Bicentennial Olympiad Qualifying Round ONE

Bicentennial Olympiad – Qualifying RoundPROBLEM ONEThe figure at the right is a “magic square”with missing entries. When complete, the sum ofthe four entries in each column, each row, andeach diagonal is the same.FIND THE VALUE OFA87 124 95 1611BA AND THE VALUE OF B.PROBLEM TWOWhen asked how many gold coins he had, the king said:If I arrange them in stacks of five, none are left over.If I arrange them in stacks of six, none are left over.If I arrange them in stacks of seven, one is left over.What is the least number of coins he could have?PROBLEM THREEAlice and Brian run a 50-meter race and Alice wins by 10meters. They then run a 60-meter race, and both run atthe same speed they ran in the first race.By how many meters will Alice win the second race?

PROBLEM FOURA twelve-hour clock loses 1 minute every hour. Supposeit shows the correct time now.What is the least number of hours from now when itwill again show the correct time?PROBLEM FIVEAll the money made from the Grade 7cookie sales, consisting of 240, is goingto be divided equally among the teachers.Unfortunately, it was discovered that oneof the teachers was not eligible for hisshare because he had eaten cookies andnever paid for them. This meant that theamount to be given to each remainingteacher increased by one dollar.HOW MANY TEACHERS WILL RECEIVE A SHARE OFTHE 240?

Problem oneA 1Problem two120Problem three12Problem four720Problem five15B 13

Bicentennial Olympiad – Qualifying RoundPROBLEM ONEYour mom has decided that it is time for you toorganize your stuff, and she has provided someboxes. In fact, in your room there are 4 separatelarge boxes, and inside each large box there are 3separate small boxes, and inside each of thesesmall boxes there are 2 separate smaller boxes.HOW MANY BOXES ARE THERE ALTOGETHER?PROBLEM TWOLarry has 12 more than Curly and 15more than Moe. When they put theirmoney together they have 87.HOW MUCH DOES LARRY HAVE?PROBLEM THREEA dog takes 3 steps to walk the same distancefor which a cat takes 4 steps. Suppose 1 stepof the dog covers 1 foot.HOW MANY FEET WOULD THE CAT COVERIN TAKING 12 STEPS?

PROBLEM FOURIn the multiplication problem at the right,A Bx 6A and B represent different digits, A B isa two-digit number and B B B is a three-digit number. B B BWHAT TWO-DIGIT NUMBER DOESA B REPRESENT?PROBLEM FIVEThe Math Police have arrested four studentssuspected of trying to divide by zero. They weregiven numbers to hold and are lined up in order ofnumber size. The difference between any twoadjacent numbers (students next to each other) isthe same. The first student was given the numberone-third and the fourth student was given thenumber one-half.Grade seven:ON A NUMBER LINE, WHAT WOULD BE THE DISTANCEBETWEEN THE FIRST STUDENT’S NUMBER AND THEFOURTH STUDENT’S NUMBER?Grade eight & nine:WHAT NUMBERS ARE THE REMAINING TWO STUDENTSHOLDING?(Hint: Find the distance between the first and fourthstudent’s numbers first)

Problem one40Problem two38Problem threeProblem fourProblem five97416OR2 OR 31236

2006 BICENTENNIAL MATHOLYMPIADCHAMPIONSHIP ROUNDPROBLEM ONEConsecutive numbers are whole numbersthat follow in order such as 3, 4, 5.FIND THE SMALLEST OF THE FIVE CONSECUTIVENUMBERS WHOSE SUM IS 100.2006 BICENTENNIAL MATH OLYMPIADCHAMPIONSHIP ROUNDPROBLEM TWOThe number of Timbits in this box is more than40 but less than 80. If the Timbits aredivided evenly between 5 kids, there will be 2dougnuts left over. If they are divided evenlybetween 7 kids, there will be 4 left over.HOW MANY TIMBITS ARE THERE IN THE BOX?

