Input Output Reasoning Worksheet
How to think it through (One step, one line): Read the rule carefully: what moves (or changes) in each step? Write the list (or number) after step 1, step 2, step 3 … each on a new line. Stop at the step asked and read the answer.
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- 1.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 21 61 10 22 87 30. After step 2, what is the 6th number from the left?
- 2.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 3.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 4.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 5.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 11 66 83 91 55 52. After step 3, what is the 4th number from the left?
- 6.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 7.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 90 71 85 76 83 16. After step 2, what is the 2nd number from the left?
- 8.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 10 47 55 38 37 60. After step 4, what is the 1st number from the left?
- 9.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 43 88 68 77 56 33. After step 2, what is the 1st number from the left?
- 10.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 87 31 41 71 56 32. After step 3, what is the 5th number from the left?
- 11.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 12.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 13.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 12 17 97 28 56 13. After step 2, what is the 6th number from the left?
- 14.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 15.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 58 56 97 32 18 45. After step 3, what is the 6th number from the left?
- 16.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 73 87 39 57 93 41. After step 2, what is the 2nd number from the left?
- 17.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 18.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 19.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 16 32 80 35 20 65. After step 2, what is the 6th number from the left?
- 20.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 27 95 31 33 16 74. After step 3, what is the 2nd number from the left?
- 21.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 26 82 57 51 40 54. After step 3, what is the 2nd number from the left?
- 22.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 23.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 24.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 25.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 54 57 91 56 67 63. After step 4, what is the 4th number from the left?
- 26.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 95 79 25 57 70 64. After step 2, what is the 4th number from the left?
- 27.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 88 77 21 79 82 58. After step 2, what is the 3rd number from the left?
- 28.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 39 15 25 85 19 83. After step 3, what is the 4th number from the left?
- 29.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 44 54 51 59 24 88. After step 2, what is the 4th number from the left?
- 30.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 98 26 94 72 52 40. After step 2, what is the 5th number from the left?
- 31.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 47 67 94 28 54 99. After step 3, what is the 6th number from the left?
- 32.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 25 45 12 99 32 77. After step 3, what is the 2nd number from the left?
- 33.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 13 27 48 45 98 63. After step 3, what is the 6th number from the left?
- 34.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 65 14 96 99 95 41. After step 2, what is the 1st number from the left?
- 35.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 67 70 13 73 69 97. After step 3, what is the 4th number from the left?
- 36.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 16 73 66 30 91 26. After step 4, what is the 3rd number from the left?
- 37.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 94 58 52 95 63 77. After step 4, what is the 6th number from the left?
- 38.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 39.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 68 14 62 41 28 70. After step 2, what is the 4th number from the left?
- 40.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 58 97 53 69 35 66. After step 2, what is the 5th number from the left?
Answer key
- 30
- 97
- 190
- 191
- 66
- 68
- 85
- 60
- 33
- 41
- 15
- 66
- 13
- 11
- 45
- 41
- 147
- 83
- 20
- 27
- 57
- 67
- 41
- 38
- 57
- 57
- 77
- 15
- 54
- 72
- 54
- 77
- 45
- 99
- 67
- 66
- 95
- 229
- 62
- 69
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