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: 49 57 12 98 86 59. After step 3, what is the 1st number from the left?
- 2.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 30 79 74 29 66. After step 2, what is the 2nd number from the left?
- 3.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 2?
- 4.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?
- 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: 80 67 32 57 71 20. After step 4, what is the 6th number from the left?
- 6.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: 51 83 85 71 88 28. After step 3, what is the 1st 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: 87 71 80 77 17 76. After step 4, what is the 6th 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: 89 53 58 90 55 44. After step 2, what is the 6th 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: 13 79 80 15 42 21. After step 2, what is the 2nd number from the left?
- 10.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: 13 61 33 51 53 39. After step 3, what is the 2nd number from the left?
- 11.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 12.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 88 38 69 53 82. After step 3, what is the 4th number from the left?
- 13.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?
- 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: 98 55 42 73 71 44. After step 4, what is the 6th number from the left?
- 15.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 2?
- 16.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 17.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 69 45 81 20 87. After step 4, what is the 6th number from the left?
- 18.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 4. 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: 58 56 62 81 90 73. After step 3, what is the 1st 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: 78 25 27 26 39 20. After step 3, what is the 1st number from the left?
- 21.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: 70 61 15 65 45 38. After step 2, what is the 5th 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: 59 70 21 11 18 45. After step 3, what is the 1st number from the left?
- 23.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 24.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: 55 32 88 36 79 77. After step 4, what is the 6th number from the left?
- 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: 41 45 54 62 40 87. After step 2, what is the 4th number from the left?
- 26.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 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: 30 85 82 86 24 17. 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: 52 97 96 68 57 15. After step 2, what is the 2nd number from the left?
- 29.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 2. What comes out after step 2?
- 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: 10 56 27 60 19 54. After step 4, what is the 5th number from the left?
- 31.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 15 86 14 39 17. After step 2, 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: 38 82 16 13 36 51. After step 2, what is the 3rd 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: 82 93 34 42 88 98. After step 2, what is the 5th number from the left?
- 34.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: 63 10 22 85 81 47. After step 2, what is the 2nd 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: 31 35 65 30 11 13. After step 4, 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: 50 62 38 28 12 91. After step 3, what is the 5th number from the left?
- 37.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 38.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 86 85 17 64 16. After step 2, what is the 2nd number from the left?
- 39.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 67 50 62 84. After step 3, what is the 6th number from the left?
- 40.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 74 22 43 50 33. After step 3, what is the 4th number from the left?
Answer key
- 98
- 74
- 38
- 78
- 71
- 88
- 17
- 44
- 15
- 33
- 9
- 30
- 66
- 73
- 25
- 200
- 20
- 56
- 90
- 20
- 65
- 70
- 41
- 79
- 54
- 254
- 30
- 96
- 11
- 56
- 17
- 38
- 42
- 22
- 30
- 28
- 22
- 85
- 84
- 35
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