2006 BICENTENNIAL MATH OLYMPIADCHAMPIONSHIP ROUNDPROBLEM THREEEach of the three diagrams at the rightshows a balance of weights usingdifferent objects.HOW MANY“ s” WILLBALANCE A“O”?2006 BICENTENNIAL MATH OLYMPIADCHAMPIONSHIP ROUNDPROBLEM FOURThe square at the right is divided into fourcongruent rectangles. The perimeter of eachof the four congruent rectangles is 25 units.HOW MANY UNITS ARE THERE IN THE PERIMETER OFTHE SQUARE?

2006 BICENTENNIAL MATH OLYMPIADCHAMPIONSHIP ROUNDPROBLEM FIVETickets for the Rolling Stones concertcost 20 each for children and 50 eachfor adults. A group of thirty peopleconsisting of children and adults paid atotal of 870 for the concert.HOW MANY ADULTS WERE IN THE GROUP?2006 BICENTENNIAL MATH OLYMPIADCHAMPIONSHIP ROUNDANSWER KEYPROBLEM ONE18PROBLEM TWO67PROBLEM THREE6PROBLEM FOUR40PROBLEM FIVE9

2006 BICENTENNIAL MATH OLYMPIAD GRADE SEVENPROBLEM ONETwo cash registers of a store had acombined total of 300. When themanager transferred 15 from oneregister to the other register, eachregister then had the same amount.HOW MUCH DID THE REGISTER WITH THE LARGERAMOUNT HAVE BEFORE THE TRANSFER WAS MADE?2006 BICENTENNIAL MATH OLYMPIAD GRADE SEVENPROBLEM TWOSuppose the time is now 2 o’clock on atwelve-hour clock which runs continuously.WHAT TIME WILL IT SHOW 1000HOURS FROM NOW?

2006 BICENTENNIAL MATH OLYMPIAD GRADE SEVENPROBLEM THREEIn the figure at the right, eachnumber represents the length ofthe segment which is nearest it.HOW MANY SQUARE UNITSARE IN THE AREA OF THE FIGURE IF THERE IS ARIGHT ANGLE AT EACH CORNER OF THE FIGURE?2006 BICENTENNIAL MATH OLYMPIAD GRADE SEVENPROBLEM FOURLisa went to Mic Mac Mall with a pocket full ofmoney. She spent one-third of her money atThe Gap. Then she went to the food court andspent one-third of what remained. When Bartasked to borrow some money, Lisa checked herpockets and discovered that she had twelvedollars left.HOW MUCH MONEY DID LISA HAVE TO BEGIN WITH?

2006 BICENTENNIAL MATH OLYMPIAD GRADE SEVENPROBLEM FIVEA restaurant has a total of 30 tableswhich are of two types. The firsttype seats two people at each table;the second type seats five people ateach table. A total of 81 people areseated when all seats are occupied.HOW MANY TABLES FOR TWO ARE THERE?2006 BICENTENNIAL MATH OLYMPIADANSWER KEYPROBLEM ONEPROBLEM TWO1656:00PROBLEM THREE58PROBLEM FOUR27PROBLEM FIVE23GRADE SEVEN

2006 BICENTENNIAL MATH OLYMPIADPROBLEM ONEGRADE EIGHTA slow 12-hour clock loses 3 minutes everyhour. Suppose the slow clock and a correctclock both show the correct time at 9 AM.WHAT TIME WILL THE SLOW CLOCKSHOW WHEN THE CORRECT CLOCK SHOWS 10 O’CLOCKTHE EVENING OF THE SAME DAY?2006 BICENTENNIAL MATH OLYMPIADPROBLEM TWOGRADE EIGHTLast June, the average amount of rain thatfell during the last week of school (Mondayto Friday - five days) was 6 cm. If Friday’srainfall is not counted, the average of thefour remaining days is 7 cm.HOW MUCH RAIN FELL ON THE LAST DAY OF SCHOOLLAST YEAR?

