Problem solving

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2011 Problem Solving
(Problem, Hints, Solution and Answer)

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Problem solving

  1. 1. 2011 Calendar Problem Solving
  2. 2. LORETO MORALES MARIELLA ALEXES ROMBAOA MECHILLE LACUESTA DIAN MENESES CAROLYN GRANDEFree Powerpoint Templates JOYCE ESTEBAN MYRELL
  3. 3. Click thered arrow to open theproblemonths
  4. 4. 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1516 17 18 19 20 21 2223 24 25 26 27 28 2930 31 BACK TO LIST
  5. 5. FEBRUARY 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 56 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 BACK TO LIST
  6. 6. MARCH 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  7. 7. APRIL 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 910 11 12 13 14 15 1617 18 19 20 21 22 2324 25 26 27 28 29 30 BACK TO LIST
  8. 8. MAY 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30 31 BACK TO LIST
  9. 9. JUNE 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 BACK TO LIST
  10. 10. JULY 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  11. 11. AUGUST 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  12. 12. SEPTEMBER 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 BACK TO LIST
  13. 13. 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  14. 14. NOVEMBER 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 BACK TO LIST
  15. 15. DECEMBER 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  16. 16. Batman has been imprisoned by the Riddler. To escape he must find the quickest way to move the tower ofplutonium disks from one post to another so that the disks have the same arrangement as on the original post. Hemay move only one disk at a time. What is the minimum number of moves he mustmake in order to move the ten disk tower and have it appear the same? Hint and answer
  17. 17. Hints:1) Batman can put all disks on one post and then switch tothe second post in 20 moves. How would he reduce his task?Answer: The quickest way is to move each diskonto the first post except for the last disk -> which is 9moves. Then move the last disk to the secondpost which is one move. Then move each of the disks on the firstpost to the second post which is an additional 9 moves. 9 + 9 + 1 = 19 moves BACK
  18. 18. Seth and Bob each began reading a HardyBoys book today. If Seth reads 8 pages eachday and Bob reads 5 pages each day, whatpage will Bob be reading when Seth isreading page 56? (Hint: Complete the table.) Day Seths Page Bobs Page 1 8 5 2 16 10 3 24 15 Hint and answer
  19. 19. Day Seths Page Bobs Page 1 8 5 2 16 10 3 24 15 4 32 20 5 40 25 6 48 30 7 56 35BACK
  20. 20. How many differentcubes can you make ifeach face of a givencube has a lineconnecting the centerpoints of two oppositeedges?Hint and answer
  21. 21. Hint:1) There are three sets of opposing faces that will be split into four. BACK 23 = 8 cubes
  22. 22. Find the number of faces, edges and vertices on the figure shown.•What would this figure be called?•What would the two figures contained in it be called? Hint and answer
  23. 23. Hints:NONE!Answer: 17 edges 9 faces 10 verticesPentagonal Prism contains a rectangular prismand a right trianglular prism. BACK
  24. 24. Scientists have just discovered people on Neptune. There are 3villages, 2 cities and 1 super city on Neptune. These are thepopulations in 1994 and 1996. 1994 1996 Eilosa 129 204 Vertu 308 292 Pridi 90 50 Dedrun 500 600 Antran 700 693 Maran 1200 1500List the places in order of increasing size in 1994 and 1996.In which year was the population of the planet greater? Hint and answer
  25. 25. Hints:Sum each column!Solution and Answer: 1994 1996 Eilosa 129 204 Vertu 308 292 Pridi 90 50 Dedrun 500 600 Antran 700 693 Maran 1200 1500 ----------------- 2927 3339 3339 - 2927 = 412 therefore the population in 96 is greater BACK
  26. 26. Can you find allof the spokes? Adigit on a hubdenotes thenumber ofspokes that meetthere. Spokesnever cross andin the endeverything willbe connected. Answer
  27. 27. Answer BACK
  28. 28. A farmer grows 252 kilograms of apples. He sells them to a grocer who divides them into 5 kilogram and 2 kilogram bags. If the grocer uses the same number of 5 kg bags as 2kg bags, then how many bags did he use in all?Need A Hint? And Answer
  29. 29. Hints:1) Let x = total number of bagsAnswer: Let x = total number of bags5(1/2 x) + 2 (1/2 x) = 252 2.5x + 1x = 252 3.5x=252 x = 72 bags. BACK
  30. 30. This is a turtle graphics problem.A bug is walking across the doorstep of a house. When hestarts out he is facing the house at the opposite side of thedoorstep. If he goes 3 units left, 1 unit right, 2 units left, 8units left, what will the bug have to do to get back wherehe started as quickly as possible without retracing hissteps? Hint and answer
  31. 31. Hints:1) Remember, you face the direction you go!2) Draw a diagram. HOUSE Answer: 1 unit left and 3 units left. BACK
  32. 32. Three ducks and two ducklingsweigh 32 kg. Four ducks and threeducklings weigh 44kg. All ducksweigh the same and all ducklingsweigh the same. What is the weightof two ducks and one duckling?Hint and answer
  33. 33. Hints: 1) Set up two equationsAnswer: Let D = the weight of one duck d = the weight of one ducklingSolve:(3D + 2d = 32)*3 ------> 9D + 6d = 96 (4D + 3d = 44)*2 ------> 8D + 6d = 88 ______________ 1D + 0d = 8 -----> D = 8 Substitute to solve for d: 4D + 3d = 444(8) + 3d = 44 32 + 3d = 44 3d = 12 d=4Thus, 2D + d = 2(8) + 4 = 20 kgs. BACK
  34. 34. It takes one man one day to dig a 2m x 2m x2m hole. How long does it take 3 menworking at the same rate to dig a 4m x 4m x4m hole? If you can finish these problem, youll be smarter than I am.Hint and answer
  35. 35. Hints:1) Find rate of one manAnswer: Let x = rate of one man = 23 m3/ 1 day = 8m3/day 3x = rate of three men = 3(8m3/day) = 24m3/dayVolume to be shoveled = 64m3Therefore, it would take three men 64m3/(24m3/day) = 2 2/3 days BACK
  36. 36. Hints: 1) Try putting addition signs between the different numbers. 2) Try this example: ANSWER:1) 9+8+7+65+4+3+2+1 = 99 -> 7 addition signs.2) 9+8+7+6+5+43+21 = 99 -> 6 addition signs. BACK
  37. 37. A 800 seat multiplex is divided into 3 theatres. There are 270 seats in Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many seats are in Theatre 2?Hint and answer
  38. 38. Hints:1) Let x = seats in Theatre 3. Then number of seats in Theatre 2= x + 150 seats.Answer: Let x = number of seats in Theatre 3 T1 = Theatre 1 = 270 seats T2 = Theatre 2 = 150 + x T1 + T2 + T3 = 800 seats 270 + (150 + x) + x = 800 420 + 2x = 800 x = 190If there are x = 190 seats in theatre 3,then Theatre 2 has150 + 190 = 340 seats BACK
  39. 39. HINT:1) Draw a diagram -> use least common multiples. x = Frog 1 o = Frog 2ANSWER:• How many numbers between 1 and 18 are multiples of 2 and 3?• 6, 12, 18[ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o]• 1 2 3• There will only be 3 lily pads that both frogs jump on• - Number 6, 12 and 18. BACK
  40. 40. ANSWER: (3/10)*? = 24 and 24/(3/10) = 80. Aunt Helen is 80 years old. BACK
  41. 41. Question: It takes one man one day to dig a 2m x 2m x 2m hole. How long does it take 3 men working at the same rate to dig a 4m x 4m x 4m hole?Hint and answer
  42. 42. Hint: Find rate of one manAnswer:Let x = rate of one man = 23 m3/1day = 8m3/day 3x = rate of three men = 3(8m3/day) = 24m3/day Volume to be shoveled = 64m3 Therefore, it would take three men 64m3/(24m3/day) = 2 2/3 days BACK
  43. 43. Hint and answer
  44. 44. Hint: To find the answers, multiples of 2.Answer: To find the multiples of a number, multiply that number by 0, 1, 2, 3, 4, 5…… 2 (0) = 0 2 (1) = 2 2(2) = 4 2 (4) = 8 2 (5) = 10 The next 3 garbage bins are placed near the 6th, 8th, and 10th houses. BACK
  45. 45. Question: A farmer grows 252 kilograms of apples. He sells them to a grocer who divides them into 5 kilogram and 2 kilogram bags. If the grocer uses the same number of 5 kg bags as 2kg bags, then how many bags did he use in all?Hint and answer
  46. 46. Hint: Let x = total number ofbagsAnswer: Let x = total number of bags 5(1/2 x) + 2 (1/2 x) = 252 2.5x + 1x = 252 3.5x = 252 x = 72 bags. BACK
  47. 47. Question:A 800 seat multiplex is divided into 3 theatres. There are 270 seats in Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many seats are in Theatre 2?Hint and answer
  48. 48. Hint :Let x = seats in Theatre 3. Then number of seats inTheatre 2 = x + 150 seats .Answer: Let x = no. of seats in Theatre 3 T1 = Theatre 1 = 270 seats t2 = Theatre 2 = 150 + x T1 + T2 + T3 = 800 seats270 + (150 + x) + x = 800 420 + 2x = 800 x = 190 If there are x = 190 seats in theatre 3, thenTheatre 2 has150 + 190 = 340 seats BACK
  49. 49. Question: In 1969 the price of 5 kilograms of flour was P0.75. In 1970 the price was increased 15 percent. In 1971, the 1970 price was decreased by 5 percent. What was the price of 5 kilograms of flour in 1971?Hint and answer
  50. 50. Hint: Let 1970 cost = (P0.75)*1.15Answer: If the price of 5 Kg of flour in 1969 = P0.75, then 1970 = P0.75 x 1.15 = P0.8625 1971 = (PO0.75 x 1.15) x .95 = P0.82 BACK
