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: 13 42 60 33 51 88. After step 2, what is the 6th 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: 78 33 48 83 60 10. After step 4, 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: 68 30 89 53 17 47. After step 2, what is the 4th number from the left?
- 4.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 2?
- 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: 79 88 22 15 36 77. After step 2, what is the 4th 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: 15 84 69 45 91 97. 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: 25 39 14 88 56 32. After step 3, what is the 5th 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: 39 67 47 27 68 25. After step 4, what is the 1st number from the left?
- 9.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 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: 29 31 35 36 15 33. After step 2, what is the 2nd number from the left?
- 11.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?
- 12.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: 77 62 34 85 47 19. After step 2, 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: 56 47 50 95 15 17. After step 3, 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: 14 30 75 41 12 82. After step 2, what is the 6th 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: 64 40 34 67 33 32. After step 2, what is the 4th number from the left?
- 16.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 43 13 48 78 32. After step 4, 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: 68 19 28 30 81 36. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 40 86 53 15 66 23. After step 3, what is the 6th 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: 41 11 47 26 19 83. After step 4, what is the 2nd number from the left?
- 20.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 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: 76 68 13 97 28 53. After step 4, what is the 6th 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: 27 58 82 54 35 33. After step 2, what is the 6th number from the left?
- 23.A number machine multiplies a number by 3 and then adds 5. 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: 74 51 59 66 54 99. After step 4, what is the 4th number from the left?
- 25.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 2. What comes out after step 2?
- 26.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 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: 29 56 32 50 73 89. After step 2, what is the 4th 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: 12 18 47 52 72 66. After step 4, what is the 4th number from the left?
- 29.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 86 61 12 38 27. After step 2, what is the 1st number from the left?
- 30.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?
- 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: 73 34 81 86 17 54. After step 3, what is the 5th 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: 98 84 27 57 94 48. After step 4, what is the 6th 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: 62 53 59 94 14 76. After step 2, what is the 2nd 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: 18 37 76 67 92 82. After step 4, what is the 2nd number from the left?
- 35.A number machine multiplies a number by 3 and then adds 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 3 and then takes away 5. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 32 95 60 59 43 37. After step 4, what is the 5th 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 3. What comes out after step 2?
- 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: 92 25 85 22 24 68. After step 4, what is the 6th 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: 35 65 77 58 13 36. After step 4, what is the 2nd number from the left?
Answer key
- 88
- 78
- 53
- 51
- 88
- 15
- 88
- 68
- 65
- 35
- 254
- 62
- 56
- 82
- 40
- 43
- 30
- 23
- 47
- 60
- 97
- 33
- 56
- 66
- 20
- 84
- 56
- 47
- 12
- 229
- 17
- 48
- 53
- 82
- 22
- 61
- 32
- 27
- 85
- 35
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