// BEGIN editorial data var i = 0; var AJMathQuiz = new Array(); AJMathQuiz.ID = "AJMathQuiz"; AJMathQuiz.ID_WB = 12773418; AJMathQuiz.navsectionID = "3033054" AJMathQuiz.sPubDate = "5/14/2006 1:54:18 AM GMT"; AJMathQuiz.quiztype = 1; AJMathQuiz.appFmt = 0; AJMathQuiz.bDispQNums = 1; AJMathQuiz.appWidth = 460; AJMathQuiz.appHeader = "Take a sample quiz"; AJMathQuiz.appDeck = new Array("Try your hand at sample Mathcounts questions. Some of these are practice questions, and others were used in the national competition. Choose your answers and click Submit at the bottom for the correct answers and explanations.","You answered of questions correctly. Scroll down to see answers for each question. "); AJMathQuiz.appFooter = "Source: Mathcounts Foundation"; AJMathQuiz.headHeight = 40; AJMathQuiz.copyMargin = 9; AJMathQuiz.copyBorder = 0; AJMathQuiz[1] = new Array(); AJMathQuiz[1][0] = new Array("With approximately 20,000 runners, the Boston Marathon is one of the most, if not the most, well-known marathons. Every year, hundreds of thousands of Americans run in marathons and participate in triathlons. The ratio of the number of Americans running marathons to the number of Americans doing triathlons is 18:13, with 125,000 more people running marathons than doing triathlons. How many Americans do triathlons each year?"); AJMathQuiz[1].answer = "According to the given ratio, there are 18x Americans doing marathons and 13x Americans doing triathlons each year. The difference between these two numbers is 5x, so we have 5x = 125,000. Dividing both sides of the equation by 5, we get x = 25,000. This means the number of Americans doing triathlons is 13x = 13(25,000) = 325,000 people."; AJMathQuiz[1][1] = new Array("20,000",'',0); AJMathQuiz[1][2] = new Array("125,000",'',0); AJMathQuiz[1][3] = new Array("325,000",'',1); AJMathQuiz[1][4] = new Array("650,000",'',0); AJMathQuiz[2] = new Array(); AJMathQuiz[2][0] = new Array("One of the most prevalent mistakes when filling out the paperwork for a tax return happens when a person is writing his/her Social Security Number (SSN). A person’s SSN is a nine-digit code, and messing up any of those nine digits can cause a lot of headache. Suppose we know Talia accidentally reversed two consecutive digits of her SSN, and her correct SSN is 123-45-6789. (Two digits separated by a dash are still considered to be consecutive.) How many possible nine-digit codes could she have written on her paperwork?"); AJMathQuiz[2].answer = "We know Talia reversed two of the consecutive digits of her SSN, but we don’t know which two digits. It’s possible it was the first two, which would result in 213-45-6789. It’s also possible it was the last two digits, which would result in 123-45-6798. It could have been a pair of consecutive digits that don’t involve the first or last digit, too. There are a total of eight pairs of consecutive digits that could have been reversed (1,2; 2,3; 3,4; 4,5; 5,6; 6,7; 7,8; 8,9), so she could have written eight different SSN codes instead of her correct one."; AJMathQuiz[2][1] = new Array("8",'',1); AJMathQuiz[2][2] = new Array("32",'',0); AJMathQuiz[2][3] = new Array("16",'',0); AJMathQuiz[2][4] = new Array("9",'',0); AJMathQuiz[3] = new Array(); AJMathQuiz[3][0] = new Array("New graduate Greg is going to earn this salary of $56,549 next year. He will be paid twice a month (on the 15th of the month and the last day of the month), and every paycheck will be the same amount throughout the year. What will Greg’s “take-home” or net pay be each month if he estimates each paycheck will be reduced by 25 percent due to taxes? Express your answer to the nearest whole dollar."); AJMathQuiz[3].answer = "Since Greg is receiving two paychecks each month (as opposed to a paycheck every two weeks), we can simply divide his annual gross pay by 12 to see that his monthly gross pay will be $4,712.42. If his take-home pay is only 75 percent of this, he will be bringing home 4,712.42(0.75) = $3,534 each month after taxes, to the nearest whole dollar."; AJMathQuiz[3][1] = new Array("$4,156",'',0); AJMathQuiz[3][2] = new Array("$4,712",'',0); AJMathQuiz[3][3] = new Array("$5,890",'',0); AJMathQuiz[3][4] = new Array("$3,534",'',1); AJMathQuiz[4] = new Array(); AJMathQuiz[4][0] = new Array("VH1 Classic did a fundraiser for Hurricane Katrina relief. Viewers could request one music video to be played for every $25 donation. If the average video lasts 3 minutes, 44 seconds, how many videos could be played during an hour? (Express your answer to the nearest whole number.)"); AJMathQuiz[4].answer = "If each video averages 3 minutes, 44 seconds, then there can be 60/(3 \+ 44/60) = 16 videos played in one hour, to the nearest whole number."; AJMathQuiz[4][1] = new Array("20",'',0); AJMathQuiz[4][2] = new