  51. 51. Question: A rectangular sheetof wood has four smallsquares removed. It isthen cut to make a boxthat is 5cm by 4cm witha volume of 60cm3.(Four pieces of size A4are removed.) Find theoriginal area of thesheet of wood.Hint and answer
  52. 52. Hint: Open top boxAnswer: l x h x w = 60 h(5)(4) = 60 h=3A(1) = 4 x 5 = 202A(2) = 2(3)(5) = 302A(3) = 2(3)(4) = 244A(4) = 4(3)(3) = 36 Total A = A(1) + 2A(2) + 2A(3) + 4A(4) = 20 + 30 + 24 + 36 = 110cm2 BACK
  53. 53. Question: Mary has $50.00. She goes to the mall and buys lipstick and then she buys shampoo, which is half the price of the lipstick. She then spends half of what she has left on a purse, leaving her with $15.00. How much did the shampoo cost? How much did the lipstick cost?Hint and answer
  54. 54. Hint: Purse cost $15.00Answer: Let x = price of lipstick 1/2 x = price of shampoo Cost of lipstick AND shampoo,combined = x + 1/2xMoney spent on lipstick and shampoo combined: $50.00 - ($15.00)*2 = $20.00Therefore, x + 1/2 x = $20.00 1.5x = $20.00 x = $13.33 Lipstick cost: x = $13.33 Shampoo cost: 1/2 x = 1/2 * $13.33 = $6.67 BACK
  55. 55. Question: Stephanie had P40.00 savings. Her mother gave her another P30.00 and her grandmother gave her P10.00 to buy a pair of cleats. The pair of cleats Stephanie wants costs P54.99. If Stephanie buys the cleats at a no TAX sale, write an equation using a variable to describe the amount of money that Stephanie will have to contribute from her savings. Solve for the variable.Hint and answer
  56. 56. Hint :Stephanie spends all of money from her mother and grandmotherAnswer:Let x = Stephanie‘s contribution.P30.00 + P10.00 = P40.00P40.00 + x = P54.99 x = P14.99 BACK
  57. 57. Question: Given a rectangular prism. If the sides of the rectangle A have the same ratio to each other as the sides of rectangle B, then what is (a) The surface area of the prism? (b) The volume of the prism? Hint and answer
  58. 58. Hint: 1.Find length of x first 2.Find area of A and area of BAnswer: Dimensions B: 5/8 = 8/x 64 = 5x 12.8 = x (a) Surface Area = 2 * Area A + 2 * Area B + Area (top) + Area (bottom) = 2(8*5) + 2(8*12.8) + 2(5*12.8) = 412.8(b) Volume = l x w x h = (12.8)(5)(8) = 512 BACK
  59. 59. Question: The trails in a park resemble the following diagram. Find the total length of the trails, given that all the circles have the same area and circle 2 is tangent to the midpoint of L.Hint and answer
  60. 60. Hint: W = diameter = 2rAnswer:2r + 3L + 3w + 3pi*a = 2(10) + 3(100) + 3(20)+3pi(20) = 568.50m(2r+L) + 2L + 3W + 3piW = (2(10)+40) + 2(40) + 3(20) 3pi(20) = 388.50 m BACK
  61. 61. Question:The rent-a-stall horse barn has stalls for 1000 horses. Forty percent of the stalls are for ponies. On Tuesday, there were 200 ponies and a bunch of quarter horses at the horse barn. The horse barn was 75 percent full.How many quarter horses were in the stalls?Hint and answer
  62. 62. Hint: Find total number of stalls filledAnswer: 75% full = 75% * 1000 horses = 750 horsesIf there are 200 ponies, there must be (750 - 200) = 550 quarter horses BACK
  63. 63. Question: A rectangular chalk board is 3 times as long as it is wide. If it were 3 meters shorter and 3 meters wider, it would be square. What are the dimensions of the chalk board?Hint and answer
  64. 64. Hint: Sides of square are equalAnswer:Let x= width of chalkboard Therefore, 3x = length of chalkboardSince sides of square are equal, 3x - 3 = x + 3 2x = 6 x=3 Dimensions of chalkboard: width = x = 3 meters widelength = 3x = 9 meters long BACK
  65. 65. Question: Three people share a car for a period of one year and the mean number of kilometers traveled by each person is 152 per month. How many kilometers will be traveled in one year?Hint and answer
  66. 66. Find total number of kilometersHint:traveled per monthAnswer: 3 x 152km/month x 12 months/year = 5472 km/year BACK
  67. 67. Question:A car dealer claims that by buying a new car Mike will pay 1/5 less for gas then he pays for the car he currently drives. If the car Mike currently drives costs 1/6 less to gas up than Daves car, and Dave pays $700.00 per year, what will it cost Mike to put gas in a new car for one year (assuming all cars will be traveling the same distance)?Hint and answer
  68. 68. Hint: 1/6 less than 700 = 5/6(700)Answer: (700.00)(5/6)(4/5) = $466.67 BACK
  69. 69. Question:A side of the equilateral triangle A is twice the length of a side of triangle B.How many triangle B will fit into triangle A?Hint and answer
  70. 70. Hint: Draw triangle A and fit triangle Bs into it 2) How manytimes will the area of B divide the area of A?Answer: 4 triangles BACK
  71. 71. Question: A storage facility has space for 225 - 8 liter boxes and 515 - 27 liter boxes. What is the volume of the facility? What percent of the total volume is filled by 150 of the 8 liter boxes and 5 of the 27 liter boxes?Hint and answer
  72. 72. Hint: Total volume = 8 * 225 + 27 *515Answer:a) 225*8litres+515*27liters=TotalVol 15705 litres = 15.705 kilolitresb) [(150*8 + 5*27) / 15705] x 100 percent = 8.500 percent. BACK
  73. 73. Question: Marvins Taxi Service charges $0.30 for the first kilometer and $0.05 for each additional km. If the cab fare was $3.20, how far did the Taxi go?Hint and answer
  74. 74. Hints:Total volume = 8 * 225 + 27 * 515Answer:Cost of first kilometer = $0.30 Total cost of additional kilometers = (3.20 - 0.30) = 2.90Total number of kilometers = 1 +($2.90/$0.05) = 1 + 58 = 59 km BACK
  75. 75. Question: What fraction of this square is shaded?Hint and answer
  76. 76. Hints:Use table to calculate total amount of gas used by eachpersonAnswer:Total area of square = (1/4 + 3/4)*(2/3 + 1/3) =1*1 =1Shaded area = (2/3 * 3/4) = 0.5Fraction of Total area shaded =0.5/1 = 50% BACK
  77. 77. Question: The number of hours left in a day on Mars was 1/4 of the number of hours that had already passed. How many hours were left in the day? Day on Mars 40 hours.Hint and answer
  78. 78. Hints:Total area of square = (1/4 + 3/4) * (2/3 + 1/3) = 1*1=1 Answer:Let x = the number of hours that had already passed1/4 x = the number of hours remaining IF total number of hours in a day = 40, THEN x + 1/4x = 40 5/4x = 40 160x = 5 x = 160/5 x = 32Hours remaining = 1/4 x = 1/4(32) =8 BACK
  79. 79. Question: A cereal company decided to increase the height of its boxes by 30 percent and reduce the width in order to maintain the same volume. If initially, length 20cm height 40cm width = 30cm What will the new height and width be if length stays the same?Hint and answer
  80. 80. Hints:An increase in the height h by 30% is (1+0.3)h=1.3h.Answer: Volume = l * w * h = (20)(30)(40)cm3 = 24000cm3New height = initial h + 0.3h = 1.3h = 1.3 * 40cm = 52 cmIF height = 52 cm, solve for w:Volume = l * w * h 24000 cm3 = (20cm)(w)(52cm) 24000 cm3 = 1040(w)cm2 w = 23.08 cm BACK
  81. 81. Question: of times a dog barks depends on the The number number of cars passing. How many cars have passed when a dog barks 22 times? How many barks for 5 cars? Cars Barks ------+------- 6 | 4 7 | 7 8 | 10 9 | 13 10 | 16 Hint and answer
  82. 82. Hint: Look for a pattern: Begin at the bottom of the column - subtractthe first number from the next number and compare to the difference of thecorresponding two numbers in the other column.Answer: Pattern: 6 - 13 = 3 10 - 7 = 3 0-9=1 8-7=1 3 barks for 1 car Therefore, 22 barks for 12 cars. BACK
  83. 83. Hints: Divide the face of the clock into three parts with two lines so that the sum of the numbers in the three parts are equal. 1) Divide the clock into three parts with two lines. Add up the numbers in each section. Are they equal? If not try again.Answer: 26+26+26 = 78 BACK
  84. 84. PROBLEM  According to experts the first 4 moves in a chess game can be played in 197299 totally different ways. If it takes 30 seconds to make one move, how long would it take one player to try every possible set of 4 moves?Hint and answer
  85. 85. Hints: 1) 197299 sets of four moves 2) Each of the 4 moves takes 30 seconds.Answer: 30 seconds * 4 * 197299 = 23675880 seconds. BACK
  86. 86. PROBLEM  A man has to be at work by 9:00 a.m. and it takes him 15 minutes to get dressed, 20 minutes to eat and 35 minutes to walk to work. What time should he get up?Hint and answer
  87. 87. Hints: 1) Add up time required 2) Subtract this time from the time he has to be at work. Eg. 9:00 - 20 min= 8:40Answer: 9 hours - (15 + 20 + 35) 9 hours - 70 minutes 7 hours + 120 minutes - 70 minutes = 7 hours and 50 minutes = 7:50 AM BACK
  88. 88. Question: There are 360 degrees in a circle. If the population of various planets are represented by a circle graph, match the percentage of the population of the solar system that is found on each planet with an area on the graph. Planet Percent -----------+---------- Earth 27.78% Mars 20.80 Venus 1 6.67 Jupiter 2.78 Mercury 2.78 Neptune 6.11 Pluto 1.67Hint and answer
  89. 89. Hint: You will only find 99.98 percent Answer: BACK
  90. 90. Question: A tire shop that sells only one size of tire, .75 meters in diameter, decides to sell tires for big rigs that are 1.5 meters in diameter. If the cost of the .75 meter tires is $100.00 for four, how much will it cost for the 18 tires required for a big rig? Prices increase proportionally with size.Hint and answer
