Seventh Grade Test - Excellence in Mathematics Contest - 2009
1.For work, Pauline rides the Metro twice a day for five days each week. Over a four week period in February, how much does she save by buying one $68 pass for February compared to buying a $2.25 one-ride ticket each time she rides the Metro?
A.$22B.$22.50C.$23D.$23.50E.$24[FV1]
2.By exchanging the positions of two digits in the number 965,142, the new number is 19,980 smaller than the original number. What is the sum of the two digits exchanged?
A.7B.8C.9D.10E.13[FV2]
3.When working on her bicycle, Alicia tried the7/8 inch wrench which was too large but the 3/4 inch wrench was too small for the bolt.
Which is the only wrench of these five sizes (in inches) which might work for Alicia?
A.11/16B.15/16C.6/8D.21/32E.13/16[FV3]
4.At the Local Harvest restaurant, Rick bought a bowl of vegan chili for $6.25 and a cup of coffee for $1.35 . Basing each percent on the total cost of the chili and coffee, Rick left a 12% tip and paid 8% sales tax. From a $10 bill, what is the least number of coins (using only pennies, nickels, dimes, and quarters) Rick could have received in change?
A.7B.8C.9D.11E.12[FV4]
5.What is sum of the two distinct prime factors of 2009?
A.48B.90C.98D.294E.2009[FV5]
6.If is a simplified fraction (that is, reduced to lowest terms) and is between 0 and 2, how many values are possible for N?
A.16B.18C.20D.22E.24[FV6]
7.A family buys a half-dozen eggs per week for three weeks. For the next two weeks, they buy one dozen eggs per week. Then they buy 2 dozen eggs in one week.
On the average, how many eggs per week did they purchase?
A.9B.C.10.5D.11E.22[FV7]
8.The sum of the reciprocals of 0.4 and 3 is between:
A.0 and 1B.1 and 1.5C.1.5 and 2D.2 and 2.5E.2.5 and 3[FV8]
9.From 1970 to 2000, Missouri’s percentage of the total US population dropped from 2.30% of 204 million Americans to 1.99% of 281 million Americans.
Approximately, what was the loss or growth of Missouri’s population from 1970 to 2000?
A.Loss of 900,000 B. Loss of 90,000C.Loss of 900
D. Gain of 900,000E. Gain of 90,000[FV9]
10.Point A is the vertex of a square, 4 cm on each side.
What is the length in centimeters of segment AB?
A.10[FV10]B.14C.
D. E.
11.With any combination of nickels, dimes, and quarters, how many ways can you make change for 55 cents?
A.8B.10C.11D.18E.20[FV11]
12.How many numbers belong to both of these arithmetic sequences?
A.3B.4C.5D.6E.7[FV12]
13.In the diagram, the perimeter of the rectangle is 36 cm and its width w equals 10 cm.
To the nearest square centimeter, what is the area of the circle?
A.28 B. 50 C. 78 D. 113 E. 201[FV13]
14.How many of the following five numbers are between and ?
A.1B.2C.3D.4E.5[FV14]
15.An 8-foot long rod is cut into three pieces with lengths in the ratio 5:3:4.
In inches, what is the length of the longest of the three pieces?
A.32B.36C.40D.48E.60[FV15]
16.A cylinder is a snug fit for four spheres (you might call them tennis balls), each of radius r.
If the height of the cylinder is 28 cm, what is the circumference of each sphere?
Round to the nearest tenth of a centimeter.
A.8.7 B. 9.6 C. 22.0 D. 44.0 E. 38.5[FV16]
17.In his comeback in the 2009 Tour of California, Lance Armstrong took 14th place in the
15-mile time trial by completing it in 31 minutes, 56 seconds.
Rounded to the nearest tenth, what was his average speed in miles per hour?
A.28.1 mphB.28.2 mphC.28.5 mphD.28.6 mphE. 28.9 mph[FV17]
18.20 fence posts are used to build a fence around a square plot. With one pole at each corner, the distance between adjacent poles on the fence is 6 m. What is the area, in square meters, of the square?
A.150B. 576C.625D.900E.961[FV18]
19.Rick uses this weighted average formula to grade his Calculus class.
“25% of HW average plus 75% of Test average”
What is Zan’s current grade if her HW average is 72% and her test average is 97%?
A.84.5%B.88%C.88.5%D.90%E.90.75[FV19]%
20.Of 100 students, 84 are taking Algebra, 30 are taking Chinese, while 24 are taking both Algebra and Chinese. How many of the 100 students are taking neither Algebra nor Chinese?
A.6B.10C.12D.20E.34[FV20]
21.A wooden square, 1 foot on each side, is cut into small squares, each 2 inches on a side. All of these small squares are placed side-by-side in one long row. What is the length of this row?
A.1 footB.2 feetC.3 feetD.4 feetE.6 feet[FV21]
22.Two fair standard 6-sided dice are rolled. What is the probability that the sum of the two numbers rolled is 11 or 12?
A.1/12B.1/18C.2/11D.1/6E.1/9[FV22]
23.The surface area of a cube is 150 cm2. In cubic centimeters, what is the volume of the cube?
