1. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Welcome To The Mathematics Challenge 50:50 How good are you at Maths? The questions in this quiz have all been taken from publications by the Australian Mathematical Trust (in association with The Mathematical Association of Victoria). Click on the correct answer to each question to move to the next level. If you choose the wrong answer you will get a message. Be warned – the questions get harder the further you go. See how much your knowledge of Maths could gain you. Click button to start quiz Note: You can use the 50:50, Telephone and Group icons if you need assistance, but only one time each. Stop

2. A: 3 kg C: 5 kg B: 9 kg D: 8 kg 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 A set of scales for weighing pumpkins has a set of three weights: 1kg, 4kg and 7kg Using these weights, what is the lightest pumpkin which cannot be weighed if all the pumpkins weigh a whole number of kilograms? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

3. A: 23 degrees C: 27 degree B: 25 degrees D: 29 degrees 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 The maximum daily temperatures for a week are shown on the graph. If the average temperature for the 5 days was 25 degrees what was the temperature on Friday? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution Mon TueWedThuFri 24 22 28

4. A: 20 C: 21 B: 22 D: 19 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 A basketball player averaged 17 points in his first eight games and 24 points in his next six games. What is his overall average for the 14 games? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

5. A: $160 C: $140 B: $150 D: $130 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Joanne plans to open a savings account and a cheque account. She has decided to deposit a total of $45 per week - $20 goes into the cheque account each week and the remaining money goes into the savings account. When she has deposited a total of $200 into her savings account, how much will she have deposited into her cheque account? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

6. A: 12 C: 16 B: 14 D: 18 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Lisa collected 50 seashells over a period of five days. Each day she collected three more than she had collected the day before. How many shells did she collect on the fifth day? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

7. Youve Reached the $1,000 Milestone! Congratulations! C o n g r a t u l a t i o n s ! Click button to continue StopPrevious

8. A: 25 C: 42 B: 36 D: 49 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 In the year 5 classroom the desks are arranged in equal rows. Aaron sits at the desk that is fourth from the front and third from the back. There are four desks on the right of Aarons desk but only one to the left. How many desks are there in the room? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

9. A: 6 C: 4 B: 5 D: 3 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Remember - click on one of these lifelines if you need assistance Mels crayons are red, green and blue and he has at least one green crayon. If all of them are green except two, all of them are blue except 2 and all are red except 2, how many crayons does Mel have? StopPrevious See Solution

10. A: 25kg C: 34kg B: 28kg D: 53kg 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Sally and Fred weigh a total of 59kg when they stand on the scales together. Sally and Anne together weigh only 53kg. Fred and Anne together weigh 62kg. How much does Sally weigh? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

11. A: 9 C: 11 B: 10 D: 12 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 In a soccer tournament eight teams play each other once, with two points awarded for a win, one point for a draw and zero for a loss. How many points must a team score to ensure that it is in the top four (ie has more points than at least four other teams)? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

12. A: 16kg C: 10kg B: 13kg D: 8kg 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 A large watermelon weighs 20kg, with 98% of its weight being water. It is left to stand in the sun, and some of the water evaporates so that now only 95% of its weight is water. What does it now weigh? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

13. Youve Reached the $32,000 Milestone! Congratulations! C o n g r a t u l a t i o n s ! Click button to continue StopPrevious

14. A: 50kg C: 70kg B: 60kg D: 80kg 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 A large container of rice is one- third full of rice. 20kg of rice is then added and this makes the container half full. How many more kilograms of rice are needed to fill the container? 50:50 Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

15. A: 6 hours C: 4 hours B: 5 hours D: 2 hours 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Three water pipes are used to fill a tank. The first pipe, by itself, takes 8 hours to fill the tank The second pipe, by itself, takes 12 hours to fill the tank The third pipe, by itself, takes 24 hours to fill the tank How long would it take to fill the tank, from empty, if all the pipes were used at the same time? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

16. A: Cheung & Evita C: Dilip & Abdul B: Abdul & Betty D: Evita & Betty 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Abduls class has a set of 30 lockers arranged in 3 rows of 10 and numbered 1 to 30 starting from the top left hand corner and counting across each row from left to right until reaching the bottom right hand corner. If: Abdul has locker number 7 Bettys locker is below Abduls and 2 to the left Cheung has a locker with a number 6 more than Bettys locker Dilip has a locker two rows above Cheungs Evitas locker is five to the right and one below Dilips which two students have lockers next to each other? Remember - click on one of these lifelines if you need assistance 3029282726252423 2221 2019181716151413 1211 109876543 21 StopPrevious See Solution