Array("16",'',1); AJMathQuiz[4][3] = new Array("10",'',0); AJMathQuiz[4][4] = new Array("12",'',0); AJMathQuiz[5] = new Array(); AJMathQuiz[5][0] = new Array("For those videos, how much money would be donated?"); AJMathQuiz[5].answer = "This works out to be 16 x $25 = $400."; AJMathQuiz[5][1] = new Array("$200",'',0); AJMathQuiz[5][2] = new Array("$375",'',0); AJMathQuiz[5][3] = new Array("$400",'',1); AJMathQuiz[5][4] = new Array("$500",'',0); AJMathQuiz[6] = new Array(); AJMathQuiz[6][0] = new Array("When there are tragedies around the world, it is often reported in the news that massive amounts of blood donations are necessary. Though that may be true, there are people in need of donated blood each and every day. Regulations in the United States allow people to donate whole blood once every 56 days. In a year, what is the greatest number of times a person could donate whole blood? Express your answer to the nearest whole number."); AJMathQuiz[6].answer = "Using 365 days in a year, we can see that a person is able to give blood 365/56 = 6.5 times in a year. So if a person donates whole blood on Jan. 1, she could give blood six times in that one calendar year, since that would require a minimum of 336 days if a donation were made every 56 days. However, because of the way the question was asked, the answer is 7, to the nearest whole number."; AJMathQuiz[6][1] = new Array("6",'',0); AJMathQuiz[6][2] = new Array("7",'',1); AJMathQuiz[6][3] = new Array("28",'',0); AJMathQuiz[6][4] = new Array("56",'',0); AJMathQuiz[7] = new Array(); AJMathQuiz[7][0] = new Array("The arithmetic mean (or average) of A, B and C is 10. The value of A is six less than the value of B, and the value of C is three more than the value of B. What is the value of C?"); AJMathQuiz[7].answer = "If the arithmetic mean of the three numbers is 10, we know that the sum of the three numbers is 3 x 10 = 30, so A \+ B \+ C = 30. We also know A = B – 6 and C = B \+ 3. Using substitution into A \+ B \+ C = 30, we have (B – 6) \+ B \+ (B \+ 3) = 30, which reduces to 3B = 33, so B = 11. Remember we need the value of C, which is B \+ 3 = 11 \+ 3 = 14."; AJMathQuiz[7][1] = new Array("10",'',0); AJMathQuiz[7][2] = new Array("11",'',0); AJMathQuiz[7][3] = new Array("14",'',1); AJMathQuiz[7][4] = new Array("22",'',0); AJMathQuiz[8] = new Array(); AJMathQuiz[8][0] = new Array("What is the greatest three-digit integer in which the product of the digits is zero? (No calculators permitted.)"); AJMathQuiz[8].answer = "In order for the product of the digits to be zero, one of the digits must be a zero. Since we are looking for the greatest three-digit integer possible, we should probably look for something in the 900s. Keeping with this thinking, we should look at something in the 990s. Needing a zero as one of our digits, our answer is 990."; AJMathQuiz[8][1] = new Array("910",'',0); AJMathQuiz[8][2] = new Array("721",'',0); AJMathQuiz[8][3] = new Array("811",'',0); AJMathQuiz[8][4] = new Array("990",'',1); AJMathQuiz[9] = new Array(); AJMathQuiz[9][0] = new Array("Carolyn, Julie and Roberta share $77 in a ratio of 4:2:1, respectively. How many dollars did Carolyn receive? (No calculators permitted.)"); AJMathQuiz[9].answer = "Since Carolyn, Julie and Roberta are sharing the money is a ratio of 4:2:1, there are then 4 \+ 2 \+ 1 = 7 parts. When we divide $77 into 7 parts, each part is $11. Since Carolyn was the first one mentioned, her number of parts is the first one mentioned (4), so she will get $44."; AJMathQuiz[9][1] = new Array("$11",'',0); AJMathQuiz[9][2] = new Array("$22",'',0); AJMathQuiz[9][3] = new Array("$33",'',0); AJMathQuiz[9][4] = new Array("$44",'',1); AJMathQuiz[10] = new Array(); AJMathQuiz[10][0] = new Array("February is the only month that has a different number of days depending on the year. As you know, every fourth year is a leap year. From 2006 through 2025, inclusive, what is the average number of days in February each year? Express your answer as a decimal to the nearest hundredth."); AJMathQuiz[10].answer = "The years 2006 through 2025, inclusive, are 2025 – 2005 = 20 years. During this time there are five leap years (2008, 2012, 2016, 2020 and 2024). Therefore, 15 years have 28 days each, for a total of 420 days and five years have 29 days each for a total of 145 days. This is a grand total of 420 \+ 145 = 565 days, and an average of 565/20 = 28.25 days per February during that span of time."; AJMathQuiz[10][1] = new Array("28.25",'',1); AJMathQuiz[10][2] = new Array("28.50",'',0); AJMathQuiz[10][3] = new Array("28.75",'',0); AJMathQuiz[10][4] = new Array("29.00",'',0); AJMathQuiz.profiles = new Array();var i=0; AJMathQuiz.profiles[i++]= new Array(0,19,"
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