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: 32 83 51 90 45 27. After step 4, what is the 1st number from the left?
- 2.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 3.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 93 14 21 91 43. After step 4, what is the 1st number from the left?
- 4.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 11 77 55 29 84. After step 4, what is the 3rd number from the left?
- 5.A number machine multiplies a number by 2 and then takes away 5. 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: 74 57 88 26 32 15. After step 4, what is the 4th 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: 20 13 93 12 10 37. After step 3, what is the 3rd number from the left?
- 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: 84 68 54 62 33 64. After step 3, what is the 1st number from the left?
- 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 12 22 40 83 21. After step 3, what is the 5th number from the left?
- 10.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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: 79 81 37 40 85 63. After step 3, what is the 2nd number from the left?
- 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: 18 83 55 19 78 45. After step 2, what is the 4th number from the left?
- 13.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?
- 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: 21 95 17 56 68 10. After step 2, what is the 2nd 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: 91 27 18 63 50 73. After step 2, what is the 3rd number from the left?
- 16.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 2?
- 17.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 18.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 19.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 36 62 44 39 41 90. After step 3, 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: 22 96 98 30 89 23. After step 2, what is the 4th 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: 37 36 98 17 77 96. After step 4, what is the 2nd 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 2. What comes out after step 3?
- 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: 96 63 45 77 47 24. After step 4, what is the 5th 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: 92 11 43 64 15 60. After step 2, what is the 2nd number from the left?
- 26.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 3. 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: 36 67 31 80 60 68. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 46 10 45 66 24 94. After step 2, what is the 2nd number from the left?
- 29.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 30.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 3. 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: 21 79 82 61 60 50. After step 4, what is the 6th number from the left?
- 32.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?
- 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: 62 82 71 88 52 25. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 22 80 35 15 13 92. After step 4, what is the 1st number from the left?
- 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: 69 94 25 66 35 20. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 55 41 79 68 97 80. After step 3, what is the 2nd number from the left?
- 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: 70 33 36 14 74 42. After step 3, what is the 3rd 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: 16 96 42 28 92 66. After step 3, what is the 4th 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: 52 43 62 24 80 88. After step 4, what is the 2nd 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: 58 34 33 36 26 86. After step 4, what is the 3rd number from the left?
Answer key
- 90
- 54
- 14
- 55
- 9
- 57
- 20
- 33
- 22
- 46
- 81
- 55
- 269
- 68
- 91
- 73
- 59
- 8
- 42
- 62
- 30
- 36
- 67
- 45
- 64
- 94
- 67
- 24
- 30
- 68
- 50
- 9
- 52
- 92
- 20
- 55
- 36
- 16
- 43
- 34
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