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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 11 72 88 96 59 82. After step 4, what is the 2nd number from the left?
- 2.A number machine multiplies a number by 2 and then takes away 5. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 3.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: 53 25 59 95 20 37. After step 4, what is the 4th number from the left?
- 4.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 5.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 36 73 60 71 84. After step 2, what is the 6th number from the left?
- 6.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: 18 72 46 95 57 11. After step 2, what is the 3rd number from the left?
- 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: 42 92 53 95 54 20. After step 2, what is the 4th number from the left?
- 8.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 9.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 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: 35 98 33 30 14 83. After step 4, what is the 5th number from the left?
- 11.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: 90 29 86 98 14 22. After step 4, what is the 1st number from the left?
- 12.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 13.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: 52 13 34 80 29 41. After step 2, what is the 2nd number from the left?
- 14.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: 29 73 30 58 38 55. After step 2, what is the 1st number from the left?
- 15.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: 80 99 55 84 96 45. After step 3, what is the 4th 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: 43 59 64 83 23 84. After step 2, what is the 3rd number from the left?
- 17.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: 23 62 65 75 12 64. After step 2, what is the 4th number from the left?
- 18.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 39 15 13 82 59. After step 3, what is the 5th number from the left?
- 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: 96 71 35 54 11 81. After step 2, what is the 3rd 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: 58 63 80 34 57 28. After step 2, what is the 5th 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: 71 90 33 73 11 65. After step 2, what is the 2nd number from the left?
- 22.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: 36 42 30 15 16 93. After step 4, what is the 2nd number from the left?
- 23.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: 28 49 89 72 82 36. After step 3, what is the 1st number from the left?
- 24.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 25.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: 15 53 63 65 27 48. After step 4, what is the 1st 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 58 40 98 55 68. After step 3, what is the 2nd number from the left?
- 27.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: 66 70 93 49 30 31. After step 4, what is the 2nd 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: 30 35 76 62 33 44. After step 4, what is the 3rd 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: 72 32 14 77 27 67. After step 3, what is the 5th number from the left?
- 30.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 80 56 70 99 88 43. After step 3, what is the 4th number from the left?
- 32.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: 84 68 99 27 73 76. After step 4, what is the 5th number from the left?
- 33.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: 78 67 31 19 18 94. After step 3, what is the 6th number from the left?
- 34.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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: 32 47 60 24 96 94. After step 2, what is the 5th number from the left?
- 36.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: 59 42 49 25 70 84. After step 4, what is the 5th number from the left?
- 37.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: 43 25 54 29 20 66. After step 2, what is the 4th number from the left?
- 38.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?
- 39.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 40.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 9. What comes out after step 3?
Answer key
- 88
- 17
- 53
- 49
- 71
- 72
- 53
- 75
- 29
- 30
- 14
- 78
- 29
- 29
- 99
- 59
- 65
- 82
- 71
- 80
- 73
- 42
- 89
- 107
- 15
- 95
- 31
- 44
- 14
- 21
- 56
- 84
- 94
- 70
- 60
- 70
- 25
- 67
- 45
- 58
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