. March 14 D. March 19 E. March 28
17. The measure of one angle of a triangle is 12 o . The measure of each of the other angles is N o .
What is N?
A. 78 o B. 84 o C. 86 o D. 94 o E. 168 o
18. The width of a rectangle is 24 m and the area of the rectangle is 240 square meters.
What is the perimeter of this rectangle?
A. 10 m B. 34 m C. 40 m D. 68 m E. 96 m
19. How many two-digit prime numbers have a units’ digit of “ 7 ”?
A. 4 B. 5 C. 6 D. 7 E. 8
20. What is the positive difference between the mean and the median of this set of five numbers?
A. 2.4 B. 2.6 C. 3.4 D. 6.4 E. 6.6
21. In one hour of watching TV, there are 13
1
2
minutes of commercials.
What percent of one hour is that?
A. 20% B. 21.5% C. 22.5% D. 24% E. 25%
22. Exactly one of the following five numbers is a prime number. Which one is it?
A. 85 B. 86 C. 87 D. 89
23. Simplify
𝟐
𝟐
𝟑
5
𝟕
𝟓
𝟗
A.
6
.
B.
2
9
C.
1
6
D.
2
3
E. 91
E.
5
9

Sixth Grade Test - Excellence in Mathematics Contest – 2011
24. Since 1+2 = 3 ; 1+2+3 = 6 ; 1+2+3+4 = 10 ; 1+2+3+4+5 = 15…;
3, 6, 10, and 15 are examples of Triangular Numbers .
What is the smallest 3-digit Triangular Number ?
A. 101 B. 102 C. 103 D. 104 E. 105
25. How many positive integers less than a 1000 can be written using only the digits “ 0
”
and/or “ 5 ”?
A. 4 B. 5
26. 30% of 50 is what percent of 60?
C. 6 D. 7 E. 8
A. 15% B. 25% C. 50% D. 60% E. 83
1
3
%
27. Find whole numbers A and B so that A 2 + B 3 = 280 . What is the sum A+B?
E. 16 A. 12 B. 13 C. 14 D. 15
28. A teacher noticed this sign in a movie cinema in Singapore.
Using 1 inch = 2.54 cm, what is the positive difference between 2.5 feet and 78 cm?
A. 0.6 cm B. 0.7 cm C. 1.2 cm D. 1.6 cm E. 1.8 cm
29. Each vertical row of numbers and each horizontal row of numbers is either an increasing arithmetic sequence or a decreasing arithmetic sequence?
(Note: 42; 37; 32; 27 is an example of a decreasing arithmetic sequence.)
What is A + B?
A. 93
C. 99
B. 95
D. 100
43 A
E. 101
30. If x = –4, what is the largest number in the set {−𝟑𝐱 , 𝟓𝐱, 𝐱
𝟐 , 𝐱 𝟑 ,
−𝐱
𝟎.𝟐
} ?
A. –3x B. 5x C. x 2 D. x 3
71
56
E.
−𝐱
𝟎.𝟐
B 49

Sixth Grade Test - Excellence in Mathematics Contest – 2011
Use the following Rule for questions #31 and #32.
An Ulam-Collatz Sequence of integers is generated by these rules:
1.
The first term is a positive integer.
2.
If a number N in the sequence is odd, the next number is 3N + 1 .
3.
If a number N in the sequence is even, the next number is N/2 .
For example : 7; 22; 11; 34; … is the start of one possible Ulam-Collatz Sequence.
31. If the first three terms of an Ulam-Collatz Sequence are: 30; 15; 46; what is the 8 th term?
A. 52 B. 53 C. 54 D. 55 E. 56
32. The Ulam-Collatz Conjecture is that EVERY Ulam-Collatz Sequence eventually will include the repeating sequence:
… 4; 2; 1; 4; 2; 1;…
If the first three terms of an Ulam-Collatz Sequence are 24; 12; 6;… in which term does “ 1 ” first occur?
A. 9 th B. 10 th C. 11 th D. 12 th E. 13 th
Use this dart board for questions #33 and #34.
The 20 identical sections are numbered 1 through 20.
33. One dart is thrown and hits the dartboard randomly in one of the 20 regions.
What is the probability that the number hit is a multiple of 3 ?
A. 15% B. 20% C. 25%
D. 30% E. 33
1
3
%
14
11
8
16
7
9
12
5 20
1
19
3 17
2
18
4
13
6
15
10
34. In one turn, Marlene throws three darts, one at a time. To win in this turn, she must score exactly
58 points. In how many different ways can she do this?
Note: Scoring 58 with 18, 20, and then 20 is considered different from scoring 58 with 20, 18, and then 20.
A. 2 B. 4 C. 6 D. 9 E. 12

Sixth Grade Test - Excellence in Mathematics Contest – 2011
35. ABC and ADE are quarter-circles each with center A.
AC = 5 cm and CE = 7 cm. What is the area of the shaded region?
Round to the nearest tenth of a square centimeter.
A. 3.1 cm 2 B. 18.8 cm 2 C. 93.5 cm 2
D. 113.1 cm 2 E. 373.8 cm 2
D
B
A
5 C 7
36. A 16 liter mixture of fruit punch and soda is 25% soda. After 75% of the mixture is drunk, 4 liters of fruit punch and 4 liters of soda are added. What percent of the new mixture is soda?
E
Round to the nearest percent.
A. 33% B. 35% C. 40% D. 42% E. 50%
37. How many positive 3-digit even numbers can be written using only the digits “ 0 ”, “ 1 ”, and “ 2 ”?
A. 8 B. 12 C. 16 D. 18 E. 27
38. In the sequence
shown below , note that exactly two sets of consecutive digits sum to 11. 7+4 = 11 and 4+1+3+3 = 11 (Note that two such sets are allowed to overlap.)
In the following sequence, how many different sets of consecutive digits sum to 11?
A. 1 B. 2 C. 3 D. 4
39. The six faces of a 5x5x10 rectangular block of wood are painted red and then the block is cut into 250 1x1x1 unit cubes.
Of these 250 unit cubes, how many have exactly 2 faces painted red?
A. 56 B. 64 C. 68
E. 80 D. 72
40. The product of the three numbers in each row and in each column is given. Without repetition, place the numbers 1 through 9 in these nine cells to produce these six products.
What is the number in the cell marked N ?
A. 1
D. 4
B. 2
E. 6
C. 3
5
35
5
E. More than 4
N
96
10
108
54
42
160