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: 86 42 97 48 49 92. After step 2, what is the 6th number from the left?
- 2.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 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: 12 50 91 82 26 77. After step 4, what is the 6th 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: 24 40 70 61 36 33. After step 4, what is the 2nd number from the left?
- 5.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 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: 14 13 35 94 69 44. 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: 26 48 32 88 53 60. After step 2, what is the 3rd number from the left?
- 8.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 9.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 86 48 31 18. After step 2, what is the 3rd number from the left?
- 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: 16 19 41 72 74 17. After step 4, what is the 5th 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 5. What comes out after step 3?
- 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: 26 25 95 50 52 11. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 57 75 78 62 38 88. After step 2, what is the 5th 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: 96 42 26 77 21 59. After step 2, what is the 4th 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: 55 19 61 38 64 43. After step 3, what is the 2nd number from the left?
- 16.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 2. 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: 56 84 28 40 91 19. After step 3, 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: 39 17 83 95 65 94. After step 3, what is the 1st 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: 85 71 43 95 28 70. After step 4, what is the 5th number from the left?
- 20.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 3. 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 7. What comes out after step 3?
- 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: 54 55 89 91 69 27. After step 4, what is the 5th 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: 85 61 43 21 24 62. After step 2, what is the 2nd number from the left?
- 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: 10 57 19 91 73 24. After step 3, what is the 2nd number from the left?
- 25.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 26.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 27.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 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: 63 44 82 60 36 48. After step 4, what is the 3rd 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: 39 81 55 41 15 78. After step 3, what is the 2nd 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: 13 47 58 61 72 48. After step 3, 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: 53 24 63 31 76 29. 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: 37 85 24 82 25 84. After step 3, what is the 4th 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: 90 76 22 79 39 24. After step 4, 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: 92 93 27 75 51 34. After step 4, what is the 3rd number from the left?
- 35.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: 91 94 23 75 41 73. After step 2, what is the 5th 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: 63 56 40 43 26 16. After step 2, what is the 1st number from the left?
- 37.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 38.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 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: 88 19 17 71 84 47. After step 2, what is the 2nd number from the left?
- 40.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?
Answer key
- 49
- 48
- 26
- 33
- 281
- 44
- 26
- 201
- 35
- 16
- 61
- 25
- 62
- 26
- 38
- 119
- 28
- 95
- 43
- 39
- 202
- 89
- 24
- 73
- 51
- 30
- 43
- 48
- 39
- 61
- 63
- 37
- 90
- 75
- 41
- 63
- 38
- 45
- 19
- 10
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