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: 28 55 40 15 51 50. After step 3, what is the 3rd number from the left?
- 2.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 11 89 92 44 68 35. After step 4, what is the 4th 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 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: 11 57 65 52 81 15. After step 3, what is the 1st 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: 99 79 42 18 75 90. After step 2, what is the 2nd number from the left?
- 7.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 8.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 93 39 36 21 40. After step 3, what is the 1st number from the left?
- 9.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 2?
- 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: 50 92 98 24 62 12. After step 4, what is the 2nd 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: 23 64 17 37 26 68. After step 4, what is the 4th 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: 27 41 23 57 32 33. After step 2, what is the 2nd number from the left?
- 13.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 14.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 28 81 99 65 90 18. After step 4, what is the 6th 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 6. 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: 34 54 60 38 24 21. After step 2, what is the 6th 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: 83 37 45 42 27 96. After step 4, what is the 2nd number from the left?
- 19.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 7. 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: 64 31 53 88 56 92. After step 4, what is the 2nd 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: 26 90 28 87 36 91. After step 4, 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: 94 18 14 33 32 23. After step 2, what is the 2nd number from the left?
- 23.A number machine multiplies a number by 3 and then adds 4. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 15 51 29 82 57 80. After step 3, what is the 1st 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: 39 30 53 55 80 45. After step 4, what is the 2nd number from the left?
- 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: 32 48 10 80 85 36. After step 3, what is the 6th number from the left?
- 27.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 18 51 29 63 33 86. After step 4, what is the 2nd 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: 25 41 14 58 59 71. After step 3, what is the 1st number from the left?
- 30.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 35 99 38 96 36. After step 4, what is the 2nd 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: 28 12 36 55 40 59. After step 4, what is the 4th 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: 14 29 94 86 83 11. After step 4, what is the 1st number from the left?
- 33.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 2?
- 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: 96 63 20 74 66 76. After step 3, what is the 1st number from the left?
- 35.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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: 92 33 73 17 98 78. After step 3, what is the 4th number from the left?
- 37.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?
- 38.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 39.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 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: 52 26 22 86 28 87. After step 2, what is the 5th number from the left?
Answer key
- 50
- 24
- 44
- 69
- 11
- 90
- 242
- 21
- 40
- 24
- 26
- 41
- 16
- 85
- 90
- 123
- 21
- 83
- 241
- 88
- 87
- 18
- 52
- 82
- 55
- 85
- 77
- 29
- 14
- 96
- 40
- 94
- 43
- 20
- 217
- 92
- 9
- 39
- 10
- 28
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