Seventh Grade Test - Excellence in Mathematics Contest - 2004
1. The bar graph shows the grades of
students from two Algebra I classes.
What percent of these students
received an A, B, or C?
A. 70%B. 75%
C. 77.5%D. 80%
E. 82.5%
2.When her father retired from farming, Jeanne inherited of a 1200-acre farm and of an 800-acre farm. What fraction of the total area of the two farms did she inherit?
A. B. C. D. E.
3.Kilroy incorrectly converted 4.35 minutes to 4 minutes and 35 seconds.
By how many seconds was he in error?
A. 0B. 2C. 5D. 14E. 15
4.What fraction of this square is shaded?
A. B. C.
D. E.
5.How many hundreds are there in one trillion?
A. 10 million B. 100 million C. 1000 million D. 10 billion E. 100 billion
6.Write any two-digit whole number. Create a four-digit number by writing one “9” in front of your number and one “9” behind your number. Add your two-digit and four-digit numbers and divide the sum by 11. From that answer, subtract your original two-digit number and then divide that result by 21.
What is the final answer?
A. 17B. 25 C. 39D. 52E. None of these
7. What is the product of the 9th and 10th prime numbers?
A. 323B. 551C. 621D. 667E. 713
8.Evaluate .
A. B. C. D. E.
9.To attend Zan’s graduation from Williams College, Rick drove of the 1260-mile drive on Monday and 60% of the remaining distance on Tuesday. To reach Williams College on Wednesday, how many miles must Rick drive?
A. 84B. 168C. 252D. 336E. 504
10.In a 10-kilometer race, a runner averaged 3.5 minutes per km for the first 2 kilometers. She crossed the finish line with a total time of 41 minutes. For the final 8 km, how many minutes per km did she average?
A. 3.5B. 3.75C. 4D. 4.25E. 4.5
11. Create seven equations (three horizontal and four vertical)
by placing any one of the four basic operations:
in each of the ten blank boxes.
If the value of each symbol is:
$1 for +; $2 for - ; $4 for ; and $8 for;
what is the total value of the ten symbols used?
A. $28B. $36C. $37D. $40E. $47
12.An equilateral triangle and a square have equal perimeters. If the length of one side of the triangle is 14 cm, what is the area in square centimeters of the square?
A. 42B. 56C. 100.25D. 110.25E. 196
13. The colors of the five rings shown are Blue, Green, Red, Purple, and Yellow,
not necessarily in that order. Given:
- The Blue ring does not intersect the Green Ring
- The Purple ring intersects only the Blue Ring
- The Red ring is to the right of the Green Ring
and is on the same horizontal level as the Green Ring
Which ring is colored Yellow?
A. 1B. 2 C. 3D. 4E. 5
14.The Congressional Budget Office projects that total US debt will increase from 6.2 trillion dollars in 2002 to 8.9 trillion dollars in 2014. What is the projected average annual increase in debt for this 12-year period?
A. $22.5 billion B. $225 billion C. $2,250 billion D. $22.5 million E. $225 million
15.Use the four digits 1, 2, 3, and 4 (without repetition) to make two two-digit
numbers whose product as is large as possible – call that product L.
Repeat the process, but this time make the product of the two two-digit
numbers as small as possible – call that product S.
What is the difference L-S?
A. 960B. 970C. 980D. 990E. 1000
16.A positive integer less than or equal to 50 is randomly selected. What is the probability that the number selected is a multiple of 5 but not a multiple of 3?
A. 10%B. 14%C. 16%D. 18%E. 20%
17.A square has sides of 20 cm. As shown, two congruent circles are tangent to each other and are tangent to the square. In square centimeters, what is the area of the shaded region outside the circles? Round to the nearest tenth.
A. 85.8B. 242.9C. 289.4D. 321.5E. 337.2
18.At Perry’s Produce Packers, each parer pares a pair of pears every 6 minutes.
How many pears do two sets of triplets pare in a pair of hours?
A. 60B. 120C. 160D. 240E. 480
19.On this number line, which one of these five dots is closest to ?
A. UB. VC. WD. XE. Y
20.If , determine the sum of these three numbers: ; ; and .
A. –140B. –120C. –20D. 60E. 80
21.How many whole numbers are between and ?
A. 16B. 17C. 42D. 43E. 716
22.When this network of six squares is folded into a cube,
what is the sum of the numbers on the three faces which include vertex V?