  91. 91. Hints:1) Find the cost of a .75 m tire2) Use to find cost of big rig tireAnswer: Let x = price for each big rig tire Size Price/tire 0.75m $100/4 = $25.00 each 1.5m xSolve for x: 0.75m/$25.00 = 1.5/x 0.75x = 1.5 * $25.00 0.75x = $37.50x = $50.00/tireTherefore: Price for 18 tires = 18($50.00) = $900.00 BACK
  92. 92. Question:Four friends buy a pizza that costs $20.00. Each person contributes a the following amount of money. Jane $5.00 Mike 8.00 Mary 3.00 Joe 4.00Each person will eat an amount of pizza proportional to the amount of money they paid.1)Draw a circle graph that represents the amount each eat.2)Draw the circle graph if Mike only eats half of his pizza and gives half of what he has left to Mary.Hint and answer
  93. 93. Hints: Find the proportion of money paid by each personAnswer: Cost of Pizza=$20.00 PROPORTIONS:Jane:520=1/4 Jane: 5/20 =1/4Mike:8/20=4/10=2/5 Mike: 8/20-4/20 = 4/20 = 1/ 5Mary:3/20 Mary: 3/20 + 4/20 = 7/20Joe: 4/20 = 15 Joe: 4/20 = 1/5 BACK
  94. 94. Question: A boy ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?Hint and answer
  95. 95. Hint: Let x = the number of cookies eaten the first dayAnswer:Let x = the number of cookies eaten on the first day Cookies Eaten Day 1 x 2 x + 1(6) 3 x + 2(6) 4 x + 3(6) 5 x + 4(6) TOTAL 5x + 10(6) = 100 cookies Solve for x: 5x + 10(6) = 100 5x + 60 = 100 5x = 40 x=8 BACK
  96. 96. Question: M and N are the midpoints of the sides of a square. What is the ratio of the area of triangle AMN to the area of the complete square?Hint and answer
  97. 97. Hints:Triangle AMN: base = height = 1/2 sAnswer: Since s = sides of square Area square = s^2 Area triangle = (1/2)b*h = (1/2)(1/2 s)(1/2 s) = 1/8 s^2Ratio = Area triangle/Area square = 1/8 BACK
  98. 98. Question: There are 6 short pieces of link chain, each having 4 links. It takes 10 seconds to cut a link and 25 seconds to weld it back together. What is the shortest possible time to make the longest chain?Hint and answer
  99. 99. Hints:Connecting 2 chains requires one cut and oneweld . Answer: Time to connect two chains = 1 cut + 1 weld = 10s + 25s To connect all chains together = 5 connections =5(10+25)s =5(35) = 175 BACK
  100. 100. Question:Magic HexagonFind the magic constant and fill in the numbers so that every column or diagonal has the same sum.Hint and answer
  101. 101. Hints: Use the sum of the column of numbers given tofind the target total for each column or diagonalAnswer: BACK
  102. 102. Question: An artist draws a picture of a house with a rose bush in front. In his picture the rose bush is 1.5cm high and the house is 7.5cm high. In reality the rose bush is .75 meters high. How tall is the house (in meters)?Hint and answer
  103. 103. Hints:1) Convert meters to centimeters2) Find the artists scale, as indicated by the actual size of the rosebush compared to the size of the artists drawingAnswer: Let x = artists scale1) Convert meters (m) to centimeters (cm)In reality, rose bush = .75m*100 cm/m = 750 cm2) Solve for x 1.5x = 750 x = 750/1.5 x = 500 cm IF artists scale = 1 cm:500cm THEN In reality, house = 7.5cm * 500 cm = 3750 cm = 3.75 m BACK
  104. 104. Question:This picture shows a triangle in which 3 lines are drawn to one or the other of the opposing sides from each of two vertices. This divides the triangle into 16 no overlapping sections.If 4 lines are drawn in the same way, how many no overlapping sections will the triangle have?Hint and answer
  105. 105. Hint: The three lines divide the two sides in 4 pieceseach. Look at how many sections there would be if fourlines were extended from each vertex. Answer: When 3 lines are extended from vertex, opposite side is divided into four sections When 3 lines are extended from two vertices: Number of non over lapping sections formed = 42 = 16If 4 lines are extended from vertex, opposite side is divided into five sectionsTherefore, when 4 lines are extended from two vertices: Number of non over lapping sections formed = 52 = 25 BACK
  106. 106. Question: The sports commentator on the CFXU radio station summarized the points scored by the St. F. X. Basketball Team during this season as follows: "The SMU scored a total of 1729 points in the last season. This year St. F. X. scored of 1653 points. ST. F.X. received 38 percent of the points for the total season of all 4 teams. SMU finished in second place. Acadia received only 14 percent of the points and was beaten for third place by Dalhousie by 50 points." If there were only 4 teams in the season, how many points did each team receive?Hint and answer
  107. 107. Hints: ST. F.X. scored 1653 points, which was 38 percent of thetotal points. Find total number of points for all 4 teams. Answer: Let x = total number of points for the season1653 points were scored by ST. F.X., but ST. F.X. had only 38 percent of the total points for all four teams.Solve for x: x= 1653/0.38 = 4350 pointsACADIA: 14% * 4350 = 609DALHOUSIE: Acadia + 50 = 609 + 50 = 659 SMU: 4350 - (1653 + 609 + 659) = 1429 BACK
  108. 108. Question: Rachel and Stephanie earn $5.15/hour. Rachel works 13 hours each week and Stephanie works 20 hours per week. Stephanie does not get any paid vacation time. How long a vacation would Stephanie have to take to make the same amount of money as Rachel in one year?Hint and answer
  109. 109. Hints:Look at Stephanies weekly salary to determine how many weeks shemust work to make the same amount of money as Rachel makes inone yearAnswer: Rachel: WEEKLY: $5.15/hr * 13 hrs/wk = $66.95/wkYEARLY: $66.95/wk * 52 weeks = $3481.40/yr Stephanie: WEEKLY: $5.15/hr * 20 hrs/wk = $103/wk YEARLY: $103 * 52 weeks = $5356/yrIF Stephanie and Rachel make the same amount of money in one year, THEN Stephanie must only work: ($3481.40/yr)/($103/wk) = 33.8 weeks Therefore, she must take 52 - 33.8 = 18.2 weeks/yr Unpaid Vacation Time BACK
  110. 110. Question:The Town of Antigonish has decided to put a paved path around Columbus Field. The path will be built so that the area of the park remains the same. If the path is to be 3m wide...a) What will be the perimeter of the path and the park? The dimensions of the park are 210m x 460m.b) What will be the area of the paved portion of the park?Hint and answer
  111. 111. Hints:Draw a sketchAnswer: p = 2(6 + 210) + 2(6+460) = 432 + 932 Area of paved path = 2*3*466 + 2*3*210 = 4056 m2 BACK
  112. 112. Question:  Joe buys a cup of coffee that costs $1.08. He pays with a two dollar coin.  If the cashier gives him 8 coins for his change, what could these coins be?Hint and answer
  113. 113. Hints:There is more than one solution Answer: Amount of change Joe receives: $2.00 - $1.08 = $0.92 Two possible variations of coins received: (i) 3 quarters, 3 nickels, 2 pennies 3(.25) + 3(.05) + 2(.01) = .92 (ii) 2 quarters, 4 dimes, 2 pennies 2(.25) + 4(.10) + 2(0.01) = .92 BACK
  114. 114. Question: Square ABCD has the centers of 4 equal circles as its vertices. Find the shaded area. Shawn bought a car for $5600.00. He sold it to Rachel for 5/6 the price he paid for it. Rachel sold it to Raelene for 1/5 less than she paid. Raelene sold it to Rick for 3/4 what she paid. What did Rick pay for the car?Hint and answer
  115. 115. Hints:Length of sides of square equal 2 * radius of circle (circlesare equal)2) The square contains 4 quarters of equal circles Answer:Area of circle = pi * r2Side of square = 2 * r = 2r Area of square = (2r)2 = 4r2Area of shaded region = Area of square 4 * (1/4 area of each circle) = 4r2 - 4 * 1/4(pi * r2) = 4r2 - pi r2 = (4 - pi)r2 BACK
  116. 116. Question: Points A and B on a map are 12km apart if you follow the path. A troop of boy scouts leaves point A at 11:00 a.m.. They are all carrying packs and travel 3km/hr until they reach point C at 12:45. If they want to reach point B by 2:00, how fast will they have to goHint and answer
  117. 117. Hints: 1) Distance = Rate * Time2) Rate = Distance/TimeAnswer: Travel time from A to C = 12:45 -11:00 = 1 hr 45 min = 1.75 hr Distance travelled:D = Rate * Time = 3 km/hr * 1.75 hr = 5.25 km Distance remaining (from point C to B): = (12 - 5.25) km = 6.75km Time remaining = 2:00 - 12:45 = 1 hr 15 min = 1.25 hr Rate at which distance must be travelled: Rate = Distance/Time = 6.75 km / 1.25 hr = 5.4 km/hr BACK
  118. 118. Question: Water conservation can be a big problem in some parts of the world. If a communitys water pump drips 3 drops every second and each drop is 1 1/3ml, how much water will be wasted in one year ?Hint and answer
  119. 119. Hints:1) Look at how much water drips every second2) Calculate number of seconds in one year Answer: Water lost per second:3 * (1 1/3 mL) = 4mL Number of seconds in one year: 60s/min x 60 min/hr x 24hr/day x 365d/y = 31 536 000 s Water lost in one year = 4mL/s * 31 536 000 s = 126 144 000 Ml Convert to Litres:126 144 000mL * 1L/1000 mL = 126 144 litres BACK
  120. 120. Question:  Shawn bought a car for P5600.00. He sold it to Rachel for 5/6 the price he paid for it. Rachel sold it to Raelene for 1/5 less than she paid. Raelene sold it to Rick for 3/4 what she paid.  What did Rick pay for the car?Hint and answer
  121. 121. Hints:1) Calculate price each person paid for the car,working from Rachel to Raelene, to RickAnswer:PURCHASE PRICE:Rachel: 5/6 * P5600.00 = P4666.67Raelene: 4/5 * P4666.67 = P3733.33Rick: 3/4 * P3733.33 = P2800.00OR you can take a shortcut:Rick paid: P5600.00 (5/6)(4/5)(3/4) = P2800.00 BACK
