Seventh Grade Test - Excellence in Mathematics Contest – 2011
1. 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
B. Thursday, 5 PM
D. Thursday, 7 PM
E. None of These
C. Wednesday, 7 PM
2. 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
3. How many two-digit prime numbers have a units’ digit of “7”?
A. 4
B. 5
C. 6
D. 7
E. 8
4. This is part of a Mother Goose rhyme:
As I was going to St. Ives, I met a man with seven wives;
Every wife had seven sacks; Every sack had seven cats;
Every cat had seven kits.
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
5. In this design, ACEG is a square and each of the four triangles is equilateral.
What is the measure of the marked angle BCD?
o
o
A.
90
B. 120
D.
150o
E. 165o
C. 145
B
H
D
G
2
3
B.
12−16
9−12
C.
7
1−3
D.
−24
18
E
F
6. Which one of these five expressions is not equal to the other four expressions?
A. −2 +
C
A
o
E.
1−5
4−1
7. On a multi-day bike ride across Missouri, a cyclist leaves Wentzville at 7:00 AM and averages 18
mph. At 10:00 AM, his support crew leaves Wentzville in a van along the same route and they
average 52 mph. At 11:30 AM, how many miles is the cyclist still ahead of the support crew?
A. 3 miles
B. 5 miles
C. 8 miles
D. 10 miles
E. 12 miles
8. 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 𝐁 ∗ 𝐂 − 𝐃 ?
A.
14
B. 20
C. 23
D. 24
E.
None of These
Seventh Grade Test - Excellence in Mathematics Contest – 2011
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%
10. 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 ft3
B. 276 ft3
C. 1440 ft3
D. 2880 ft3
E. 17,280 ft3
11. 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
12. 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
13. 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
14. What is the sum of the square root of 25 and the square of 64?
A. 13
B. 633
C. 1936
D. 4101
15. If x = –4, what is the largest number in the set {−𝟑𝐱 , 𝟓𝐱, 𝐱 𝟐 , 𝐱 𝟑 ,
A. –3x
B. 5x
C. x2
−𝐱
}
𝟎.𝟐
E.
4721
?
D. x3
E.
−𝐱
𝟎.𝟐
16. My daughter Zan was born on the Nth 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
Seventh Grade Test - Excellence in Mathematics Contest – 2011
17. The measure of one angle of a triangle is 12o. The measure of each of the other angles is No.
What is N?
A. 78o
B. 84o
C. 86o
D. 94o
E. 168o
18. What is the positive difference between the mean and the median of this set of five numbers?
{𝟗𝟖,
A. 2.4
B. 2.6
𝟕𝟓,
𝟖𝟖,
C. 3.4
𝟕𝟗,
𝟔𝟖}
D. 6.4
E. 6.6
Use the following Rule for questions #19 and #20.
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.
19. If the first three terms of an Ulam-Collatz Sequence are: 30; 15; 46; what is the 8th term?
A. 52
B. 53
C. 54
D. 55
E. 56
20. 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. 9th
B. 10th
C. 11th
D. 12th
E. 13th
1
21. In one hour of watching TV, there are 13 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. 4567
B. 2,345
C. 456
D. 567
E. 161
Seventh Grade Test - Excellence in Mathematics Contest – 2011
𝟓
𝟗
𝟐
𝟐
𝟑
𝟕
23. Simplify
A. 2
24.
5
6
.
B. 2
2
9
C. 2
1
D.
6
2
23
E.
5
29
A teacher noticed this sign in a movie cinema in Singapore.
Children under 2.5 feet or under
78 cm are admitted free.
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
25. How many positive integers less than a 1000 can be written using only the digits “0” and/or “5”?
A. 4
B. 5
C. 6
D. 7
E. 8
C. 120%
D. 124%
E. 125%
26. 30% of 50 is what percent of 12?
A.
50%
B. 80%
27. Find positive integers A and B so that A2 + 2B2 = 2011. What is the sum A+B?
A. 48
B. 49
C. 50
D. 51
E. 52
28. Two congruent, over-lapping circles of radius 12 cm are
inscribed in a rectangle. If the centers of the circles are 4 cm apart,
what is the area of the rectangle?
