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: 52 28 90 55 68 96. After step 4, what is the 2nd 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: 31 72 14 53 41 57. After step 2, what is the 4th 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: 42 32 40 64 97 58. After step 4, what is the 4th number from the left?
- 4.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 76 38 58 86 30. After step 3, what is the 6th number from the left?
- 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: 67 74 75 80 11 89. 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: 90 14 24 34 42 44. After step 2, what is the 1st 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: 72 74 87 53 17 45. After step 3, what is the 2nd number from the left?
- 8.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 9.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 3?
- 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: 95 35 63 86 39 25. After step 3, what is the 6th number from the left?
- 11.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 2. What comes out after step 2?
- 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: 13 76 81 36 42 14. After step 3, what is the 6th number from the left?
- 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: 88 85 29 40 15 45. After step 3, what is the 4th 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: 68 94 62 57 88 70. After step 4, what is the 3rd 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: 73 29 26 65 79 67. After step 2, what is the 2nd 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: 62 23 82 54 27 74. After step 2, what is the 6th 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: 98 89 97 66 55 24. After step 2, what is the 1st 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: 20 85 39 24 11 17. After step 3, what is the 2nd 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: 61 45 89 74 92 96. After step 4, what is the 2nd 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: 85 28 56 52 21 44. After step 2, what is the 4th number from the left?
- 21.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 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: 17 70 61 15 87 18. 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: 22 53 68 77 38 30. After step 3, what is the 2nd number from the left?
- 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: 68 50 59 23 77 75. After step 4, what is the 3rd number from the left?
- 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: 14 11 59 68 38 16. After step 3, what is the 4th number from the left?
- 26.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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: 56 62 46 10 40 73. After step 3, what is the 3rd number from the left?
- 28.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: 50 47 61 74 75 89. After step 4, what is the 6th 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: 34 77 83 20 26 36. After step 3, what is the 3rd number from the left?
- 30.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 31.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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: 98 80 97 95 93 58. After step 4, what is the 4th number from the left?
- 33.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?
- 34.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 3?
- 35.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 88 55 81 78 69. After step 2, what is the 1st 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: 58 31 32 75 24 73. After step 3, what is the 6th number from the left?
- 37.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?
- 38.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: 39 46 57 75 90 60. After step 2, what is the 4th number from the left?
- 39.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 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: 15 37 92 20 77 32. After step 4, what is the 3rd number from the left?
Answer key
- 90
- 14
- 42
- 30
- 89
- 90
- 45
- 91
- 178
- 86
- 17
- 14
- 88
- 70
- 73
- 27
- 24
- 39
- 92
- 56
- 84
- 70
- 68
- 59
- 14
- 269
- 56
- 89
- 34
- 134
- 100
- 95
- 190
- 228
- 55
- 24
- 147
- 75
- 133
- 37
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