  122. 122.  Elmer Fudd decided to grow a garden so he could make salad. He wants to make it 10.1 m long and 4.2 m wide. However, in order to avoid Bugs Bunny from entering his garden he must make a fence surrounding the garden. He decides to make the fence 11.2 m long and 5.0 m wide. What is the area between the fence and the garden?Hint and answer
  123. 123. Hints:1) Find area for the garden.2) Remember area equals length multiplied by width.3) Find the area of the space surrounded by the fence.Answer:13.58 m2 BACK
  124. 124.  Jenny bought 7 t-shirts, one for each of her seven brothers, for P9.95 each. The cashier charged her an additional P13.07 in sales tax. She left the store with a measely P7.28. How much money did Jenny start with?Hint and answer
  125. 125. Hints:1) What is the total amount the shirts would cost without the sales tax?2) If there is an additional P13.07 sales tax how much did the cashier charge her in total?3) How much did Jenny start with?Answer: P90.00 BACK
  126. 126.  a) What is the least fraction of a full turn you could turn this geoboard for the shape to look the same? b) Try making your own figure on the same geoboard with the same turn symmetry.Hint and answer
  127. 127. Hints:1) How many times could you turn the board and the shape still looks the same?2) Try labelling the figure and turning your sheet of paper.3)One full turn is when 1 returns to its original position.Answer:1/4 turn. BACK
  128. 128.  Jill was given 3 red candies, 2 blue candies and 2 yellow candies. Use several ratios to describe the candies Jill has.Hint and answer
  129. 129. Answer:3 red : 2 blue5 red and blue :2 yellow3 red : 7 candy. BACK
  130. 130. A number line from 0 to 2 is divided into seven equal segments. What fraction names point A? What fraction names point B?Hint and answer
  131. 131. Hints:• 1) What fraction, with denominator 7 reduces to a value of 2?• Example:• 12/6 = 2 but we want ?/7 = 2• (What is ?)• 2) If the line is divided into 7 segments, what would each point be labelled 0, 1/7, ... , ?/7=2 ?• 3) Or should they be named 0, 2/7, 4/7, 6/7, ......14/7 ?• 4) What is the fraction of A and BAnswer: BACK
  132. 132.  a) If you saved P2.00 on January 1, P4.00 on February 1, P6.00 on March 1, P8.00 on April 1, and so on, how much money would you save in one year?  b) If you saved P2.00 on January 1, P4.00 on February 1, P8.00 on March 1, P16.00 on April 1, and so on. How much money would you save in one year?Hint and answer
  133. 133. Hints:• 1) Make a chart to help you along with the problem. January 2 February 4 March 6 April 8 May ? June ? July ? August ? September ? October ? November ? December ? 2) How would you find the total amount of money you saved?• 1) Do the same as in the last problem.Answer:• a) 2+4+6+8+10+12+14+14+18+20+22+24 = P156.00• b) P8190.00 BACK
  134. 134.  What is the number you started with?Hint and answer
  135. 135. Hints:1) What are the factors of 12?2) Can the other number be 3? Why or why not? The numbers cannot be 3 because the greatest common factor of both of the numbers is 6. (3 cannot have a factor).3) Can the other number be 6? Why or why not?Answer:(462 * 3) / 0.1 = 13860 - 13860 / 308 = 45 ? = 45 BACK
  136. 136. A Drug Store parking lot has space for 1000 cars. 2/5 of the spaces are for compact cars. On Tuesday, there were 200 compact cars and some standard size cars in the parking lot. The parking lot was 3/4 full.  How many standard size cars were in the parking lot?Hint and answer
  137. 137. Hints:1) The parking lot is 3/4 full, how many cars are in the parking lot?2) If 200 of these cars in the parking lot are compact cars, how many are standard sized cars?Answer: 750 - 200 = 500 standard sized cars. BACK
  138. 138.  How many triangles are in this figure?Hint and answer
  139. 139. Hints:1) Count all the triangles you can see. 2) Some triangles are formed from smaller triangles.Answer: 12+6+2+6+1+6+2+2 = 37 BACK
  140. 140. • Can you solve this magic square?• Put the remaining numbers from 0 to 15 in the 16 small squares. The sum of the four numbers in each row, column and two diagonals must be 30.• 15 | | | 12 ----+----+----+---- | 10 | 9 | ----+----+----+---- | | |11 ----+----+----+---- 3| | | 0 Hint and answer
  141. 141. Hints:1) Start with a block you know you can fill then find the rest of the sums.Answer: 15 | 1 | 2 | 12 ----+----+----+---- 4 | 10 | 9 | 7 ----+----+----+---- 8 | 6 | 5 | 11 ----+----+----+---- 3 | 13 | 14 | 0 BACK
  142. 142. • Mary and Jason were making propellers for their wooden helicopters. Mary put a number on her propellor and noticed that when she turned the propellor she had the same number. • Jason was trying to think of a number that he could put on his that had the same rotational synmetry (looks the same turned upside down). What is the next larger number that has this property?Hint and answer
  143. 143. Hints:1) What other numbers have this same property?2) 0, 1, 6, and 8, 9, have this property?3) What is be the next lower number?Answer: 6009 BACK
  144. 144.  Farmer Tom put a square fence around his vegetable garden to keep the deer from eating his corn. One side was 10m in length. If the posts were placed 2m apart, how many posts did he use?Hint and answer
  145. 145. Hints:1) How many posts on one side of the square fence?2) If there are 4 sides how many posts are there all together?3) Remember if you found your answer to be 20 that you have counted the corner posts more than once.Answer: 5 posts/10m 16 BACK
  146. 146. Ammie passed around a basket of strawberries to the girls at her party. Before the party she ate 5 strawberries and gave a friend 3. Eight girls arrived at the party. The first girl took a strawberry, the second girl took 3 strawberries, the third girl took 5 strawberries and so on. After the last girl took her strawberries, the basket was empty. How many strawberries were in the basket at the beginning?Hint and answer
  147. 147. Hints:1) How many more strawberries did the second girl take then the first?2) Make a chart and look for a pattern. Girl | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 -------------+---+---+---+---+---+---+---+--- number of | | | | | | | | strawberries |1|3|5| | | | | taken | | | | | | | | -------------+---+---+---+---+---+---+---+--- total number | | | | | | | | taken |1|4|9| | | | | | | | | | | | | -------------+---+---+---+---+---+---+---+---3) What was the TOTAL amount taken?Answer: 72 BACK
  148. 148. A side of square B is four times the length of a side of square A. How many times greater is the area of square B than the area of square A?Hint and answer
  149. 149. Hints:1) If the side of square A = 1cm, what is the length of side B?2) What are the areas of square A and B?3) How many times greater is the area of square B than the area of square A?Answer:Let side of square A = 1 cmLet the side of square B = 4cm Area square A = 1 cm2Area square B = 16 cm2The area of square B is 16 times greater than the area of square A. BACK
  150. 150.  Shane the Snail started at the dot. What side will he be on when he has crawled 13/20 of the distance around the regular pentagon of equal sides?Hint and answer
  151. 151. Hints: 1) If side A has a length of 2cm, then what is the perimeter of this pentagon? 2) If he has crawled 13/20 of the total distance (perimeter) then how far has he crawled? And what side would this have to be?Answer: Let one side of a pentagon = 2 cm Therefore, perimeter = 10cm*(13/20) = 6.5cm SIDE D BACK
  152. 152.  The number of hours that were left in the day was one-third of the number of hours already passed. How many hours were left in the day?Hint and answer
  153. 153. Hints:1) If there were 9 hours left in the day, what was 1/3 of the number of hours that had already passed? Are they equal?2) If there were 8 hours left in the day, what was 1/3 of the hours that already passed? Are they equal?3) Try different numbers to find the number of hours left in a day that equals one-third of the number of hours that had already passed.Answer:9 hours left = 1/3 (15) 6 hours left = 1/3 (18)9 is not equal to 5 6 hours = 6 hours6 hours were left in the day. BACK
  154. 154. A rectangular kitchen table is three times as long as it is wide. If it were 3m shorter and 3 m wider it would be a square. What are the dimensions of the rectangular table?Hint and answer
  155. 155. Hints:1) If the length is 4m, what is the width of the rectangular table?2) Is this table a square? Why or why not?3) Make a table to help you. Length of Width of Length of Width of Correct? Rectangle Rectangle Square Square Trial #1 3x4m=12m 4m 12m 3m=9m 4m+3m=7m NO Trial #2 3x2m=6m 2m 6m-3m=3m 2m+3m=5m NO Trial #3Answer: width: 3m ; length: 3*3 = 9 width + 3 = 6 = length - 3 => a square BACK
  156. 156. What is the starting number (?) ?Hint and answer
  157. 157. Hints:1) When you square a number, you multiply the number by itself.ex: 2x2=4 = 2^2 3x3=9 = 3^22) Reverse your steps. (Work backwards starting with the result of 50).Answer: 42 is the starting number. BACK