17. A: 2 C: 4 B: 3 D: 5 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 In a survey of 50 students: 42 said they disliked eating spinach 37 said they disliked eating cabbage 31 students said they disliked both spinach and cabbage How many students liked eating both spinach and cabbage? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

18. A: 10 C: 12 B: 11 D: 13 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 When a class of students is split into groups of four, there are two students left. When split into groups of five, there is one left. There are 15 girls in the class and a smaller number of boys. How many boys are in the class? Remember - click on one of these lifelines if you need assistance StopPrevious See Solution

19. YOU WIN Congratulations! C o n g r a t u l a t i o n s ! StopPrevious

20. …………….. so the answer must be the 9kg pumpkin A set of scales for weighing pumpkins has a set of three weights: 1kg, 4kg and 7kg Using these weights, what is the lightest pumpkin which cannot be weighed if all the pumpkins weigh a whole number of kilograms? One Side of ScaleOther Side of Scale A 1kg pumpkinPumpkin1kg A 2kg pumpkinPumpkin + 1kg + 4kg7kg A 3kg pumpkinPumpkin + 1kg4kg A 4kg pumpkinPumpkin4kg A 5kg pumpkinPumpkin1kg + 4kg A 6kg pumpkinPumpkin + 1kg7kg A 7kg pumpkinPumpkin7kg A 8kg pumpkinPumpkin7kg + 1kg A 9kg pumpkinNo combinationpossible The possible combinations to balance both sides are: Return

21. Since the average temperature for the 5 days was 25 degrees then the sum of the temperatures for 5 days is 5 * 25 = 125 Therefore Fridays temperature must be 125 - 24 - 22 - 22 - 28 = 29 degrees The maximum daily temperatures for a week are shown on the graph. If the average temperature for the 5 days was 25 degrees what was the temperature on Friday? Return Mon TueWedThuFri 24 22 28

22. Average Score = Total Points Scored divided by Games Played Therefore: Total Points = (17 × 8) + (24 × 6) = 280 Total Games = 14 Average = 280 ÷ 14 = 20 A basketball player averaged 17 points in his first eight games and 24 points in his next six games. What is his overall average for the 14 games? Return

23. The ratio of money in the cheque account to the money in the savings account is: Cheque ÷ Savings = 20 ÷ 25 = 4 ÷ 5 So the money in the cheque account is 4 ÷ 5 of $200 = $160 Joanne plans to open a savings account and a cheque account. She has decided to deposit a total of $45 per week - $20 goes into the cheque account each week and the remaining money goes into the savings account. When she has deposited a total of $200 into her savings account, how much will she have deposited into her cheque account? Return

24. Lets say Lisa collected 1 shell on the first day. Then, over the five days the number of shells she would have collected is 1 + 4 + 7 + 10 + 13 = 35. This is 15 short of the 50 she actually collected, so working backwards from this, she must have collected an extra 15 ÷ 5 = 3 shells per day. Therefore, she must have collected 4, 7,10, 13, 16 shells on each of the five days, and so …………………….16 shells were collected on the fifth day. Lisa collected 50 seashells over a period of five days. Each day she collected three more than she had collected the day before. How many shells did she collect on the fifth day? Return

25. Since Aaron sits at a desk fourth from the front and third from the back, there must be 6 rows of desks. Since there are four desks to the right of Aarons and one to the left, there must be 6 columns of desks. Since there are then 6 rows and 6 columns of desks in the classroom, there are ……………………. 6×6 = 36 desks in total In the year 5 classroom the desks are arranged in equal rows. Aaron sits at the desk that is fourth from the front and third from the back. There are four desks on the right of Aarons desk but only one to the left. How many desks are there in the room? Return

26. Since the statements imply that there is at least one green, one blue and one red crayon, then for each of the statements all of them are green except two, all of them are blue except two, all of them are red except two, to be true, there can be no more then 3 pens, one of each colour, otherwise at least one of the above statements would be false. …………… so Mel has three crayons. Mels crayons are red, green and blue and he has at least one green crayon. If all of them are green except two, all of them are blue except 2 and all are red except 2, how many crayons does Mel have? Return

27. Fred and Anne together weigh 62kg and Fred and Sally together weigh 59kg. This means that Anne weighs 3kg more than Sally. Now, since Sally and Anne together weigh 53 kg, if we take 3 kg from the 53 kg (= 50kg), this must be twice Sallys weight. …………… so Sally weighs 50 ÷ 2 = 25kg Sally and Fred weigh a total of 59kg when they stand on the scales together. Sally and Anne together weigh only 53kg. Fred and Anne together weigh 62kg. How much does Sally weigh? Return

