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: 99 31 38 94 40 24. 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: 36 22 82 17 81 90. After step 4, what is the 5th number from the left?
- 3.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 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: 48 59 65 20 41 39. After step 4, what is the 2nd 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 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: 13 35 76 79 75 22. After step 2, 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: 24 17 95 89 27 16. After step 4, what is the 5th 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: 87 84 89 44 79 15. After step 2, what is the 3rd 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: 91 29 39 36 12 25. After step 4, what is the 6th 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: 54 41 90 79 88 84. 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: 47 70 31 50 30 82. After step 3, what is the 1st number from the left?
- 12.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 2?
- 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: 10 93 33 79 18 77. After step 2, what is the 6th 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: 90 72 53 23 65 99. After step 2, what is the 4th number from the left?
- 15.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 2?
- 16.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?
- 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: 32 65 58 63 51 66. After step 4, what is the 6th number from the left?
- 18.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?
- 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: 49 90 10 50 81 92. After step 2, what is the 1st number from the left?
- 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: 78 94 45 83 99 51. After step 2, what is the 1st number from the left?
- 21.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 31 72 68 42 61. After step 2, what is the 5th number from the left?
- 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: 99 37 22 45 70 26. After step 2, what is the 1st number from the left?
- 23.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 7. 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: 25 70 32 19 26 67. After step 2, 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: 21 20 85 19 25 14. After step 2, 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: 19 15 98 40 86 67. After step 3, what is the 2nd 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: 17 40 88 35 59 33. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 16 80 49 14 73 30. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 18 63 76 40 71 62. After step 2, what is the 2nd number from the left?
- 30.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 3?
- 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: 32 42 76 65 17 71. After step 2, what is the 5th number from the left?
- 32.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?
- 33.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?
- 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: 35 86 95 70 87 54. After step 3, what is the 6th number from the left?
- 35.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 36.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 88 86 21 63 48 31. After step 2, what is the 6th number from the left?
- 38.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 26 93 62 19 80. After step 3, what is the 1st 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: 16 90 70 64 86 40. After step 3, what is the 1st number from the left?
- 40.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 2. What comes out after step 3?
Answer key
- 38
- 22
- 28
- 39
- 71
- 76
- 17
- 87
- 25
- 84
- 82
- 38
- 77
- 53
- 27
- 10
- 51
- 45
- 92
- 99
- 42
- 99
- 31
- 19
- 19
- 19
- 17
- 73
- 71
- 18
- 65
- 15
- 5
- 54
- 31
- 7
- 48
- 19
- 90
- 80
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