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: 75 60 21 71 35 67. After step 3, what is the 5th 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: 71 35 41 29 72 54. After step 2, what is the 2nd number from the left?
- 3.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: 86 93 14 97 79 24. After step 4, what is the 2nd number from the left?
- 4.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 5.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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: 76 14 86 70 49 16. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 23 17 46 22 85 94. After step 2, what is the 6th number from the left?
- 8.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 9.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: 27 11 92 70 64 96. After step 4, what is the 4th 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: 25 33 27 41 77 43. After step 2, what is the 1st number from the left?
- 11.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 43 59 21 98 26. After step 4, what is the 2nd number from the left?
- 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: 21 62 49 29 38 17. After step 4, what is the 4th number from the left?
- 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: 11 20 62 53 51 49. After step 3, what is the 5th number from the left?
- 14.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: 34 59 70 97 23 35. After step 3, what is the 6th number from the left?
- 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: 24 50 93 29 16 75. After step 3, what is the 3rd number from the left?
- 16.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 3. 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: 84 62 65 35 40 64. After step 2, what is the 5th number from the left?
- 18.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: 86 24 84 40 38 57. After step 2, what is the 3rd number from the left?
- 19.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?
- 20.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: 84 23 30 54 17 85. After step 2, what is the 4th 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: 65 11 85 89 71 31. After step 2, what is the 3rd number from the left?
- 22.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 16 26 19 58 97. After step 3, what is the 1st number from the left?
- 23.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 4. 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: 83 91 90 93 51 64. After step 3, what is the 6th number from the left?
- 25.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 26.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 65 68 50 37 86. After step 4, what is the 1st 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: 63 72 78 65 34 82. After step 2, 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: 60 83 21 22 56 20. After step 2, what is the 2nd number from the left?
- 29.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 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: 80 31 89 64 77 35. After step 2, what is the 1st 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: 85 92 49 62 15 30. After step 4, what is the 4th number from the left?
- 32.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 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: 99 18 92 28 98 12. After step 4, what is the 2nd 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: 84 85 17 48 44 28. After step 3, what is the 4th number from the left?
- 35.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 2?
- 36.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 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: 97 39 34 16 17 61. After step 2, what is the 2nd number from the left?
- 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: 86 12 29 76 90 13. After step 3, what is the 5th number from the left?
- 39.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 40.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 3. What comes out after step 3?
Answer key
- 21
- 71
- 93
- 33
- 18
- 76
- 94
- 15
- 64
- 77
- 59
- 29
- 20
- 35
- 50
- 42
- 40
- 24
- 15
- 30
- 65
- 16
- 40
- 93
- 29
- 23
- 63
- 60
- 150
- 31
- 49
- 77
- 18
- 84
- 5
- 46
- 17
- 29
- 68
- 120
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