  158. 158.  Derek started his car (automatic shift) drove 9 km and spent 3 minutes waiting at traffic lights. About how much gasoline did Dereks car use?  CHART GIVEN: AUTOMOBILE FUEL USAGE Starting .015 Liters Idling for 1 minute .047Litres Moving Manual Shift 30km 3.0 Litres Automatic Shift 27km 3.0 LitresHint and answer
  159. 159. Hints:1) If he spent 3 minutes idling, how much fuel did he burn in this amount of time?2) If it takes him 3.0 liters to go 27 km, how many liters can he go for 9km?3.0L/27km x 9km = ??3) What is the total amount of gasoline Dereks car used?Answer:Starting 0.015 + 3(0.047L) + (3.0L/27km * 9km) = 1.156 Liters of fuel BACK
  160. 160. Heres a question for you!!!  One of these things does not belong here, one of these things is not the same. Can you tell which cube?Hint and answer
  161. 161. Hints:1) Look at the patters on the cubes carefully.2) If it helps, try making paper cubes with these symbols.Answer:The third cube from left. BACK
  162. 162.  Two carpenters decided to design desks for students at the Junior High. The dimensions of the desk are as shown. How much wood would they need for 30 desks? (in cm2).Hint and answer
  163. 163. Hints:1) What is the area of one desk?2) Find the area of each part and add all the areas to find the total area.3) If there are 30 desks, how much wood in square centimetres do they need?Answer:Area of rectangle = 70cm x 30cm = 2100cm2Triangles 2*(1/2 20cm x 30cm) = 600cm2 2100cm2 + 600cm2 = 2700cm230*(2700cm2) = 81000cm2 of wood BACK
  164. 164.  Chatterbox made the following figures with a piece of wood, 12 nails and an elastic band. What is the area of the figure (in units2)? Explain your method:Hint and answer
  165. 165. Hints:1) You can do this in many different ways. You can divide the figure into different shapes to actually find the area of the figure. Or you may want to try a different way.Answer:There are different methods a student may have in mind. But here is one: Build a square around the shape. It has an area of 4 units. Then substract the area of the two triangles.Area = 2 ½ BACK
  166. 166.  Do these parallelograms have the same area? How do you know?Hint and answer
  167. 167. Hints:1) How do you find the area of a parallelogram?Answer:Yes, since you multiply the base and height, its really the same numbers, so it doesnt matter which is the base and which is the height. BACK
  168. 168. PROBLEM  Find the next 3 numbers in the following sequence. 2, 5, 11, 23, ____, _____, ______.Hint and answer
  169. 169. Solution and Answer 1.Find the next 3 numbers in the following sequence. 2, 5, 11, 23, ____, _____, ______. Pattern : x 2 + 1 47, 95, 191 BACK
  170. 170.  .If this pattern was formed to make a cube, what numbers would appear where the question marks are?Hint and answer
  171. 171.  2. If this pattern was formed to make a cube, what numbers would appear where the question marks are? ?=1 ?=4 ?=2 BACK
  172. 172.  The number of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points.Hint and answer
  173. 173.  .Thenumber of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points. 1 Points 2 3 4 5 ...... 8 9 n 0 4 Lines 1 3 6 10 ...... 28 36 n(n-1) 2 5 + + + + + + + ...... 2 3 4 5 7 8 9 BACK
  174. 174.  For the hexagon with 42 dots, how many dots are there on each side?Hint and answer
  175. 175.  Forthe hexagon with 42 dots, how many dots are there on each side? No. of dots 6 12 18 ...... 42 n (n 6)+ Dots per side 2 3 4 ...... 8 1 BACK
  176. 176.  Look for a common element in each of the following. This is a RUMDA. This is a not RUMDA. This is a RUMDA. Is this a RUMDA (A)? This is a RUMDA. Is this a RUMDA (B)? This is a not RUMDA.Hint and answer
  177. 177.  Look for a common element in each of the following. This is a RUMDA. This is a not RUMDA. This is a RUMDA. Is this a RUMDA (A)?YES This is a RUMDA. Is this a RUMDA (B)?NO This is a not RUMDA. BACK
  178. 178.  If the figure on the left is continued, how many letters will be in the J row?  Which row will contain 27 letters?  A BBB CCCCC DDDDDDHint and answer
  179. 179. Solution and AnswerLetter A B C D E ...... J K L M N GeneralNumeral 1 2 3 4 5 ...... 10 11 12 13 14 nOrderTotal No. 1 3 5 7 9 ...... 19 21 23 25 27 2n-1 BACK
  180. 180.  The Adams family was going to buy a car for $5800. The car dealer offered the Adams family two options for buying the car. They could pay the full amount in cash, or they could pay $1000.00 down and $230.00 a month for 24 months on the installment plan. How much more would they pay for the car on the installment plan?Hint and answer
  181. 181.  Hints: 1) Try and calculate the amount of money that they would have to pay for the installment plan. 2) Calculate the difference between the installment plan and the initial amount if they paid today. Answer: 1000.00 + 230.00 * 24 = $6520.00 6250.00 - 5800.00 = $720.00 more for the installment plan. BACK
  182. 182.  Lisa Lilly was the best runner in the eighth grade. One day she ran 100m in 40 seconds, 200m in 1 minute and 10 seconds, and 200m over low hurdles in one and a half minutes. How many more seconds did it take her to run the 200m over low hurdles then it did to run the 200m dash?Hint and answer
  183. 183.  Hints: 1) What information is important in this question? 2) How long did it take her to run 200m in seconds? Answer: To run the 200m: 1 min = 60s + 10s = 70s To run 200m with hurdles: 60s + 30s = 90s 90s - 70s = 20s longer. BACK
  184. 184.  Three students have to write a make up test. Mark scored 24/60 on his first test and 32/40 on his make up test. Jake scored 35/70 on his first test and 54/60 on his makeup test. Marilyn scored 27/90 on her first test and 45/50 on her second test.  A) Which student improved the most and by what percentage?  B) If the teacher gives each student a final grade using 70% of the makeup test mark and 30% of the first test mark, what mark would each student receive? Who did the best overall?Hint and answer
  185. 185. Hints:1) Make a chart of the percentages scored on each test for each student. As the following: PERCENTAGE FOR FIRST TEST PERCENTAGE FOR SECOND TEST DIFFERENCEMARKJAKEMARILYN2) If you forget how to do percent, heres a hint: divide the denominator into the numerator and multiply by 100%Part BHint:1) Try making another chart with percentages of each test. Like the following: 30% of first test 70% of second test SumFinal MarkMARKJAKEMARILYNAnswer: A) | PERCENTAGE PERCENTAGE | FOR FIRST TEST FOR SECOND TEST DIFFERENCE---------------+--------------------------------------------------------MARK | 40% 80% 40%JAKE | 50% 90% 40%MARILYN | 30% 90% 60%B) | 30% of 70% of Sum Final | first test second test Mark---------------+--------------------------------------------------------MARK | 12% 56% 68%JAKE | 15% 63% 78%MARILYN | 9% 63% 72%Jake did the best overall. BACK
  186. 186.  George, Sam, Andrew and Brandon each had four dates to four different Parish Center Dances with four different girls, named Cher, Connie, Melissa and Kendra. On the second date, George dated Connie and Brandan dated Kendra. On the third date Andrew went out with Melissa and Sam went out with Connie. Melissa went out with George and Cher went out with Sam on the fourth date. What couples went out together on the first date if no pairs went out more than once?Hint and answer
  187. 187. Hints: 1) Make a chart to help you use logical reasoningAnswer: Cher dated George. Brandan dated Melissa Connie dated Andrew Sam dated Kendra BACK
  188. 188.  A large piece of construction paper is .01mm thick. It is cut in half and one piece is placed on the other to make a pile. These are cut in half and all four pieces are placed in a pile. These four are cut in half and placed in a pile, and the process is continued. After the pieces have been cut and piled for the tenth time, what is the height of the pile in cm.Hint and answer
  189. 189. Solution and Answer Hints:1) Try to draw a sketch of how many sheets are piled as the pile is cut each time.2) Now try to find a pattern in the numbers.3) How many sheets will you have after the sheets are cut and piled 10 times.4) How many cm high is this pile. Dont forget to change your mm to cm. Answer: 1 cut ---> 2 sheets 2 cuts---> 4 sheets 3 cuts---> 8 sheets 4 cuts---> 16 sheets ... 10 cuts--> 210 sheets 1024 (.01) = 10.24mm = 1.024 cm BACK
  190. 190.  What is the sum of all the digits in the sequence 1, 2, 3, 4, 5, 6, 7,...99, 100?  NOTE: (Sum of the digits, not the numbers!)Hint and answer
  191. 191. Hints:1) When all else fails, make a chart or a table. Start by writing the numbers in columns and rows.ex. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | | | | | | | | | | | | | | | | | | | |2) Now examine the digits in the rows (horizontal). What do you notice about digits? Try and find a pattern in the ones place.3) Carry on to find a pattern in the tens place.4) Dont forget about the number 100!!Answer: 10 (45) + 10 (45) + 1 = 901 1 + 10 * (the sum of the digits 1 to 9) + 10 * (the sum of the digits 1 to 9) = 901 BACK
  192. 192.  Silvers Cleaners decided to raise the price of dry cleaning a sports coat from $4.00 to $5.00. The same percentage increase was applied to dry cleaning a jacket. The old cost of dry cleaning a jacket was $10.00. What is the new cost of dry cleaning a jacket?Hint and answer