A. 19 B. 25 C. 37 D. 41 E. 49
23.Evaluate
A. 2B. 1C. 0.5D. 0.25E. 0.125
24.A bag contains only blue marbles and green marbles. There are 60 green marbles in the bag. If one marble is drawn at random from the bag, the probability it is blue is 60%. How many blue marbles are in the bag?
A. 36B. 72C. 90D. 100E. 120
25.If x2 + y2 = 392 and x and y are positive integers, what is the sum x+y?
A. 39B. 43C. 47D. 51E. 55
26.In the last time trial on the way to victory in the 2003 Tour de France, Lance Armstrong rode 30.4 miles in 54 minutes and 19 seconds. To the nearest tenth, what was his average speed in miles per hour?
A. 24.7B. 26.4C. 28.9D. 31.2E. 33.6
27.Six cups numbered 1 through 6 must be placed on the six squares
labeled 1 through 6, one per square, according to these rules:
- The number on a cup never matches the number in the square
- Cup #3 is on a square adjacent to and right of Cup #1
- Cup #6 is on a square adjacent to and below Cup #4
According to these rules, Cup #2 must be placed in which square?
A. 1B. 3C. 4D. 5E. 6
28.Fortunately, Big Guy stayed awake long enough for me
to complete this sketch.
How many triangles are in this drawing of Big Guy?
A. 12 B. 14 C. 15 D. 16 E. 18
29.If you write out the natural numbers one, two, three, four, five, … , and stop when you get to sixty, how many times have you written the letter “f”?
A. 32B. 33C. 41D. 42E. 43
30.The edges of a cube are each 10 cm. All of the edges of a cube are reassembled to form a square. In square centimeters, compute the difference: (Area of square) – (Surface area of cube).
A. –200B. 0C. 300D. 400E. 500
31.Given:
What is the least positive difference between two distinct numbers from set S?
A. B. C. D. E.
32.The arithmetic mean of ten distinct positive integers is 10.
What is the greatest possible number in the set?
A. 51B. 55C. 66D. 82E. 91
33.In this triangle of six numbers, the value of each number in row two
and in row three equals the positive difference between the two
numbers immediately above it.
For example, C equals B-A or A-B, whichever is positive.
Replace the letters A through E with the numbers 1 through 5 (once each)
in a way that follows the above rule.
What does C equal?
A. 1B. 2C. 3D. 4E. 5
34.A 900-mile flight from Boston to Atlanta is scheduled to depart at 8:30 am and arrive at 10:10 am. It actually departs at 8:50 am, but the pilot is allowed to fly 60 mph faster than the average speed of the original flight plan. Which of the following times is closest to the arrival time in Atlanta?
A. 10:05 amB. 10:10 amC. 10:15 amD. 10:20 amE. 10:25 am
35.For the next seven years, the St. Louis Cardinals will pay Albert Pujols an average of 14.7 million dollars per year. Twenty-five $20-bills weigh 0.9 ounces. If Albert were to insist on being paid in $20-bills, how many pounds would the $14.7 million weigh? Round to the nearest pound.
A. 1,654B. 8,148C. 26,460D. 33,075E. 41,344
36.The number of intersection points of a circle and a triangle CANNOT be:
A. 3B. 4C. 5D. 6E. All of these answers: 3, 4, 5, and 6, are possible.
37. At 3:00 pm while driving on highway US 2 towards Oakton and Trenary, Karela sees the sign: “Oakton 37 miles; Trenary 57 miles.” At 3:15 pm, Karela sees another sign and notices that Trenary is now twice as far ahead as Oakton. What was Karela’s average speed between 3:00 pm and 3:15 pm?
A. 60 mphB. 62 mph C. 64 mphD. 65 mphE. 68 mph
38.If the St. Louis Rams field goal kicker, Jeff Wilkins, makes 28 field goals in 32 attempts this year, then he must have a streak of making at least N consecutive field goals. Under these conditions, what is the longest streak N of consecutive field goals that Jeff is guaranteed to have?
A. 5B. 6C. 7D. 8E. 9
39.Note: 7+241+83+569 is a sum of prime numbers that uses each of the digits 1 through 9 exactly once.
What is the least possible sum of primes that uses each digit 1 through 9 exactly once?
A. 207B. 218C. 225D. 228E. 252
40.This network of eight equilateral triangles can be folded to form a regular octahedron.
To construct a Magic Octahedron, replace the letters A, B, C, D, and E with the numbers2, 4, 6, 7,and 8 (without repetition) so that the sum of the four numbers on the four faces that share each vertex has the same sum S.
On your Magic Octahedron, what does B+D equal?
A. 6B. 7C. 8D. 9E. 10
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