Seventh Grade Test - Excellence in Mathematics Contest - 2007
1.
The title of this competition is the “The 10th Prime Contest”. What is the 10th prime number?
A. 23
2.
C. $5.30
D. $5.40
E. $5.50
B. 1887
C. 1857
D. 1863
E. 1867
B. 2.4
C. 2.8
D. 3
E. 3.2
B. 103
C. 106
D. 109
E. 1012
B. 36o
C. 40o
D. 42o
E. 45o
B. 99.5
C. 100
D. 100.5
E. 101
B. x2
C. x3
D. x4
E. x5
The Davis’ house had 1200 square feet of living space before they added-on a 20 foot by 15 foot
rectangular room. By what percent had their amount of living space increased?
A. 2.9%
11.
B. $5.20
If x = –0.5, which is the least of these five numbers?
A. x
10.
E. 375
What is the average of the first 200 positive integers?
A. 99
9.
D. 300
At 1:20 PM, a clock’s hour hand is how many degrees from a vertical position?
A. 30o
8.
C. 225
MB2
Let T=1 trillion, H= 1 thousand, M = 1 million, and B = 1 billion. What is the value of
?
TH 2
A. 1
7.
B. 200
The weight of a box with 30 identical chocolates is 21 ounces. When 6 chocolates are removed
and eaten, the weight of the box and remaining chocolates is 17.4 ounces. In ounces, what is the
weight of the empty box?
A. 2.2
6.
E. 37
“Four score and seven years” after 1776, President Lincoln gave his famous speech at the
Gettysburg battlefield in Pennsylvania. Given that a ‘score’ represents 20 years, in what year was
the Gettysburg Address given?
A. 1787
5.
D. 31
A 2.5 pound fish costs $8.50. At the same unit cost, how much does a 1.5 pound fish cost?
A. $5.10
4.
C. 29
The total value of 750 dimes equals the total value of how many quarters?
A. 150
3.
B. 27
B. 10%
C. 12.5%
D. 20%
E. 25%
A pyramid has a square base and four equilateral triangles as its faces. How many edges does it
have?
A. 6
B. 8
C. 10
D. 12
E. 16
Seventh Grade Test - Excellence in Mathematics Contest - 2007
12.
In feet and inches, the heights of five students are:
49; 411; 47; 54; 47
In inches, what is the positive difference between the mean and the median of these five heights?
A.
13.
0.6
1
D.
1.4
E.
3
B. 6
C. 7
D. 8
E. 9
B. 35%
E. 53%
C. 38%
How many different numbers can be expressed as the sum of exactly three different numbers
from the set {1, 2, 3, 9, 10} ?
A. 6
16.
C.
A target consists of four concentric squares of side
lengths 1, 3, 5, and 7. What per cent of the target is shaded?
Round to the nearest percent.
A. 33%
D. 43%
15.
0.8
How many two-digit prime numbers (for example, 23) can be formed by selecting two digits
(possibly the same) from the set: {1, 2, 3, 4, 5, 6}?
A. 5
14.
B.
B. 7
C. 8
D. 9
E. 10
In 2006, poor Pluto was demoted and is no longer classified as a “planet”. Assume that Pluto and
the Earth are both spheres and that the diameter of Pluto is 2296 km while the diameter of the
Earth is 12756 km. The volume of a sphere of radius R is given by: V 
4
R 3 .
3
Approximately what is the ratio of the volume of Earth to the volume of Pluto?
A. 5.6
17.
C. 171
D. 243
E. 1321
Find the largest 3-digit multiple of 9 which does not contain the digit 9.
What is the product of its three digits?
A. 72
18.
B. 31
3
B. 75
C. 76
D. 128
E. 256
N
N
N
 4 ; that is,
is between 3 and 4. If
is a proper reduced fraction, what is the sum
12
12
12
of all possible values of N?
A. 84
19.
B. 168
C. 184
D. 252
E. 462
With exactly 8 coins, each a penny, a nickel, or a dime, their total CANNOT be:
A. 25¢
B. 26¢
C. 27¢
D. 28¢
E. 29¢
Seventh Grade Test - Excellence in Mathematics Contest - 2007
20.
If the United States population of 302 million grows by 0.9% in 2007, what would be the average
daily increase in population in 2007? Select the closest answer.
A. 7,447
21.
 and
If 6 ( 2
A. –7
26.
B. 32
B. 11
B. 56.9
E. 66
B. 15
28.
