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: 70 76 77 25 61 60. After step 4, 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: 64 47 95 49 39 24. 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: 26 22 38 91 28 21. After step 2, 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: 27 15 48 83 92 63. After step 4, what is the 5th number from the left?
- 5.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?
- 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: 95 15 90 10 24 11. After step 3, what is the 3rd number from the left?
- 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: 58 55 95 68 31 82. After step 4, what is the 1st 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: 28 41 94 22 25 91. After step 2, what is the 6th 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: 11 54 45 94 88 96. After step 2, 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: 25 12 78 59 76 29. After step 2, what is the 4th 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: 11 91 71 40 34 89. After step 2, what is the 5th 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: 19 30 20 12 54 84. After step 2, what is the 3rd 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: 27 28 92 88 71 22. After step 2, what is the 6th number from the left?
- 14.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 3?
- 15.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 16.A number machine multiplies a number by 2 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: 66 35 30 75 20 16. After step 2, what is the 1st 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: 28 71 96 35 85 66. After step 4, what is the 2nd number from the left?
- 19.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?
- 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: 75 35 88 62 63 57. After step 4, what is the 4th 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: 89 54 53 43 96 38. After step 2, what is the 2nd number from the left?
- 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: 33 20 67 84 72 51. After step 4, what is the 5th number from the left?
- 23.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 5. 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: 59 72 24 27 58 79. After step 2, what is the 6th number from the left?
- 25.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?
- 26.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 2?
- 27.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: 84 38 74 49 31 27. After step 2, what is the 1st number from the left?
- 28.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 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: 43 22 86 14 45 96. After step 2, what is the 3rd number from the left?
- 30.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: 47 26 84 21 30 80. After step 4, what is the 6th number from the left?
- 31.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?
- 32.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 33.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 21 57 56 85 41. After step 3, what is the 3rd 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: 75 81 87 34 28 67. After step 3, what is the 2nd 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: 39 19 51 80 29 95. After step 3, what is the 4th 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: 77 94 81 38 88 35. After step 4, what is the 3rd number from the left?
- 37.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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: 20 56 53 92 11 82. After step 2, what is the 2nd 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: 25 36 90 12 26 72. After step 3, what is the 3rd number from the left?
- 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: 22 95 82 28 14 40. After step 3, what is the 5th number from the left?
Answer key
- 61
- 39
- 21
- 83
- 48
- 24
- 31
- 25
- 96
- 12
- 40
- 19
- 22
- 49
- 69
- 51
- 75
- 85
- 42
- 62
- 43
- 84
- 65
- 58
- 61
- 27
- 27
- 26
- 43
- 80
- 47
- 23
- 56
- 81
- 39
- 77
- 100
- 82
- 36
- 82
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