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: 84 96 43 32 14 73. After step 4, what is the 3rd 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 19 92 87 25 32. After step 4, what is the 3rd number from the left?
- 3.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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: 62 98 10 86 77 64. After step 4, what is the 6th number from the left?
- 5.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: 56 26 14 82 67 97. After step 4, what is the 5th number from the left?
- 6.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 3?
- 7.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?
- 8.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 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: 16 15 26 30 34 71. After step 2, what is the 1st 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: 32 18 65 97 13 91. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 32 98 45 13 76 29. After step 2, what is the 6th 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: 54 98 21 18 60 55. After step 2, what is the 5th number from the left?
- 13.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 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: 47 99 33 56 52 31. After step 4, 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: 22 10 46 93 13 90. After step 4, what is the 5th 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: 38 37 23 67 51 98. After step 3, what is the 1st 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: 58 66 16 41 33 63. After step 4, what is the 2nd 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: 24 11 71 48 79 97. After step 3, what is the 1st number from the left?
- 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: 48 23 99 13 72 65. After step 3, what is the 2nd 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: 32 55 67 36 12 75. 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: 28 24 96 99 32 95. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 26 82 36 75 88 30. After step 3, what is the 4th 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: 10 34 11 72 62 96. After step 3, what is the 4th number from the left?
- 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: 67 28 68 21 24 83. After step 3, 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 6. What comes out after step 2?
- 26.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 27.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 7. 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: 17 23 39 51 95 93. After step 3, what is the 5th number from the left?
- 29.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 30.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 31.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 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 2. 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: 53 19 32 75 15 10. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 38 90 45 10 12 92. After step 2, what is the 3rd number from the left?
- 35.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 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: 75 41 88 76 58 86. After step 2, what is the 4th number from the left?
- 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: 46 26 25 19 34 17. After step 2, what is the 4th number from the left?
- 38.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 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: 58 36 63 52 81 18. After step 2, what is the 2nd 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: 91 88 96 54 62 22. After step 3, what is the 6th number from the left?
Answer key
- 73
- 36
- 282
- 10
- 82
- 67
- 15
- 20
- 71
- 18
- 76
- 18
- 42
- 99
- 93
- 98
- 33
- 97
- 72
- 36
- 28
- 26
- 10
- 24
- 33
- 190
- 16
- 23
- 50
- 8
- 256
- 5
- 32
- 38
- 80
- 88
- 26
- 34
- 63
- 22
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