MATHCOUNTS Name School Chapter 2006 State Competition Target Round Problems 1 and 2 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This round of the competition consists of eight problems, which will be presented in pairs. Work on one pair of problems will be completed and answers will be collected before the next pair is distributed. The time limit for each pair of problems is six minutes. The first pair of problems is on the other side of this sheet. When told to do so, turn the page over and begin working. Record your final answer in the designated space on the problem sheet. All answers must be complete, legible and simplified to lowest terms. This round assumes the use of calculators, and calculations may also be done on scratch paper, but no other aids are allowed. Total Correct Scorer s Initials Founding Sponsors National Society of Professional Engineers National Council of Teachers of Mathematics CNA Foundation National Sponsors General Motors Foundation Lockheed Martin National Aeronautics and Space Administration Northrop Grumman Foundation Raytheon Company Shell Oil Company Texas Instruments Incorporated 3M Foundation Xerox Corporation Copyright MATHCOUNTS, Inc. 2006. All rights reserved.
1. A magazine advertisement states that a subscriber saves 75.6% off the cover price at news stands by purchasing a 17-issue subscription rather than purchasing the 17 issues separately at the cover price. If a 17-issue subscription costs $10.99, what is the average cover price of each magazine when bought at a news stand? Express your answer as a decimal to the nearest hundredth. 1. $ 2. A triangle has a side of length 6 cm, a side of length 8 cm and a right angle. What is the shortest possible length of the remaining side of the triangle? Express your answer as a decimal to the nearest hundredth. 2. centimeters Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2006 State Target Round
MATHCOUNTS 2006 State Competition Target Round Problems 3 and 4 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. Total Correct Scorer s Initials Founding Sponsors National Society of Professional Engineers National Council of Teachers of Mathematics CNA Foundation National Sponsors General Motors Foundation Lockheed Martin National Aeronautics and Space Administration Northrop Grumman Foundation Raytheon Company Shell Oil Company Texas Instruments Incorporated 3M Foundation Xerox Corporation Copyright MATHCOUNTS, Inc. 2006. All rights reserved.
3. A set of four consecutive integers has a sum of 22. If each integer of the set is increased by 2 and then multiplied by 20, what is the sum of the new set of integers? 3. 4. The triple bar graph shows the results of a survey conducted in California, Alaska and Texas. Residents of the three states were asked how they most often refer to soft drinks. Each person could give only one answer. All values on the graph are exact integers, and only the statistics for the top three responses are shown. In all, 8300 people were surveyed in California, 300 people in Alaska and 7250 people in Texas. When the three states are considered together, how many more people surveyed call soft drinks Coke than call soft drinks Soda? Percent of People Surveyed in the State 80 70 60 50 40 30 20 10 Soda Pop Coke 4. people California Alaska Texas Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2006 State Target Round
MATHCOUNTS 2006 State Competition Target Round Problems 5 and 6 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. Total Correct Scorer s Initials Founding Sponsors National Society of Professional Engineers National Council of Teachers of Mathematics CNA Foundation National Sponsors General Motors Foundation Lockheed Martin National Aeronautics and Space Administration Northrop Grumman Foundation Raytheon Company Shell Oil Company Texas Instruments Incorporated 3M Foundation Xerox Corporation Copyright MATHCOUNTS, Inc. 2006. All rights reserved.
5. One complete lap around a particular circular track is 400 meters. Jun and Quan each start running at the starting line and run around the track; Jun runs clockwise at 3 meters per second, and Quan runs counterclockwise at 5 meters per second. When they meet for the sixth time after starting, they stop and both walk back together along the track to the starting line. What is the shortest distance they could walk back on the track together? 5. meters 6. Richard has a 9-inch by 13.5-inch sheet of cardboard. He wants to create a closed cube with the largest possible volume. There are no restrictions on the way he can cut the cardboard or tape it back together, and no cardboard is lost when he makes a cut. What is the greatest volume possible? Express your answer as a decimal to the nearest thousandth. 6. cubic inches Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2006 State Target Round
MATHCOUNTS 2006 State Competition Target Round Problems 7 and 8 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. Total Correct Scorer s Initials Founding Sponsors National Society of Professional Engineers National Council of Teachers of Mathematics CNA Foundation National Sponsors General Motors Foundation Lockheed Martin National Aeronautics and Space Administration Northrop Grumman Foundation Raytheon Company Shell Oil Company Texas Instruments Incorporated 3M Foundation Xerox Corporation Copyright MATHCOUNTS, Inc. 2006. All rights reserved.
7. The figure below represents a figure with a total of 120 triangles and n points labeled as vertices on the horizontal base. What is the value of n? 7. P A 1 A 2 A 3 A 4 A 5 A n 1 A n 8. My three-digit code is 023. Reckha can t choose a code that is the same as mine in two or more of the three digit-positions, nor that is the same as mine except for switching the positions of two digits (so 320 and 203, for example, are forbidden, but 302 is fine). Reckha can otherwise choose any three-digit code where each digit is in the set {0, 1, 2,..., 9}. How many codes are available for Reckha? 8. codes Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2006 State Target Round