Seventh Grade Test - Excellence in Mathematics Contest - 2003
1. (1980, #14) A girl buys lemons at 4 for 71 cents. She will sell them at 5 for 95 cents. In order to make a profit of $3.50, how many lemons must she buy and sell?
A. 160 B. 200 C. 240 D. 280 E. 320
2. (1981, #34) No prime number greater than 11 ends with the digit:
A. 1 B. 3 C. 5 D. 7 E. 9
3. (1982, #24) On the television program, Little House on the Prairie, Mr. Ingall’s wagon has front wheels 7 feet in circumference and back wheels 9 feet in circumference. When the front wheels have made 10 more revolutions than than the back wheels, how far has the wagon moved?
A. 180 feet B. 270 feet C. 315 feet D. 350 feet E. 630 feet
4. (1983, #9) Which one of the following fractions is greater than and less than ?
A. B. C. D. E.
5. (1984, #11) The temperature on a hot summer afternoon in St. Louis could be:
A. B. C. D. E.
6. (1985, #3) While checking out the coconut trees, a monkey follows each path exactly once, in the direction indicated. Where did the monkey start and end?
A. Start at M; End at N B. Start at J; End at K
C. Start at K; End at J D. Start at N; End at M
E. Start and End at M
7. (1986, #12) A rectangle with width 4 cm and length 10 cm has the same perimeter as a square. How much larger is the area of the square than the area of the rectangle?
A. 0 cm2 B. 4 cm2 C. 6 cm2 D. 8 cm2 E. 9 cm2
8. (1987, #7) The temperature at 8:00 am Monday is . The temperature increases at a constant rate of per hour until 6:00 pm; then it decreases at a constant rate of per hour. What will the temperature be at 8:00 am Tuesday morning?
A. B. C. D. E.
9. (1988, #12) How many different prime numbers are factors of 1988?
(Note: The number 1 is not a prime number.)
A. 2 B. 3 C. 4 D. 5 E. 6
10. (1989, #11) Mr. and Mrs. Lavorsky have seven children; who each have five children, who each have three children, who each have two children. What is the total number of children, grandchildren, great-grandchildren, and great-great-grandchildren that Mr. and Mrs. Lavorsky have?
A. 210 B. 240 C. 280 D. 327 E. 357
11. (1990, #38) Write the largest possible eight-digit number such that:
· Each of the digits 1, 2, 3, 4, 5, 6, 7, and 8 are used exactly once;
· No two adjacent digits differ by one.
What are the two middle digits, in order, of the eight-digit number?
A. 53 B. 64 C. 73 D. 74 E. 75
12. (1991, #13) Suzanne’s score in a game was -6. In the next five rounds of the game, she gained 14 points, lost 20 points, gained 9 points, lost 5 points, and lost 10 points. What is her score now?
A. -6 B. -9 C. -12 D. -15 E. -18
(This was my daughter Suzanne’s 7th grade debut!)
13. (1992, #4) 0.6 0.08 0.2381 0.00741 0.306
If the above five numbers are arranged in order from smallest to largest, what is the middle number?
A. 0.2381 B. 0.08 C. 0.6 D. 0.00741 E. 0.306
14. (1993, #3) Place one digit in each box
to make a correct subtraction problem.
What is the sum of the digits in the five boxes?
A. 25 B. 26 C. 27 D. 28 E. 29
15. (1994,#40) Using the four digits 1, 2, 3, and 4, number the regions on this map so that if two regions share a border, they are numbered differently. Four regions are numbered already.
Region R must be labeled:
A. 1
B. 2
C. 3
D. No solution exists
E. More than one solution exists
16. (1995, #8) If the value of one share of Diversified Industries stock decreases from , by how much does the value of 200 shares decrease?
A. $175 B. $225 C. $250 D. $275 E. $625
17. (1996, #4) The perimeter of the square is 32 feet.
In square feet, what is the area of the inscribed circle?
A. 4p B. 8p C. 12p
D. 16p E. 64p
18. (1997, #9) A lily pad grows so that each day it doubles its area. On the 20th day it completely covers the pond. On what day was the pond half covered?
A. 9th B. 10th C. 11th D. 15th E. 19th
19. (1998,#13) In 1880, a man bought some apples at 2 apples for 3 cents and bought the same number of apples at 2 apples for 5 cents. He sold all of the apples at 3 apples for 7 cents. For each one dozen apples, how much did he gain?
A. 2 cents B. 3 cents C. 4 cents D. 6 cents E. 8 cents
(Adapted from Henry’s Arithmetical Analyses, 1883)
20. (1999, #15) A Leap Year has 366 days and the year 2000 was a Leap year. Rick’s 49th birthday on April 1, 1999, was on a Thursday. Rick’s 50th birthday was on a
A. Tuesday B. Wednesday C. Friday D. Saturday E. Sunday
21. (2000, #24) For HOW MANY of these five values for x is: x3 < x ?
