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: 70 80 75 40 20 68. After step 4, what is the 4th number from the left?
- 2.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 84 93 36 75 17 80. After step 4, what is the 1st number from the left?
- 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: 21 55 41 30 34 74. After step 3, what is the 5th 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: 30 77 25 53 37 10. After step 3, what is the 2nd number from the left?
- 6.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 7.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?
- 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: 65 93 30 51 38 28. After step 3, what is the 3rd 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: 52 47 66 84 45 97. After step 3, what is the 5th 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 3. 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: 15 23 10 50 98 48. After step 3, 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: 78 53 38 25 11 63. After step 4, what is the 2nd number from the left?
- 13.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 3?
- 14.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 18 67 42 48 82. After step 2, what is the 1st number from the left?
- 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: 42 66 88 31 23 28. After step 2, what is the 4th 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: 20 87 71 41 30 16. After step 3, 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: 78 52 92 18 88 34. After step 4, what is the 3rd 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: 16 90 88 43 98 37. After step 2, what is the 1st number from the left?
- 19.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: 35 61 76 33 19 74. After step 4, what is the 1st number from the left?
- 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 3?
- 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: 12 29 19 73 31 30. 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 92 90 69 37 68. After step 3, what is the 1st number from the left?
- 23.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 93 89 86 41 77. After step 3, what is the 1st number from the left?
- 24.A number machine multiplies a number by 2 and then takes away 5. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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: 48 45 88 93 75 96. After step 2, what is the 1st number from the left?
- 26.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 94 71 24 92 19. After step 2, what is the 1st number from the left?
- 27.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 2?
- 28.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 27 43 30 35 83. After step 4, what is the 6th 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: 46 49 93 40 15 11. After step 4, what is the 6th 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: 24 31 62 29 76 23. After step 2, what is the 5th number from the left?
- 31.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 32.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 3?
- 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: 26 61 97 62 19 70. After step 4, 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: 59 75 81 41 37 22. After step 2, what is the 6th number from the left?
- 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: 38 53 92 43 34 18. After step 3, what is the 6th number from the left?
- 36.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: 46 54 10 52 62 20. After step 2, what is the 4th number from the left?
- 37.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 3. 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: 29 81 72 44 41 48. After step 3, what is the 6th 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: 16 42 25 23 88 33. After step 3, what is the 6th 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: 77 34 60 26 32 45. After step 2, what is the 2nd number from the left?
Answer key
- 70
- 18
- 93
- 30
- 53
- 92
- 30
- 51
- 84
- 9
- 98
- 63
- 11
- 18
- 66
- 71
- 52
- 16
- 19
- 10
- 31
- 99
- 93
- 9
- 45
- 94
- 22
- 83
- 11
- 29
- 70
- 63
- 62
- 22
- 43
- 10
- 39
- 48
- 33
- 60
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