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: 17 20 44 24 95 34. After step 2, what is the 4th 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: 80 12 63 50 66 71. After step 3, what is the 1st number from the left?
- 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: 53 86 18 58 38 15. After step 2, what is the 5th 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: 79 43 75 53 13 28. After step 4, what is the 1st number from the left?
- 5.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 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: 94 91 96 20 66 36. After step 2, what is the 6th 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: 66 25 64 43 54 21. After step 2, what is the 3rd 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: 19 21 86 67 34 22. After step 2, what is the 4th number from the left?
- 9.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 3?
- 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 20 14 70 37 38. After step 2, what is the 6th 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: 46 50 36 37 55 86. After step 3, what is the 1st 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: 91 10 40 74 34 25. 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: 89 22 24 58 30 45. After step 3, what is the 1st number from the left?
- 14.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 8. 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: 45 40 73 77 21 22. After step 3, what is the 5th number from the left?
- 16.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 85 65 66 71 23. After step 2, what is the 2nd number from the left?
- 17.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?
- 18.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 19.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 20.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 2. What comes out after step 2?
- 21.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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 18 58 33 73 51. After step 3, what is the 3rd number from the left?
- 23.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 63 30 40 28 82. After step 4, what is the 6th number from the left?
- 24.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?
- 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: 41 39 13 67 36 46. After step 4, what is the 2nd number from the left?
- 26.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 3?
- 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 5. What comes out after step 2?
- 28.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 29.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 13 50 52 42 90. After step 2, what is the 1st number from the left?
- 30.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?
- 31.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 7. 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: 89 66 90 30 91 32. After step 3, what is the 3rd 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: 26 37 53 34 86 67. After step 3, what is the 1st 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: 76 65 70 71 99 96. After step 3, what is the 5th number from the left?
- 35.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?
- 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: 38 46 69 82 12 42. After step 4, what is the 6th 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: 14 26 68 23 18 58. After step 2, 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: 86 90 46 19 51 76. After step 4, what is the 2nd number from the left?
- 39.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 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: 67 35 19 17 10 94. After step 2, what is the 6th number from the left?
Answer key
- 24
- 80
- 58
- 79
- 23
- 36
- 25
- 21
- 37
- 37
- 86
- 40
- 89
- 44
- 73
- 65
- 46
- 10
- 61
- 14
- 58
- 51
- 82
- 20
- 46
- 86
- 41
- 151
- 90
- 5
- 42
- 66
- 26
- 70
- 15
- 12
- 26
- 86
- 11
- 94
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