  193. 193.  Hints: 1) To find the percentage increase in the dry cleaning of a sports coat, set up an algebraic equation. 4 * x = 5.00 2) Now what is the price of the new cost of dry cleaning a jacket? Answer: Let x = percent increase 4.00 * x = 5.00 x = 5.00/4.00 * 100% = 125% 10.00 * 125% = $12.50 is the new cost of cleaning a jacket BACK
  194. 194. A Christmas gift is tied with ribbon as shown. The bow requires 47cm of ribbon. What is the total length of the ribbon in metres?Hint and answer
  195. 195.  Hints: 1) How many faces / sides are on a cube. How long is the piece of ribbon on each side? Find the total length of the ribbon on the sides. 2) Now the top and the bottom look like: What is the total length of the ribbon for the top and bottom? 3) Find the total length of all the ribbon in meters. Answer: On 4 sides 20cm of ribbon each = 80cm on the top and bottom. .5 * 10cm = 25cm 2 * 25cm = 50cm Total amount of ribbon 47cm + 50 cm + 80cm = 177cm = 1.77m BACK
  196. 196.  Fourstrips of paneling 40 cm long and 4cm wide are arranged to form a square. What is the area of the inner square in cm2?Hint and answer
  197. 197.  Hints: 1) Draw and label the diagram with the dimensions given. 2) Now find the inner dimensions of the paneling and find the area. Answer: 362 = 1296 cm2 BACK
  198. 198.  In the following diagram of the front view of the Great Pyramid, the measure of the angle PRQ is 120 degrees, and the measure of the angle PST is 110 degrees. What is the measure of the angle RPS in degrees?Hint and answer
  199. 199.  Hints: 1) Do you remember how many degrees there are in a triangle or a straight line? 2) There are 180 degrees in a triangle. That is the sum of the angles in a triangle is 180 degrees. A straight line is 180 degrees. 3) Say your diagram was as the following: ? = 180 degrees - 150 degrees ? = 30 degrees 4) Solve the problem!!! Answer: 180 degrees - 120 degrees = 60 degrees 180 degrees - 110 degrees = 70 degrees 60 degrees + 70 degrees = 130 degrees 180 degrees - 130 degrees = 50 degrees BACK
  200. 200.  Mr. MacDonald recorded the test marks for his eighth grade class of 25 students. He used the marks recorded to calculate the average to be 72. Sandras mark of 86 was incorrectly marked as 36. What was the correct average for the test?Hint and answer
  201. 201.  Hints:1) What does Mr. MacDonald have to do to find the average mark of his class?2) Average means the sum of the test marks divided by the number of students. So, what was the sum of all the tests?3) After you have the sum of all the tests you can find the correct average by correcting Mr. MacDonalds sum and finding the correct average. Answer: x / 25 = 72 x = 1800 = the sum of all the grades 1800 - 36 + 86 = 1850 1800 / 25 = 74% BACK
  202. 202.  Chip said to Dale "If you give me one acorn, then we will have an equal number of acorns." Dale replied with delight "If you give me one acorn, then I will have double the number you have!" What was the total number of acorns they had in their tree? How many did Chip have and how many did Dale have?Hint and answer
  203. 203.  Hints:1) Try different numbers that will satisfy the conditions given in the number.2) The sum of the numbers of acorns is twice six. Find out the how many Chip had and Dale had. Answer: Let C = # of acorns Chip had and D = # acorns Dale had. Then C + 1 = D - 1 ; D=! = 2(C-1). Solve to get C = 5 and D = 7. BACK
  204. 204.  Bart Simpson decided to make a graph of his weekly earning of $120.00 from his paper route. To make the size of each sector proportional to the amount distributed what does the angle x in degrees have to be?Hint and answer
  205. 205.  Hints:1) One way to overcome this problem is to think of percentages. What is the percent of $15 out of the total $120 earnings?2) Now we know what percent of his total earnings is. How many degrees are in a circle?3) The percent of money he spends on music is how many degrees in the circle? Answer: 45 degrees Percentages: $15/$120 *100% = 12.5% 360 degrees * 12.5% = 45 degrees BACK
  206. 206.  Jane was walking the long way home from school. She started walking East. She walked 3 km East when she met a dog. She ran back to the school and decided to take the alternative route. So she walked North 4 km to her home. If she had walked straight home from where she met the dog, how far would it have been to her home?Hint and answer
  207. 207.  Hints:1) Show diagram.2) Do you remember how to find the missing side of a right triangle?3) The Pythagorean theorem says, the hypotenuse, which is the longest side opposite the right angle, is equal to the square root of the sums of the squares of the other two sides.Z 2 = X2 + Y24) How many additional meters would she have to walk? Answer: 42 + 33 = ?2 25 = ?2 5km = ? 3km + 5km = 8km She would have to walk an additional 4 kilometers to get home from where she met the dog. BACK
  208. 208.  The Gilliss house has a pool with the shape as shown. They want to make a cover for it for the harsh winter. How much to the nearest cent are they going to have to spend on material if it costs $5.00/m2.Hint and answer
  209. 209. 1) You must find the total area of the pool.2) The pool can be divided into 3 different shapes.3) The area of a circle is A = Pi * r24) Find the total amount of money given that it costs $5.00 per meter squared.Answer: Areas: semi circle: area = Pi * radius squared = 1/2 Pi * r2 = 1/2 Pi (2m)2 = 1/2 Pi (4m,sup>2) = 2Pi m 2 triangle : area = 1/2 base * height = 1/2 (3m)(4m) = 6 m2 rectangle : area = (4m)(6m) = 24 m2 Total area = 24 + 2Pi + 6 = 36.28 m2. Cost = $5.00/m * 36.28 m,sup>2 = $181.42 BACK
  210. 210.  Batman must solve the following problem to escape the Riddler. The mid- points of the sides of a square are joined as shown. A fraction of the original square is shaded. What is the fraction? Can you help him?Hint and answer
  211. 211.  Hints:1) Divide the square into 4 equal parts. Can you see the answer? Answer: 1/4 BACK
  212. 212.  Matthew is at a zoo. He takes a picture of a one-metre snake beside a brick wall. When he developed his pictures, the one-metre snake is 2cm long and the wall is 4.5cm high. What was the actual height of the brick wall in cm.Hint and answer
  213. 213. Hints:1) If the snake is one meter long in real life and 2cm long in the picture, how high is the building if it is 4.5cm long in the picture.2) The easiest way to do this is to set up a ratio like: 100 x ---- = --- 2cm 4.5cm Solve for x, which is the height of the building.Answer: The snake is one meter long. 100/2 = x/4.5 x = 450/2 = 225cm high BACK
  214. 214.  Joes rich uncle gave him a looney on his first birthday. On each birthday after that he doubled his previous gift. By the day after Joes eight birthday, what was the total amount that his uncle had given him?Hint and answer
  215. 215. Hints:1) Make a chart-> 1st birthday $1 2nd birthday $2 3rd birthday $4 | |2) How much did he get in total?Answer: 1st birthday -> $1 2nd birthday -> $2 3rd birthday -> $4 $8 $16 $32 $64 $128 ------ $255 BACK
  216. 216.  Ms. Smith, Ms. Gracia, and Ms. OLeary all teach at St. Andrew Junior High School. One of the women is a mathematics teacher, one an art teacher and one science teacher. The art teacher , an only child, has taught the least number of years. Ms. Garcia, who married Ms. Smiths brother, has taught more years than the mathematics teacher. Name the subject each woman teaches.Hint and answer
  217. 217. Hints:1) Try to limit the amount of possibilities for each teacher.Example: Ms. Garcia cant teach art because she has taught more years than the mathematics teacher, and the art teacher has taught the least number of years.Answer: Mathematics Science Art | | | Ms. Smith Ms. Gracia Ms. OLeary BACK
  218. 218.  Jim has three times as many comic books as Charles. Charles has two- thirds as many comic books as Bob. Bob has 27 comic books. How many comic books does Jim have.Hint and answer
  219. 219. Hints:1) The best way to approach this problem is to work backwards. Try starting with statements: If Bob has 27 comic books and Charles has 2/3 as many, how many does Charles have?2) Jim has 3 times as many as Charles. So how many comic books does Jim have?3) If you need help in setting up equations, heres a start: 2/3 * # of Bobs comics = # of Charles comics =>Now do the same thing for Jim: 3 * # of Charles comics = # of Jims comicsAnswer: 2/3 * 27 = # of Charles comics = 18 Jim has 3 * 18 = 54 comic books BACK
  220. 220.  FriendlysClothing Store bought handkerchiefs, six for $10, and sold them 4 for $10. They made $60 profit. How many handkerchiefs did they sell?Hint and answer
  221. 221. Hints:1) First try and calculate how much Friendlys paid for each handkerchief when they bought them and how much a customer paid for each handkerchief. You can set up algebraic expressions to help you.6p = $10 and 4s = $10p = price of hamdkerchiefs and s = selling price of handkerchief-> Find p and s2) Now how can we tackle how many handkerchiefs they sold if the store made $60.00? One way to start is to set up an algebraic expressions that will solve for the number of handkerchiefs. If the store pays $10/6 for a handkerchief and sells it for $2.50 then how many should it sell make $60.00?(s-p)*x = $60.00-> Solve this algebraic equation for x, where x is the number of handkerchiefs.Answer: 6 for $10 4 for $10.00 1 for $10/6 1 for $2.50 x$2.50 - x$10/6 = $60.00 .83x = $60.00 x = 72 handkerchiefs. BACK