D. 34
C. 12
E. 35
D. 13
E. 14
20 cm
C. 57.4
C
C. 26
are two distinct operations from the set:
D. 37
B. –4
C. –1
E. 87
, , ,  .
4)  1 , what is the value of (6   2)
4?
D. 0
E. 1
The sum of three consecutive prime numbers is:
A. Always an even number
C. Always a multiple of 3
E. None of the above
24.
C. 33
Sharon’s age is 11 years more than a perfect cube and 11 years less than a perfect square. What
is the least number of years until her age is a perfect cube?
A. 11
25.
E. 7.4
The area of right triangle ABC is 130 square centimeters. To the
B
nearest tenth of a centimeter, what is the perimeter of triangle ABC?
A. 48.2
D. 61.3
24.
D. 74
The product of three whole numbers is 36 (two of the numbers used could be the same).
What is the least possible sum of these three numbers?
A. 10
23.
C. 745
How many odd numbers between 0 and 100 are not multiples of 3?
A. 17
22.
B. 74,466
B. Always an odd number
D. Never a multiple of 3
From a solid wooden cube of side length 2, a tetrahedron with slant
lengths 1 (as shown) is cut from EACH of the eight vertices of
the cube. One such tetrahedron is shown in the diagram.
How many faces does the remaining solid have?
A. 6
B. 10
D. 14
E. 16
C. 112
1
1
1
1
With 48 m of fence, Matt enclosed a square corral for his horse.
With his 48 m of fence, Nick built a rectangular corral which was twice as long as wide.
What is the ratio of the area of Matt’s corral to the area of Nick’s corral?
A. 1:1
B. 2:1
C. 3:2
D. 7:6
E. 9:8
A
Seventh Grade Test - Excellence in Mathematics Contest - 2007
29.
30.
31.
32.
Evaluate:
100!
95!8!
D. 21,286,650
E. 1,129,312,800
A. 5/9
B. 2/3
D. 8/9
E. 1
C. 16,448,350
A
B
3
1
C. 7/9
4
2
6
5
In square units, what is the area of this triangle?
A. 25.5
B. 26
D. 27
E. 28
C. 26.5
In 1990, the average age of Tad and his older sister was 6. In 2002, the average age of Tad, his
older sister, and their twin brothers was 13. In what year were the twin brothers born?
B. 1994
C. 1998
D. 1999
E. 2000
On February 7, Julia turned 2N years old and her son Kristof turned N2 years old. Kristof was
born when Julia was 28 years old. How many years ago was the sum of their ages 80?
A. 6
34.
B. 4,460,800
Two fair spinners are divided into thirds and labeled as shown.
If each spinner is spun once, what is the probability
that Spinner B shows the larger number?
A. 1993
33.
A. 224,070
B. 8
C. 10
D. 12
E. 20
The target shown is composed of two concentric circles. The radius
of the larger circle is 50. The areas of the two shaded regions are equal.
To the nearest tenth of a centimeter, what is the radius of the smaller circle?
A. 25
B. 33.3
D. 35.4
E. 36.2
C. 34.2
35.
0
A
2
B
3
On this number line, what is the sum A+B?
A. 5/12
B. 1/2
C. 2/3
D. 1/3
E. 7/12
Seventh Grade Test - Excellence in Mathematics Contest - 2007
36.
37.
In this addition problem, each letter represents a different digit from 0 through 9.
Compute the sum L+I+V.
A. 13
B. 15
D. 17
E. 20
L
I
L
+
I
V
I
L
L
Mom turned 90 on Friday, June 2, 2006. On what day of the week was she born?
A. Sunday
38.
C. 16
B. Monday
C. Thursday
D. Friday
E. Saturday
Nine circles with radius 1 cm are inscribed in a square. A bug crawls
from A to B, staying on the sides of the square and on the circumferences
of the circles. One possible path is shown. If the bug always travels to the
right and/or upward, how many distinct paths are possible from A to B?
A. 6
B. 8
D. 16
E. 20
B
C. 12
A
39.
The first four elements of a sequence are: 7, 11, 4, –7,… Each new element is obtained by
subtracting the 2nd to last element from the last element. For example, the 4th element is –7
because: 4 – 11 = –7. What is the 2007th element of this sequence?
A. 4
40.
B. –4
C. 7
In this Magic Square, the sum of the three numbers
in each row and in each column is the same.
What is the value of B–C?
A. 5
B. –5
D. –9
E. Cannot be determined
C. 9
D. –7
E. –11
A
B
8
B
13
–3
E
8C
D
F