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: 74 20 22 53 52 85. After step 3, what is the 3rd number from the left?
- 2.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: 23 45 73 87 26 98. After step 4, what is the 1st number from the left?
- 3.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?
- 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: 74 87 12 96 13 30. After step 4, what is the 6th number from the left?
- 5.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: 18 70 19 84 29 15. After step 2, what is the 1st number from the left?
- 6.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 2?
- 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: 27 31 32 87 53 15. After step 2, what is the 1st 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: 72 45 57 67 83 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 29 69 35 48 71 49. After step 4, what is the 1st number from the left?
- 10.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 11.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 23 49 12 88 68. After step 3, what is the 6th 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: 38 98 10 48 26 13. After step 4, what is the 6th number from the left?
- 13.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 2?
- 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: 58 66 75 89 98 93. After step 2, 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: 81 72 79 19 69 14. After step 2, what is the 6th 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: 30 31 10 18 94 41. After step 4, what is the 2nd 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: 71 63 19 75 23 97. After step 2, what is the 3rd number from the left?
- 18.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 19.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 3?
- 20.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 2?
- 21.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 3. 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: 57 91 23 30 25 81. After step 2, what is the 2nd 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: 33 35 28 66 51 37. After step 2, what is the 4th 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: 18 81 63 14 96 86. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 32 61 15 68 20 69. After step 3, what is the 4th 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: 45 79 25 21 93 91. After step 2, what is the 1st number from the left?
- 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: 19 29 10 93 39 16. After step 3, what is the 1st number from the left?
- 28.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 10 31 86 74 99 87. After step 4, 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: 45 32 46 19 15 20. After step 2, what is the 3rd number from the left?
- 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: 85 12 92 47 42 37. After step 2, 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: 20 11 38 99 16 17. After step 4, what is the 5th 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: 28 13 26 43 90 32. After step 2, what is the 3rd number from the left?
- 34.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 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: 11 88 12 27 99 63. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 12 93 39 46 19 45. After step 4, what is the 1st number from the left?
- 37.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 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: 29 15 16 91 84 10. After step 2, what is the 6th number from the left?
- 39.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 62 37 77 44 99. After step 3, what is the 5th number from the left?
- 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: 44 39 50 51 68 49. After step 2, what is the 5th number from the left?
Answer key
- 53
- 23
- 77
- 13
- 84
- 44
- 87
- 45
- 29
- 25
- 68
- 13
- 92
- 58
- 14
- 18
- 71
- 19
- 79
- 6
- 107
- 25
- 66
- 18
- 61
- 21
- 93
- 93
- 31
- 32
- 47
- 11
- 28
- 55
- 27
- 12
- 24
- 10
- 37
- 50
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