2006 BICENTENNIAL MATH OLYMPIADPROBLEM THREEGRADE EIGHTAt the right, there are two largecongruent squares with sides 7 unitslong and four small congruent squareswith sides 3 units long.IF THE SHADED FIGURE IS ALSO A SQUARE, WHAT ISITS AREA IN SQUARE UNITS?2006 BICENTENNIAL MATH OLYMPIADPROBLEM FOURThe cost of a Mad Magazine in 1985 was 1and a whole number of cents. The total costof six copies of this magazine was less than 8. However, the total cost of seven copiesof the same magazine, at the same price permagazine, was more than 8.WHAT IS THE LEAST A SINGLE COPYOF THE MAGAZINE COULD HAVE COST?GRADE EIGHT

2006 BICENTENNIAL MATH OLYMPIADPROBLEM FIVEGRADE EIGHTCurious George was hired to delivernewspapers for 8 weeks at a fixed hourlyrate. But instead of being given only money,he was to be given 85 and a box ofbananas. However, Curious George got intoa little trouble with a customers’ cat andwas only able to work 5 weeks. His bossgave him 25 and the box of bananas.HOW MUCH WAS THE BOX OF BANANAS WORTH?2006 BICENTENNIAL MATH OLYMPIADANSWER KEYPROBLEM ONE9:21PROBLEM TWO2PROBLEM THREE25PROBLEM FOUR1 15PROBLEM FIVE75GRADE EIGHT

2006 BICENTENNIAL MATH OLYMPIADPROBLEM ONEGRADE NINEDuring her first week as a waitress, Aliceearned a total of 65 for working five daysafter school. Because her tips kept gettingbetter, each day after the first day she earned 2 more than she earned the day before.HOW MUCH DID SHE EARN ON THE FIRST DAY?2006 BICENTENNIAL MATH OLYMPIADPROBLEM TWOGRADE NINEABCD is a square with area 16 squaremeters. E and F are midpoints of sidesAB and BC, respectively.WHAT IS THE AREA OF TRAPEZOID AEFC, THESHADED REGION?

2006 BICENTENNIAL MATH OLYMPIADPROBLEM THREEGRADE NINEIn Beach Basketball, a field goal is worth 2points and a foul shot is worth 1 point.Suppose a team scored 72 points and made 6more field goals than foul shots.HOW MANY FOUL SHOTS DID THETEAM MAKE?2006 BICENTENNIAL MATH OLYMPIADPROBLEM FOURGRADE NINEIf you start with 3 and count by 7s, you get theterms of the sequence 3, 10, 17, , 528 where3 is the 1st term, 10 is the 2nd term, 17 is the3rd term, and so forth up to 528 which is theNth term.WHAT IS THE VALUE OFN?

2006 BICENTENNIAL MATH OLYMPIADPROBLEM FIVEGRADE NINEJimmy needs one hour to paint the fence.George, his older brother, can paint thesame fence in ½ hour.HOW MANY MINUTES WILL IT TAKE THEM TO PAINTTHE FENCE IF THEY WORK TOGETHER?2006 BICENTENNIAL MATH OLYMPIADANSWER KEYPROBLEM ONE9PROBLEM TWO6PROBLEM THREE20PROBLEM FOUR76PROBLEM FIVE20GRADE NINE

2007 MATH OLYMPIAD CHALLENGE ROUNDPROBLEM ONEAdd THIS to THAT,then divide by three.The square of THIS,you’ll surely see.But THAT toTHIS is eight toone.So figure what they are, for fun!

PROBLEM TWOMarty loves mathand marbles. He is holding a contest at school that involvesboth of these things in order to raise money to send theschool’s math team to the National Championships. Martydistributed 100 marbles among five arblesHOW MANY MARBLES ARETHERE IN EACH BAG?

PROBLEM THREEA beam of light shinesfrom point S, reflects offa reflector at point P, andreaches point T so that PTis perpendicular to RS.What is the measurement of angle x?

2006 BICENTENNIAL MATH OLYMPIAD GRADE EIGHT PROBLEM ONE A slow 12-hour clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 AM. WHAT TIME WILL THE SLOW CLOCK SHOW WHEN THE CORRECT CLOCK SHOWS 10 O’CLOCK THE EVENING OF THE SAME DAY? 2006