-5 0.8 -1
A. One B. Two C. Three D. Four E. Five
22. (2001, #21) Before conference swim championships, Suzanne’s best time in the 200 yard butterfly race was 2 minutes, 23 seconds. In the conference championships, she won 10th place by swimming the 200 yard butterfly in 2 minutes, 15 seconds. What per cent decrease is that?
A. 3.6% B. 5.6% C. 5.9% D. 6.2% E. 36.9%
23. (2002, #38) Place the nine integers: -4, -3, -2, -1, 0, 1, 2, 3, and 4 into these nine boxes (without repetition) so that the sum of the integers in any two consecutive boxes is a perfect square number.
There are two different numbers that could be in the middle square. What is the sum of these two numbers?
A. -3 B. -1 C. 0 D. 1 E. 2
(Note: Last year, I thought that there was only one solution - a teacher found the other!)
24. What is the ratio of the measure of the interior angle of an equilateral triangle to the measure of the interior angle of a square?
A. 2/3 B. 1/2 C. 3/4 D. 5/6 E. 4/3
25. What is the smallest whole number value of N such that is larger than 10 billion?
A. 5 B. 6 C. 7 D. 8 E. 9
26. In the number: , which digit is in the “ten billions” place?
A. 1 B. 4 C. 5 D. 6 E. 7
27. The Drama Club hosted a 2003 minute long dance marathon. It started at 7:00 pm Friday. On Sunday, at what time did it end?
A. 4:23 am B. 4:38 am C. 6:23 am D. 6:30 am E. 6:38 am
28. For any three consecutive months, what is the least possible number of days?
A. 88 B. 89 C. 90 D. 91 E. 92
29. For a training ride, a bicyclist first warms up by biking at 12 mph for 10 minutes and at the end cools down by biking at 8 mph for 15 minutes. In between the warm-up and cool down, he bikes at an average of 24 mph. In a two-hour training ride, how many total miles does he bike?
A. 42 B. 43 C. 44 D. 45 E. 46
30. A ream of paper containing 500 sheets is 8 cm thick. How many sheets of paper are in a stack 5.6 cm high?
A. 300 B. 310 C. 320 D. 340 E. 350
31. The bar graph shows the final course grades in one
section of College Algebra.
What per cent of these students earned a C or better?
A. 64% B. 68% C. 72%
D. 75% E. 76%
32. How many positive divisors do 36 and 48 have in common?
A. 4 B. 6 C. 8 D. 9 E. 12
33. X, Y, and Z represent three different numbers from the set:
What is the maximum possible value of ?
A. 15 B. 240 C. 333 1/3 D. 400 E. 500
34. Among the one thousand years from 1000 to 1999, inclusive, how many are written with exactly two distinct digits? (For example, 1010 and 1999.)
A. 54 B. 60 C. 63 D. 70 E. 90
35. As shown, a sculptor attaches a 4-meter cube to the top of a 7-meter cube
and then places the small 2-meter cube so that its faces touch
both the 4-meter cube and the 7-meter cube. In square meters,
what is the surface area (including the base) of the completed sculpture?
A. 362 B. 366 C. 370 D. 374 E. 382
36. Given a square. How many distinct equilateral triangles share exactly two vertices with two vertices of the square?
A. 4 B. 6 C. 8 D. 10 E. 12
37. On a copy machine, when a person selects the option x%, the copy is x% of the original where x must be 50 or larger. To reduce an original to smaller than 50% requires the user to first reduce the original and then reduce the copy. To reduce an original to exactly 48% of its size, which of these three sequences of reductions would work?
I. 50%, then 96% II. 75%, then 64% III. 70%, then 88%
A. None of these B. I only C. II only D. III only E. I and II, only
38. In the sequence: 0,1, 2, 5, 12, 29, ……; each number after 0, 1, equals twice the previous number plus the number before that. For example, 29 = 2(12) + 5 .
Which one of the following terms of the sequence is a multiple of 5?
A. 2000th B. 2001st C. 2002nd D. 2003rd E. 2004th
39. (1981, #36) A, B, C, and D are four different weights. When they are placed on a balance scale, the following observations are made:
· A and B together weigh the same as C and D together
· A and C together weigh more than B and D together
· C is lighter than D
Arranged in order from heaviest to lightest, the weights are:
A. A, D, C, B B. D, A, C, B C. D, A, B, C
D. A, B, D, C E. A, D, B,C
40. To win this game, you must start at one of the 15 buttons, follow the instruction on that button and all subsequent buttons, and end at the Exit. For example, “2D” means to move two buttons “Down”; while “3R” means to move three buttons to the “Right”.
In which column is the only button at which you could start, press all 15 buttons, and then land on the Exit button on your last move?
A. A B. B C. C
D. D E. E
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