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: 16 40 38 25 81 23. 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: 70 88 33 34 13 17. After step 2, what is the 5th number from the left?
- 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: 29 53 93 89 40 84. After step 4, what is the 2nd 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: 29 16 36 20 71 81. After step 3, what is the 1st number from the left?
- 5.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?
- 6.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 7.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 87 25 35 24 17. After step 2, what is the 5th 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: 64 13 11 70 78 88. After step 2, what is the 2nd 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: 96 47 33 78 91 57. After step 3, 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: 34 18 91 70 26 17. After step 4, what is the 1st 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: 57 14 60 55 73 95. After step 4, what is the 3rd 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: 98 20 83 13 64 22. After step 3, what is the 1st 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: 94 29 26 38 16 81. After step 2, what is the 4th number from the left?
- 14.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 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: 71 83 39 41 46 82. After step 3, what is the 1st 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: 14 44 85 19 58 48. After step 2, what is the 2nd number from the left?
- 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: 48 42 73 49 99 60. After step 2, what is the 5th number from the left?
- 18.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 12 19 71 64 48. After step 4, what is the 2nd number from the left?
- 19.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 6. 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: 87 60 55 14 92 10. After step 4, what is the 3rd number from the left?
- 21.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 2. What comes out after step 2?
- 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: 13 84 33 55 14 42. After step 2, what is the 1st 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: 92 27 30 24 86 75. After step 2, what is the 1st number from the left?
- 24.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 25.A number machine multiplies a number by 2 and then takes away 4. 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 1. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 27.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?
- 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: 71 76 12 64 28 15. After step 4, what is the 5th number from the left?
- 29.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?
- 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: 67 62 49 78 86 79. After step 3, what is the 4th number from the left?
- 31.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 99 35 82 10 49 50. After step 3, what is the 2nd 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: 31 26 18 84 83 93. After step 3, what is the 3rd number from the left?
- 34.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 12 20 96 10 34 76. After step 4, what is the 5th number from the left?
- 36.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 5. 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: 79 50 66 29 65 70. 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: 44 76 95 29 32 96. After step 3, what is the 3rd 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: 77 18 49 75 56 10. After step 2, what is the 1st 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: 27 99 78 13 79 18. After step 3, what is the 6th number from the left?
Answer key
- 38
- 13
- 89
- 16
- 41
- 19
- 35
- 78
- 57
- 91
- 60
- 98
- 29
- 97
- 83
- 19
- 49
- 19
- 34
- 60
- 30
- 13
- 24
- 19
- 44
- 55
- 38
- 12
- 119
- 67
- 19
- 82
- 31
- 47
- 96
- 11
- 65
- 76
- 10
- 18
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