28. Since there are 8 teams, there are 7 rounds of four matches and thus a total of 7 × 8 = 56 points available Now - consider a team with 10 points. It is possible to have 5 teams on 10 points and 3 teams on 2 points (when each of the top 5 draws with each other, each of the bottom 3 draws with each other and each of the top 5 wins against each of the bottom 3). So 10 points does not guarantee a place in the top 4. Consider a team with 11 points. If this team was fifth then the number of points gained by the top 5 teams is greater than or equal 55. This is impossible ( as the number of points shared by the bottom 3 teams would then be 1, as these 3 teams must have at least 3 × 2 = 6 points between them for the games played between themselves). ……………hence 11 points is sufficient to ensure a place in the top 4. In a soccer tournament eight teams play each other once, with two points awarded for a win, one point for a draw and zero for a loss. How many points must a team score to ensure that it is in the top four (i.e. has more points than at least four other teams)? Return

29. Originally, 98% of the watermelon is water, so the solids are 2% or 1/50 of its weight Hence 1/50 × 20kg = 2/5 kg. When the water becomes 95% of its weight, these solids become 5% or 1/20 of its weight Hence the watermelons weight is 20 × 2/5kg = 8kg (i.e. 1/20 of its weight must equal 2/5kg) A large watermelon weighs 20kg, with 98% of its weight being water. It is left to stand in the sun, and some of the water evaporates so that now only 95% of its weight is water. What does it now weigh? Return

30. When the 20kg of rice is added the container goes from 1/3 full to 1/2 full which is the same as from 2/6 full to 3/6 full Therefore, 20kg = 1/6 of the container which means the whole container is 120kg in size. Thus, to fill it from half full would require 60kg A large container of rice is one- third full of rice. 20kg of rice is then added and this makes the container half full. How many more kilograms of rice are needed to fill the container? Return

31. The first pipe takes 8 hours to fill the tank, the second pipe takes 12 hours and the third pipe takes 24 hours. Therefore, in a day (24 hours): The first pipe will have filled the tank 3 times The second pipe will have filled the tank 2 times The third pipe will have filled the tank once So all of the pipes will have filled the tank 6 times in 24 hours thus they will fill the tank once in 24 ÷ 6 = 4 hours Three water pipes are used to fill a tank. The first pipe, by itself, takes 8 hours to fill the tank The second pipe, by itself, takes 12 hours to fill the tank The third pipe, by itself, takes 24 hours to fill the tank How long would it take to fill the tank, from empty, if all the pipes were used at the same time? Return

32. From the information provided: Abdul has locker number 7 Betty has locker number 15 (7 + 10 - 2) Cheung has locker number 21 (15 + 6) Dilip has locker number 1 (21 - 20) Evita has locker number 16 (1 + 5 + 10) Therefore Betty and Evita have lockers next to each other Abduls class has a set of 30 lockers arranged in 3 rows of 10 and numbered 1 to 30 starting from the top left hand corner and counting across each row from left to right until reaching the bottom right hand corner. If: Abdul has locker number 7 Bettys locker is below Abduls and 2 to the left Cheung has a locker with a number 6 more than Bettys locker Dilip has a locker two rows above Cheungs Evitas locker is five to the right and one below Dilips which two students have lockers next to each other? 3029282726252423 2221 2019181716151413 1211 109876543 21 Return

33. If 31 students disliked eating both spinach and cabbage then there must be 11 students who disliked eating only spinach (42 - 31) Similarly, if 31 students disliked eating both spinach and cabbage then there must be 6 students who disliked eating only cabbage (37 - 31) This means that there are 31 + 11 + 6 = 48 students who disliked eating spinach or cabbage or both spinach and cabbage. Therefore, as there are 50 students, there must be 2 who liked eating both spinach and cabbage In a survey of 50 students: 42 said they disliked eating spinach 37 said they disliked eating cabbage 31 students said they disliked both spinach and cabbage How many students liked eating both spinach and cabbage? Return

34. Since there are fewer boys than girls, the total number of students must be between 16 and 29 When they are split into groups of 4 there are two left – so the possibility of numbers of students are 18, 22, and 26. When they are split into groups of 5 there is one student left, in this case the possibility of numbers are 16, 21, 26 The only number satisfying both conditions is 26 Therefore, there must be 26 - 15 = 11 boys When a class of students is split into groups of four, there are two students left. When split into groups of five, there is one left. There are 15 girls in the class and a smaller number of boys. How many boys are in the class? Return

35. Bad Luck Try Again! Return