  222. 222.  You, in your new red Porsche, decide to make a 160km trip to Carolina Beach, travelling at 80km/hr. You make the return trip travelling at a rate of 48km/hr. What was your average speed for the entire trip?Hint and answer
  223. 223. Hints:1) In order to find the average speed, you must find the tthe total time it took you to travel to and from Carolina beach.2) Remember: Rate = distance/time3) The average speed is the total distance divided by the total time.Answer: How many hours in total does it take you? 160km/80km/hr = 2hr 160km/48km/hr = 3.33hr Average speed = (160 + 16)0/(2 + 3.33) = 60km/hr BACK
  224. 224.  Who am I???  The names of my mother, my father, my brother, my sister and me in no particular order are Sandy, Sharon, Pat, Jennifer and Connie  Pat is younger than I am.  I am older than Connie.  Sharon is younger than Jennifer.Hint and answer
  225. 225. Hints:1) This is a reasoning problem. Use the clues to figure out the problem.Answer:· -You must be a girl,· -Your brother Pat is younger than you,· -Connie is a younger sister,· -Jennifer must be the mother,· -You are Sharon. BACK
  226. 226.  The points A, B, C, D, and E are located on a straight line in order.  The distance from A to E is 20cm.  The distance from A to D is 15cm.  The distance from B to E is 10cm.  C is halfway between B and D.  What is the distance from B to C?Hint and answer
  227. 227. Hints:1) What is the distance from D to E?2) What is the distance from B to D?3) What is the distance from D to C?Answer: DE = 5cm BE = 10cm BC = 2.5cm BACK
  228. 228.  Bob is reading a 445 page book. He has already read 157 pages. If he reads 24 pages a day, how long will it take him to finish the book? b) Bob read 157 pages of a 445 page book. He finished the rest in 9 days. How many pages did he average each day while completing the book?Hint and answer
  229. 229. Hints:1) How many pages are in the book?2) How many pages has Bob read?3) How fast does he read?4) How many page does Bob have left to read?5) If Bob had 48 pages left to read, how many days would it take?6) How should you determine the number of days it will take to read 288 pages?b)Hints:1) Try using what you learned in part a to solve b.Answer:a) 445 - 157 = 288 pages left 288/24 = 12 It will take twelve days to finish the book.b) 288/9 = 32 pages a day BACK
  230. 230.  Pioneer Video is giving away a free movie to anyone who can solve this puzzle. Place the numbers one to nine in the squares so that none of the rows, columns or diagonals have the same sum.  | |  ---+---+---  | |  ---+---+---  | |  Olivia won a free movie, what was her solution?Solution and answer
  231. 231. Solution and Answer Hints:1) This is a trial and error problem. You must first try one set and then add up the rows, columns, and diagonals. If it works youve found an answer. Answer: 2|7|3 ----------- 4|6|9 ----------- 1|8|5 6|1|2 ----------- 4|5|7 ----------- 3|9|8 1|3|5 ----------- 2|4|6 ----------- 7|8|9 BACK
  232. 232.  Homer Simpson entered a pie eating contest at the country fair. Homer was determined to win and went into training for 6 days. Each day he ate 4 more pies than the day before. Homer ate 150 pies while in training. How many pies did he eat each day?Solution and answer
  233. 233. Solution and AnswerHints:1) Make a guess then check your guess!2) If Homer ate one pie the first day how many would he eat the second day?3) If he ate 10 pies on the first day, how many would he have eaten all together at the end of the 6 days?4) Would guessing that Homer ate 20 pies on the first day be a good guess?5) Try another number!Answer: 1st -> 15 2nd -> 19 3rd -> 23 4th -> 27 5th -> 31 6th -> 35 ----------- 150 pies BACK
  234. 234.  Belgium Cheese costs $1.70 for 1/2 kilograms. How much will 2 and 1/2 kilograms of cheese cost?Solution and answer
  235. 235. Hints:1) Set up a proportional equation2) $1.70/ 1/2 kilogram = x/2.5 kilogramsSolve for xAnswer: $1.70/.5 = x/ 2.5 .5x = 4.25/.5 x = $8.50 BACK
  236. 236.  The Canadian record for the most consecutive sit-ups is 17,000 in 7 hours and 27 minutes.  At a rate of 40 sit-ups per minute, how many hours and minutes would it take to tie the record. Is this rate better than the Canadian record?Solution and answer
  237. 237. Hints:1) How many sit-ups would you have to do to tie the record?2) If you can do 40 sit-ups per minute, how many minutes does it take to do 17,000?3) To answer the secnd part, what is the rate of sit-ups/minute of the Canadian record?Whose rate is better?Answer: 17000/7*60 + 27 = 38.03 sit-ups/min -> Record 17000/40 = 425 minutes = 7 hours and 5 minutes Your rate is better!! BACK
  238. 238.  On an algebra test, I had seven times as many correct answers as incorrect ones. There were 120 items on the test, how many did I get right?Solution and answer
  239. 239. Solution and AnswerHints:1) One way to approach this problem is with algebraic expressions. Let x = # of incorrect answers. What does the number of correct answers equal in terms of x?2) The number of items on the test equals the number of incorrect answers + the number of incorrect answers.Answers: x = # of incorrect answers 7x = # of correct answers 120 = 8x x = 15 incorrect 7*15 = 105 correct BACK
  240. 240.  IfI pile grapefruit in a pyramid with 1 grapefruit in the first layer, 4 in the second layer (from the top), 9 in the third layer, and 16 in the fourth layer, how many grapefruit will I need to make a pile with 10 layers?Solution and answer
  241. 241. Solution and AnswerHints:1) Is there a pattern in piling the grapefruit?2) Make a chart and find the sum. 1st 1 2nd 4 3rd 9 | | | |37)Answer: 1 -> 4 2 -> 9 3 -> 16 4 -> 25 5 -> 36 6 -> 49 7 -> 64 8 -> 81 9 -> 100 ---------------- 385 grapefruit BACK
  242. 242.  Big-Bird wants to make a picture frame for his picture of Elmo. He is given the piece of plywood shown. He wants to make it in a shape (the shaded area). In order to do so, he must connect all the mid-points of the sides of a rectangle. What is the area of the piece of wood he will be using for the picture frame? What is the perimeter of the inside of frame?Solution and answer
  243. 243. Hints:1) Try to decide how you could break up the figure and find the area.2) How would you find the perimeter? You must know the length of the sides.3) HINT!!! Divide the figure by connecting the midpoints of each side by a line. Now do youAnswer: x squared = 22 + 1.52 Perimeter = 4(2.5) = 10cm x = 2.5 Area of a triangle = 1/2*bh = .5 * 2 * 1.5 = 1.5 Area = 4(1.5) = 6 cm2 BACK
  244. 244.  Whats the number Im thinking of? It is greater than 44 squared and less than 45 squared. 5 squared is one of its factors, and it is a multiple of 13.Solution and answer
  245. 245. Hints:1) This is a trial and error problem. Answering these questions will help you:· a) What is the value of 44 squared?· b) What is the value of 45 squared· c) What is a factor? d) What does a mulitple mean? <- CHECK!!!!Answer: 2025 > x > 1936 1950 = 13 * 150 BACK
  246. 246. A book exhibition was held for four days in a school. Number of tickets sold on first, second, third and fourth day were 1094, 1812, 2050 and 2751 respectively. Find the total number of tickets sold for the exhibitionSolution and answer
  247. 247.  Number of tickets sold on the first day = 1094 Number of tickets sold on the second day = 1812 Number of tickets sold on the third day = 2050 Number of tickets sold on the fourth day = 2751 Total number of tickets sold = 1094 + 1812 + 2050 + 2751 = 7707 Hence total number of tickets sold = 7707 Ans BACK
  248. 248.  Solve: (-7) - 8 - (-25)Solution and answer
  249. 249.  (-7)- 8 - (-25) = -7 - 8 + 25Collecting & Solving like terms = -15 + 25 = 10 Ans BACK
  250. 250.  Find cost of fencing a rectangular park whose length is 250 m, breadth = 175 m at P12 per meter.Solution and answer
  251. 251. Length of rectangular park = 250 mBreadth of rectangular park = 175 mPerimeter of park = 2 (l + b) = 2 (250 m + 175 m) = 2 (425 m)Thus, perimeter of park = 850 m Cost of fencing 1 m = P 12 Cost of fencing 850 m = P 12 x 850 = P 10200 Ans BACK
  252. 252.  The cost of 4 dozen bananas is Rs. 60. How many bananas can be purchased for Rs. 12.50 ?Solution and answer
  253. 253.  Number of bananas bought for Rs. 60 = 4 dozen = 4 x 12 = 48 Number of bananas bought for Re. 1 = Number of bananas bought for Rs.12.50= x 12.50 = 10So, number of bananas bought for Rs. 12.50 = 10 Ans BACK
  254. 254.  Aneesh made 42 runs in 6 overs. Anoop made 63 runs in 7 overs. Who made more runs in 1 over ?Solution and answer
  255. 255. Aneesh made 42 runs in 6 overs. So, number of runs made in 1 over = = 7Anoop made 63 runs in 7 overs So, number of runs made in 1 over = = 9So, Anoop made more runs in 1 over BACK
  256. 256.  The Band Committee of 100 people wishes to set up a telephone call system. The initial contact person calls three other people, each of whom call three others and so on, until all the people in the Band Committee have been contacted. What is the maximum number of people they need to make the calls.Solution and answer
