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: 72 49 16 44 55 62. After step 3, what is the 1st 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: 82 22 48 96 21 60. After step 4, what is the 2nd number from the left?
- 3.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 24 30 85 75 88. 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: 57 14 30 61 76 95. After step 4, what is the 4th number from the left?
- 5.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?
- 6.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 7.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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: 37 72 22 17 57 65. After step 4, 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: 51 96 53 85 50 16. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 95 55 66 15 50 59. After step 2, what is the 1st number from the left?
- 11.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 12.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: 61 19 85 95 90 66. After step 2, what is the 5th 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: 87 88 31 27 50 20. After step 2, what is the 6th 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 9. What comes out after step 2?
- 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: 33 21 68 54 95 88. After step 3, what is the 3rd number from the left?
- 16.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: 52 28 32 43 71 19. After step 2, what is the 3rd number from the left?
- 17.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 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: 19 11 38 74 10 40. After step 3, what is the 4th number from the left?
- 19.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 2. 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: 14 52 91 86 69 26. After step 2, what is the 5th 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 5. What comes out after step 2?
- 22.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 23.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?
- 24.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 25.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: 79 24 25 34 20 76. After step 3, what is the 6th 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: 78 50 57 27 49 90. After step 3, what is the 3rd number from the left?
- 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: 91 31 99 17 19 63. After step 4, what is the 3rd number from the left?
- 28.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 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: 72 76 71 34 18 96. After step 2, what is the 1st 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 3. What comes out after step 3?
- 31.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 32.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 9. 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 8. What comes out after step 3?
- 34.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: 38 70 96 31 23 41. After step 3, what is the 1st 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: 93 85 15 75 59 17. After step 2, what is the 1st number from the left?
- 36.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?
- 37.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?
- 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: 87 97 26 95 38 13. 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: 28 70 48 52 92 66. After step 2, what is the 4th 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: 32 22 57 11 28 49. After step 2, what is the 1st number from the left?
Answer key
- 16
- 22
- 88
- 61
- 42
- 30
- 107
- 57
- 16
- 15
- 9
- 90
- 50
- 61
- 54
- 28
- 52
- 19
- 23
- 69
- 57
- 67
- 31
- 91
- 20
- 50
- 31
- 41
- 96
- 10
- 7
- 65
- 57
- 23
- 93
- 71
- 65
- 38
- 52
- 11
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