Seventh Grade Test - Excellence in Mathematics Contest - 2002
1.
Misha left $6.00 on the table for a lunch which cost $4.80. What percent tip did he leave?
A.
2.
E.
25%
0.04
B.
0.038
C.
0.008
D.
0.00592
E.
0.002002
1 minute, 40 sec.
2 minutes, 50 sec.
B.
E.
1 minute, 50 sec.
3 minutes, 20 sec
C.
2 minutes, 30 sec.
$2
B.
$4
C.
$5
D.
$7.50
E.
$10
7:20
B.
8:00
C.
8:40
D.
9:20
E.
9:40
33
B.
43
C.
103
D.
152
E.
1003
47.9%
B.
48.3%
C.
48.5%
D.
48.7%
E.
49.0%
By putting $1.80 worth of gas in his Ford Ranger, the gas tank needle moves from 1/4 full to 3/8 full.
What additional amount must Ben pay to finish filling the gas the tank? (Assume that the needle is
always accurate.)
A.
9.
20%
In the 2002 US House of Representatives, there are 212 Democrats, 221 Republicans, and 2
Independents. What percent of these representatives are Democrats?
A.
8.
D.
What is the sum of all prime factors of 2002?
A.
7.
15%
A watch loses 10 minutes per day. At noon Saturday, it is set to the correct time. Exactly four weeks
later, at noon Saturday, what time will the watch read?
A.
6.
C.
The number of nickels in two dollars is the same as the number of quarters in how many dollars?
A.
5.
12%
A plane is cruising at 3,000 feet. If it begins to descend at a rate of 12 feet per second, how long will
it take to reach 1,200 feet?
A.
D.
4.
B.
Which of the following numbers is closest to zero?
A.
3.
10%
$5.40
B.
$9.00
C.
$9.90
D.
$10.80
E.
$14.40
60 meters of wire weigh 0.8 kg. How many meters of this wire would weigh 2 kg?
A.
24
B.
90
C.
120
-1-
D.
140
E.
150
Seventh Grade Test - Excellence in Mathematics Contest - 2002
10.
The marks on this number line are equally spaced. What is the length of line segment PQ?
Q
P
-4
A.
11.
2
-3
-2
B.
-1
7
1
3
0
0
1
C.
2
7
2
3
The bar graph indicates the number of boys and girls
who chose pizza or sandwiches for lunch.
What percent of the students chose pizza?
Round your answer to the nearest percent.
A.
73%
B.
75%
C.
77%
D.
79%
E.
88%
Pizza:
3
4
D.
8
1
3
200
150
100
Sandwiches:
50
Boys
Girls
What is the sum of one-fourth of 24 and one-fourth percent of 24?
A.
13.
E.
8
0
12.
5
6.06
B.
6.6
C.
6.96
D.
8.4
E.
12
The dimensions of a rectangular box are given.
Ross uses duct tape to secure the box, as shown.
Each of the three wrappings extends completely around
the box and there is no overlap at the ends of each wrap.
How many meters of duct tape are required?
A.
5.8
B.
7.4
D.
8.6
E.
9.0
C.
0.5 m
7.8
0.8 m
0.6 m
14.
When written, how many zeroes are in the number “One hundred billion, twenty thousand”?
A.
15.
7
B.
9
C.
10
D.
11
Each triangle in the diagram is an equilateral triangle. Each
smaller triangle is formed by joining the midpoints of the sides of
a larger triangle. What fraction of the largest triangle is shaded?
A.
1/4
B.
15/64
D.
3/16
E.
7/32
C.
1/3
-2-
E.
13
Seventh Grade Test - Excellence in Mathematics Contest - 2002
16.
X and Y are whole numbers such that X2 + Y2 = 208. What is the product XY?
A.
17.
100
D.
108
E.
144
2002
B.
3992
C.
3996
D.
4004
E.
20,020
6
B.
8
C.
10
D.
12
E.
16
72
B.
96
C.
108
D.
120
E.
180
2002 squares, each with area 36 square centimeters, are placed next to each other in one row to form a
rectangle. What is the number of centimeters in the perimeter of this rectangle?
A.
21.
C.
Five squares, each with area 36 square centimeters, are placed next to each other in one row to form a
rectangle. What is the number of centimeters in the perimeter of this rectangle?
A.
20.
96
Let S equal the number of five-pointed stars on the front cover of this test. This number S is a factor
of 2002  N , where N is a whole number. What is the smallest possible value of N?
A.
19.
B.
Leonora thinks of a secret number. In this sequence: she subtracts 5, multiplies by 5, adds 5, and then
divides by 5 to get 2002 as her answer. Don thinks of a secret number. In this sequence: he adds 5,
multiplies by 5, subtracts 5, and then divides by 5 to get 2002 as his answer.
What is the sum of their two secret numbers?
A.
18.
70
24,012
B.
24,018
C.
24,024
D.
24,030
E.
24,036
2.9
E.
3.0
The marks on this number line are evenly spaced.
P
2
5
What number does the mark at point P represent?
A.
22.
2.3
B.
2.6
C.
2.75
D.
Two circles share center C. Point B is on the smaller circle
and point A is on the larger circle. CB = 6 cm and BA = 10 cm.
What is the area, in square centimeters, of the doughnut shaped
region between the two circles?
Round your answer to the nearest whole number.
A.
63
B.
314
D.
220
E.
691
C.