  257. 257. Hints:1) Try and draw a flow chart to explain how the telephone system works.2) How many people have to do the calling in order for 100 people to be called?ANSWER: 27 + 27 + 6 + 6 = 66 BACK
  258. 258.  Mark and Fred had some money in the ratio 6:1. Mark gave half of his money to Fred. Find the ratio of the amount of money Mark had left to the amount of money Fred had in the end.Hint and answer
  259. 259. AfterThe ratio of the amount of money Mark had left to the amount of money Fred had inthe end is 3:4. BACK
  260. 260. • Carol puts some green and red unit cubes in a box. The ratio of the number of green cubes to the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5. • a) How many green cubes are there in the box? • b) How many red cubes does Carol have in the end?Hint and answer
  261. 261. AfterFrom the model, we see that: a) 3 units = 12 cubes 1 unit = 12 ÷3 = 4 cubes 4 units = 4 × 4 = 16 cubesThere are 16 green cubes in the box. b) 5 units = 5 × 4 = 20 cubesCarol has 20 red cubes in the end.BACK
  262. 262.  The weight of 25 bags of rice is 650 kg. Find the weight of hundred bags of rice?Hint and answer
  263. 263.  since the weight of 25 bags of rice is 650kg.Then the weight of 1 bag of rice is 650 ÷ 25= 26kg Then weight of 100 bags of rice is 26 x 100= 2600 kg ANSWER2600 kg BACK
  264. 264.  FindHCF of 136, 170 and 255 by division methodHint and answer
  265. 265.  First we find the HCF of 136 and 170 136)170(1 136 34 HCF of 136 and 170 = 34 Now we find the HCF of 34 and 255 34)255(7 238 17)34(2 34 0 HCF of 34 and 255 =17 Hence HCF of 136,170 and 255 = 17 Find the LCM of 20, 30 and 50 by division method: 2] 20, 30, 50 5] 10, 15, 25 2, 3, 5 LCM = 2x 5x 2x 3x 5 = 300 BACK
  266. 266.  Ken wants to make a half circle with a diameter of 5 cm, using a metal wire. How long is the wire he needs? What is the area of the half circle? Use pi = 3.14Hint and answer
  267. 267.  Length of the wire = (5 x 3.14) ÷ 2 + 5 = 12.85 cm Area = (5/2)2 x 3.14 ÷ 2 = 9.81 cm2Answer 9.81 cm2 BACK
  268. 268. A satellite orbits the earth at a height of 343 kilometers. If it makes 8 revolutions around the earth, how many kilometers does it travel? Earths diameter is 6371 kilometers. Use pi = 3.14Hint and answer
  269. 269.  The diameter of the circle that the satellite travels is 6371 + 2 x 343 = 7057 kilometers; The answer is: 7057 x 3.14 x 8 = 177271.84 kilometers Answer 177271.84 kilometers BACK
  270. 270.  Jane went to the store to buy some clothes. There was one sweater with an original price of $40. It was 15% off that day. Jane bought that sweater. (a) What was the cost of the sweater? If Jane pays 8% sales tax, how much did Jane pay for the sweater including the sales tax?Hint and answer
  271. 271.  40x 15% = $6, $40 -$6 = $34 is the cost of the sweater. Sales tax is $34 x 8% = $2.72; Therefore Jane paid $34 + $2.72 = $36.72Answera) $34, b) $36.72 BACK
  272. 272.  Charlie Joe Purple has been taking math tests. The average score of his first 3 test is 95 points. The average score of his next 2 test is 90 points. What is the Charlies average score of all 5 tests?Hint and answer
  273. 273. (95 x 3 + 90 x 2) ÷ 5 = 93Answer93 BACK
  274. 274.  5thgrade classes at Franklin Elementary completed a final science test. The average score of the female students is 82, and the average score of the male students is 79. There are 42 girls, and 38 boys in the 5th grade. What is the average test score of the entire 5th grade?Hint and answer
  275. 275. Find the total score from all the students: 82 x 42 + 79 x 38 = 6446 Divide the total score by the total number of students: 42 + 38 = 80 (82 x 42 + 79 x 38) ÷ (42 + 38) = 6446 ÷ 80 = 80.6 Answer 80.6 BACK
  276. 276.  ABCD and MNOP are squares. M, N, O, and P are at mid point of the 4 sides of square ABCD. If MN is 8 inches, what is the area of square ABCD?Hint and answer
  277. 277.  Draw lines PN and MO. You can see that area of square MNOP is half of the area of ABCD. The area of square MNOP is 8 x 8 = 64 square inches; Area of ABCD = 2 x 64 = 128 square inches Answer 128 square inches BACK
  278. 278.  Smart multiplications a) 39 x 5 x 20 b) 25 x 125 x 32Hint and answer
  279. 279.  (a) Rearrange the numbers to 39 x (5 x 20) = 39 x 100 = 3900 (b) Rearrange the numbers to 25 x 125 x 4 x 8 = 25 x 4 x 125 x 8 = 100 x 1000 = 100000 Answer BACK
  280. 280.  The area of the rectangle is 224 square inches. The length of the rectangle is 14 inches. What is the perimeter of the rectangle?Hint and answer
  281. 281. The other side of the rectangle is 224 ÷ 14 = 16. The perimeter = 14 x 2 + 16 x 2 = 60 inchesAnswer 60 inches BACK
  282. 282.  Smart multiplications a) 125 x 88 b) 108 x 125Hint and answer
  283. 283. a) Rearrange the numbers to 125 x (80 + 8) = 10000 + 1000 = 11000 b) Rearrange the numbers to (100 + 8) x 125 = 100 x 125 + 8 x 125 = 12500 + 1000 = 1350Answers a) 11000, b) 13500 BACK
  284. 284. Calculate a) 36.12 x 7.8 b) 42.3 x 3.5Hint and answer
  285. 285. Answer a) 281.736, b) 148.05 BACK
  286. 286. Jerrys train has 4 cars of different colors, yellow, green, red and blue. How many different ways can Jerry arrange his train cars?Hint and answer
  287. 287. 4 x 3 x 2 = 24Answer 24 BACK
  288. 288. A basket has 15 apples, 8 oranges and 27 plums mixed randomly. If you close your eyes and grab a fruit from the basket, what is the probability of you getting an orange?Hint and answer
  289. 289. The total number of fruits is 50. So theprobability of picking an orange is 8/50 or4/25.Answer 8/50=4/25 BACK
  290. 290.  Nina has sweaters that are pink, blue, red, and gray. She has pants that are: khaki, black and blue. How many different combinations of sweaters and pants can she wear?Hint and answer
  291. 291. 4 x 3 = 12Answer 12 BACK
  292. 292. Use the signs “+”, “-” , “x” and/or ( ) to make the equation work. Find 2Hint and answer
  293. 293. 1) 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 1002) (1 + 2) x 3 + (4 x 5) + 6 + (7 x 8) + 9 = 100Answer: 100 BACK
  294. 294.  What is the surface area of the following structure made of 5 cubes glued together. The side of each cube is 1 inch? Only consider the surfaces that are exposed.Hint and answer
  295. 295. Count the number of cube you can see systematically.Answer 22 square inches BACK
  296. 296. • Method 1: Looking from front: 4; back: 4, Left: 3, right: 3, Top: 4, Bottom: 4; The number of cube surfaces are 4 x 2 + 3 x 2 + 4 x 2 = 22 square inches • Method 2: Surfaces by cube: The four visible cubes have 5 surfaces each. The cube in the back has 2 surfaces. The number of cube surfaces are 5 + 5 + 5 + 5 + 2 = 22 square inches • what are all the factors of 124?Hint and answer
  297. 297. Answer 1, 2, 31, 62, 124 BACK
  298. 298.  Since 124 is an even number, 2 is a factor. 124 ÷ 2 = 62 which is an even number, therefore 4 is a factor. 62 ÷ 2 = 31, therefore 31 is a factor. 31 is a prime number.  What three consecutive odd numbers have a product of 15525?Hint and answer
  299. 299. Answer 23 x 25 x 27 = 15525 BACK
  300. 300. Fill in the squares with single digits (1 to 9) so that the sum of the 4 numbers equals to 120.Hint and answer
  301. 301. Start with the ones place. The sum is 0. Therefore the the sum of the 4 digits at the ones place needs to be 10 or 20. 1 + 2 + 3 + 4 = 10, or 1 + 3 + 7 + 9 = 20. The sum of the 3 digits on the tens place plus the carry over needs to be 10 or 11. Try them out and you will get the answers.AnswerThere are more answers. Here is oneexample BACK
  302. 302.  Today is Saturday. What day of the week is it 200 days from today?Hint and answer
  303. 303. There are 7 days in a week. 200 ÷ 7 = 28R4;Therefore, 200 days from today is WednesdayAnswer Wednesday BACK
  304. 304.  A, B and C each represents a different number between 1 and 9. What do A, B and C represent in the following addition problem?Hint and answer
  305. 305. Answer BACK
  306. 306.  What is the surface area of the following structure made of 8 cubes glued together. The side of each cube is 1 inch. Only consider the surfaces that are exposed.Hint and answer
  307. 307. Answer 32 square inches BACK
  308. 308. Count the number of cube you can see systematically. Looking from front: 4; back: 4, Left: 7, right: 7, Top: 5, Bottom: 5; The number of cube surfaces are 4 x 2 + 7 x 2 + 5 x 2 = 32 square inches you have a blue coin and a yellow coin. Place them in the following squares so that the blue one is always 1 row above the yellow one. How many different ways are there to place them in this manner?Hint and answer
  309. 309.  Blue one in the first row: 3, Blue one in the 2nd row: 3 x 5 = 15; Total = 3 + 15 = 18Answer 18 BACK
  310. 310.  Find the sequence and fill in the blanks  (1 ,4, 8), (2, 8, 16), (3, 12, 24), (4, 16, 32), ... The 10th group is (__, __, __)Hint and answer
  311. 311. Leading number sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Middle number sequence is 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 The ending number sequence is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80Answer (10, 40, 80) BACK
  312. 312. A farmer has 150 rabbits. There are 4 times as many female rabbits as male rabbits. How many male and female rabbits are there?Hint and answer

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