A. 288 cm2
B. 480 cm2
C. 576 cm2
D. 672 cm2
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.)
E. 768 cm2
71
B
What is A + B?
56
A.
93
B. 95
C.
99
D. 100
E.
101
43
A
49
Seventh Grade Test - Excellence in Mathematics Contest – 2011
30. 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?
Round to the nearest percent.
A. 33%
B. 35%
C. 40%
D. 42%
1.6 cm2
B. 8.5 cm2
C. 11.8 cm2
D
A
31. AB and DE are arcs of circles each with center C.
CB = 6 cm, BE = 3 cm, and the measure of angle C is 30o.
What is the area of the shaded region?
Round to the nearest tenth of a square centimeter.
A.
E. 50%
C
B
D. 28.1 cm2
E
E. 47.1 cm2
32. In the sequence 𝟐𝟏𝟓𝟕𝟒𝟏𝟑𝟑𝟑𝟒 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.)
𝟐𝟏𝟓𝟕𝟒𝟏𝟑𝟑𝟑𝟒 𝑎𝑛𝑑 𝟐𝟏𝟓𝟕𝟒𝟏𝟑𝟑𝟑𝟒
In the following sequence, how many sets of consecutive digits sum to 11?
𝟏𝟒𝟓𝟑𝟏𝟑𝟐𝟐𝟕𝟑𝟖𝟏𝟐𝟗𝟔𝟐𝟓
A.
Fewer than 3
B. 3
C. 4
D. 5
E. More than 5
Use this dart board for questions #33 and #34.
12 5 20
9
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?
1
18
14
4
11
13
8
6
16
A. 15%
B. 20%
D. 30%
1
33 3
E.
C. 25%
10
7
15
19
%
3 17 2
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
35. In the 120 mile drive from St. Louis to Columbia, a driver averaged 64 miles per hour from St.
Louis to Wentzville and then 74 miles per hour from Wentzville to Columbia. Wentzville is onethird of the way from St. Louis to Columbia. On the drive from St. Louis to Columbia, what was
the driver’s average speed? Round to the nearest tenth of a mile per hour.
A.
69.0 mph
B. 69.8 mph
C. 70.0 mph
D. 70.3 mph
E. 70.7 mph
Seventh Grade Test - Excellence in Mathematics Contest – 2011
36. How many positive 4-digit numbers that are multiples of 4 can be written using only the digits
“0”, “1”, and “2”?
A. 12
B. 18
C. 36
D. 54
E. 81
37. According to the latest Official Scrabble Players’ Dictionary, 101 different two-letter words are
permitted while playing Scrabble. Of all two-letter combinations possible in the English language
(including double letters such as MM which is permitted and XX which is not permitted), what
percent are permitted words in Scrabble? Round to the nearest tenth of one percent.
A.
9.8%
B. 12.5%
C. 14.9%
D. 15.5%
E. 31.1%
38. 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.
54
N
What is the number in the cell marked N?
A. 1
B. 2
D. 4
E. 6
42
160
C. 3
35
96
108
39. N is a whole number greater than 2. The six faces of a 5x5xN block of wood are painted red and
then the block cut into 25N 1x1x1 unit cubes. If exactly 92 unit cubes have exactly 2 faces
painted red, what is N?
A. 13
B. 16
C. 17
D. 19
E. 23
40. Three-Pile Nim is a two-person game. Pattie and Malik take turns. There are three piles of chips.
On each turn, a player takes one or more chips from any ONE pile. The player to take the last
chip wins.
At one point of the game, there are 1 chip; 2 chips; and 6 chips remaining in the three piles.
It is Malik’s turn. If both players make their best plays, there is only one winning play for Malik.
What is it?
A. Take 1 chip from the 6-chip pile
C. Take 3 chips from the 6-chip pile
E. Take 1 chip from the 1-chip pile
B. Take 2 chips from the 6-chip pile
D. Take 1 chip from the 2-chip pile