201
-3-
C
B
A
Seventh Grade Test - Excellence in Mathematics Contest - 2002
23.
A right triangle has a hypotenuse of length 35 cm and one leg of length 21 cm.
In square centimeters, what is the area of this triangle?
A.
24.
D.
588
E.
735
4
B. 5
C. 6
D.
8
E.
9
0.04
B.
0.42
C.
0.52
D.
0.64
E.
0.91
2/9
B.
5/18
C.
5/36
D.
1/9
E.
1/6
64
B.
80
C.
96
D.
128
E.
144
131
E.
180
What is the sum of all of the prime numbers between 40 and 50?
A.
29.
367.5
The length of a rectangle is twice its width. The perimeter of the rectangle is 48 cm. In square
centimeters, what is the area of the rectangle?
A.
28.
C.
Two standard six-sided dice are rolled. What is the probability that the product of the two numbers is
20 or larger?
A.
27.
294
In professional baseball, the distance from the pitching mound to home plate is 60 feet, 6 inches. How
many seconds does it take a Roger Clemens’ 98 mile per hour fast ball to arrive at home plate? Round
your answer to the nearest hundredth of a second. (There are 5280 feet in one mile.)
A.
26.
B.
How many triangles (of any size) can be found in the diagram shown?
A.
25.
84
84
B.
88
C.
90
D.
On Monday, all 435 members of the US Congress voted and Proposition PI3714 was defeated.
Another vote was held on Tuesday. Thirty-two Congressmen switched their votes from “No” to
“Yes”. Five Congressmen switched their votes from “Yes” to “No”. Of the 435 votes on Tuesday,
there were 7 more “Yes” votes than “No” votes. How many more “No” votes than “Yes” votes were
there on Monday?
A.
25
B.
29
C.
34
-4-
D.
35
E.
47
Seventh Grade Test - Excellence in Mathematics Contest - 2002
30.
In centimeters, the length of each side of a triangle is a whole number. The perimeter of the triangle is
8 centimeters. How many different (non-congruent) triangles meet this criteria?
A.
31.
D.
Three
6
B.
10
C.
12
D.
15
E.
More than three
60
60
60
100
100
100
E.
24
15
B.
20
C.
21
D.
30
E.
36
35
B.
60
C.
65
D.
70
E.
78
80%
B.
81%
C.
82%
D.
90%
E.
95%
Use four distinct digits to form a four-digit number which does not end in the digit “0”. Reverse those
four digits to write a second four-digit number. What is the maximum possible positive difference
between those two numbers?
A.
36.
Two
When Rick phones his daughter Suzanne from work, he must press 20 buttons. If he has a 99%
probability of pressing each button correctly, what is the probability that he presses all 20 buttons
correctly? Round to the nearest percent.
A.
35.
C.
A 2 cm cube is stacked (and glued) on top of a 3 cm cube. In square centimeters, what is the surface
area of this stack (including the bottom face)?
A.
34.
One
A person’s “monogram” is his or her three initials, in order: first initial, second initial, and third initial
(for example, RDA). Mr. and Mrs. Gauss wish to name their new baby so that her three-letter
monogram is in alphabetical order with no letters repeated. For example, BEG or EFG. If the third
initial is G for Gauss, how many different monograms are possible?
A.
33.
B.
An actor’s dressing room mirror is lit by three 60 Watt bulbs
and three 100 Watt bulbs. Any combination of these six bulbs
can be turned on. When three or more bulbs are turned on,
HOW MANY different levels of illumination are possible?
(For example, 180 Watts (60+60+60) and
420 Watts (60+60+100+100+100) are each possible.)
A.
32.
None
3087
B.
8532
C.
8622
D.
8712
E.
8802
There is only one pair of whole numbers whose product is 320,000 where neither factor contains the
digit “0”. What is the sum of these two numbers?
A.
1137
B.
1200
C.
1444
-5-
D.
1635
E.
10,032
Seventh Grade Test - Excellence in Mathematics Contest - 2002
37.
38.
A rectangle ABCD is inscribed in a circle of radius 8 cm. BC = 6 cm.
What is the area, in square centimeters, of the shaded region?
A
Round your answer to the nearest whole number.
A.
105
B.
112
D.
124
E.
157
C.
117
B
D
C
Place the nine integers: -4, -3, -2, -1, 0, 1, 2, 3, 4 into these nine boxes (without repetition) so that the
sum of the integers in any two consecutive boxes is a perfect square number.
What number is in the middle square?
A.
39.
40.
-3
B.
-2
C.
0
D.
1
E.
3
The numbers 1 through 16 are entered into a square grid with four rows
and four columns. The sum of the numbers in each of the columns is the same.
What is that sum?
A.
30
B.
31
C.
32
D.
34
E.
More than one answer is possible.
The new census taker has been told that Ms. Pimath always answers truthfully, but not always clearly.
With great fear, the census taker knocks on Ms. Pimath’s door. When she opens the door, he asks,
“How many children do you have?” She responds, “Three.” He continues, “What are their ages”?
Ms. Pimath answers, “The product of their ages is 90 and the sum of their ages is the address of my
house.” The census taker looks at the house number, and complains, “That’s not enough information.
Do you have a one-year old child?” When Ms. Pimath responds truthfully, he says with relief, “Thank
you, now I know their ages.”
What is Ms. Pimath’s house number? (All of the ages are whole numbers.)
A.
14
B.
16
C.
20
-6-
D.
22
E.
24