A.25B.125C.625D.1,837E.15,625[FV23]
24.Determine the sumof the first 15 terms of the geometric series: 1, 2, 4, 8, 16, 32, …. .
A.16,383B.32,767C.32,768D.65,535E.65,536[FV24]
25.How many 3-digit natural numbers are square numbers?
A.21B.22C.23D.31E.32[FV25]
26.The Fibonacci Series starts: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…
In the tens’ places of the numbers in this series, which is the last of the ten digits 0 through 9 to make its initial appearance?
A.0B.4C.6D.7E.9[FV26]
27.As shown, the centers of 3 small congruent, tangent, circles lie along the diameter of the large circle. What is the ratio of the circumference of the large circle to the sum of the circumferences of the three small circles?
A.3/2 B.2/3 C. π/3 D. 3/π E. 1[FV27]
28.To make these equations true, what is the sum of the numbers in the two boxes?
5 = =
A.10B.78C.82D.89E.250[FV28]
29.By replacing the four variables a, b, c, and d in the expression below with the four numbers
, , 2 , and 3 , what is the greatest possible value of the expression?
A.2B.3C.12D.13E.
30.When the date March 6, 2009 is written: 03/06/09, the month, day, and year form an increasing arithmetic sequence: 3, 6, 9. Including March 6, 2009, how many dates in 2009, when written in this format, form an increasing arithmetic sequence?
A.2B.3C.4 D.5E.More than 5[FV29]
31.Working together, Larry and Curly could build a garage in 10 days. Assume that Larry and Curly work at the same rate. Larry and Curly do work together for 4 days, then Curly leaves the job. By himself, Larry works 4 more days. After these 8 days, what fraction of the job is completed?
A.2/5B.3/5C.4/5D.7/10E.1/2[FV30]
32.The sum of 41 consecutive integers is 2009. What is the product of the least and the greatest of those 41 integers?
A.2100B.1932C.1960D.2001E.2030[FV31]
33.In how many 5-digit numbers does the 4-digit sequence “2009” appear?
A.18B.19C.20D.90E.100[FV32]
34.Among 14 items, the Nth item is worth $N. For example, the 3rd item is worth $3 and the 12th item is worth $12. These 14 items are shared among 3 friends so that the value of the items that each friend receives is equal.
What is the maximum number of items that one person could receive?
A.5B.6C.7D.8E.9[FV33]
33 /
35.Complete this Magic Square with the numbers 1, 2, 3, 4, 5, and 6 so that the sums of the three numbers in each of the two rows and in each of the two columns are the same. Which number is in the square marked A?
A.2B.3C.4
D.5E.6[FV34]
36.x, y, and z are integers such that x < y < z and x + y + z = –50 .
What is the greatest possible value of x?
A.–19B.–18C.–17D.–16E.–15[FV35]
37.Let A, B, and C be three distinct positive integers such that the product ABC = 120.
Which of the following five numbers CANNOT be the sum A+B+C?
A.15B.16C.18D.20E.21[FV36]
38.Lyle’s sock drawer has 8 black, 6 blue, and 4 brown socks. Getting up before dawn, without looking, Lyle reaches in and selects N socks. What is the least value of N to guarantee that, in terms of color, he selects at least two pairs of socks? (The first pair may be, but need not be, the same color as the second pair.)
A.5B.6C.7D.8E. More than 8[FV37]
39.On this 2 by 3 grid, how many distinct paths of length 3 start at vertex A? On any one path, you may never retrace any part of your route.
A.6 B. 8 C. 9 D. 10 E. 11[FV38]
40.The sum of the digits of many 6-digit whole numbers is 33.
What is the sum of the least and the greatest of these 6-digit numbers?
A.1,006,599B.1,105,599C.1,114,599D.1,123,320E.1,123,599[FV39]
[FV1]6, 7 #81 A
[FV2]6, 7, 8 #65 D
[FV3]7,8,9 #74 E
[FV4]6; 7; 8 #83 A
[FV5]6,7,8 #20 A
[FV6]6,7, 8 #12 A
[FV7]6,7,8 #16 D
[FV8]6, 7, 8 #77 E
[FV9]6, 7 #76A D
[FV10] 7 A
[FV11]6,7, 8 #3 C
[FV12]6,7,8 #15 D
[FV13]7 #11B B
[FV14]7,8 #14 B
[FV15]6,7 #27 C
[FV16] 7 #47B C
[FV17]7,8 #8 B
[FV18] #6,7 #19 D
[FV19]7,8,9, #38 E
[FV20]7,8 #29 B
[FV21]6, 7 #71B E
[FV22]7 #28B A
[FV23]7 #44B B
[FV24] #24B, B
[FV25] 7 #4B B
[FV26]6,7,8,9 #79 A
[FV27]7,8,9 #25 E
[FV28]7 #69B C
[FV29]7, 8 #68A C
[FV30]7 #54B B
[FV31]7, 8 #50 D
[FV32]#52B B
[FV33]7 #61B C
[FV34]6, 7, 8, 9 #73 E
[FV35]7,8,9 #2 B
[FV36]6,7,8,9 #80 D
[FV37]6,7,8,9 #55 B
[FV38]7, 8 #31 C
[FV39]6, 7 #30 B