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Input Output Reasoning Worksheet

Logical reasoning lesson 25: Input–output machines · Set 490 · 40 questions
TalentJR

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. 1.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 4. What comes out after step 2?
  2. 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: 40 87 30 63 49 64. After step 4, what is the 2nd number from the left?
  3. 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: 17 85 57 78 44 63. After step 4, what is the 1st number from the left?
  4. 4.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 7. What comes out after step 3?
  5. 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 9. What comes out after step 2?
  6. 6.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 3?
  7. 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: 43 15 14 46 90 55. After step 3, what is the 3rd number from the left?
  8. 8.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?
  9. 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: 46 73 56 70 31 39. After step 2, what is the 1st number from the left?
  10. 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: 26 93 83 31 43 77. After step 2, what is the 5th number from the left?
  11. 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: 29 85 63 51 33 52. After step 3, what is the 3rd number from the left?
  12. 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 80 95 89 21 68. After step 3, what is the 2nd number from the left?
  13. 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: 81 43 66 49 35 16. After step 2, what is the 2nd number from the left?
  14. 14.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?
  15. 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: 98 73 86 38 39 63. After step 2, what is the 3rd number from the left?
  16. 16.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 5. What comes out after step 2?
  17. 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: 96 31 62 49 87 18. After step 4, what is the 1st number from the left?
  18. 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: 20 23 96 55 78 43. After step 2, what is the 3rd number from the left?
  19. 19.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 3?
  20. 20.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 10 12 54 68 16. After step 2, what is the 2nd number from the left?
  21. 21.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?
  22. 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: 35 32 15 88 16 26. After step 2, what is the 6th number from the left?
  23. 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: 88 21 92 11 55 58. After step 2, what is the 4th number from the left?
  24. 24.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 4. What comes out after step 2?
  25. 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: 39 22 93 96 13 57. After step 3, what is the 2nd number from the left?
  26. 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: 61 78 67 51 74 58. After step 4, what is the 2nd number from the left?
  27. 27.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 9. What comes out after step 2?
  28. 28.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?
  29. 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: 36 78 42 64 18 25. After step 4, what is the 2nd number from the left?
  30. 30.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 3?
  31. 31.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 2?
  32. 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: 51 46 34 35 24 52. After step 3, what is the 2nd number from the left?
  33. 33.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 4. What comes out after step 3?
  34. 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: 88 93 81 20 86 73. After step 2, what is the 4th number from the left?
  35. 35.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 4. What comes out after step 2?
  36. 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: 13 39 12 54 24 60. After step 2, what is the 4th number from the left?
  37. 37.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: 42 51 88 59 68 19. After step 3, what is the 6th number from the left?
  38. 38.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 2. What comes out after step 3?
  39. 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: 23 80 53 72 70 59. After step 4, what is the 1st number from the left?
  40. 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: 91 25 65 73 80 99. After step 2, what is the 6th number from the left?

Answer key

  1. 10
  2. 64
  3. 85
  4. 150
  5. 30
  6. 70
  7. 43
  8. 39
  9. 31
  10. 43
  11. 51
  12. 89
  13. 66
  14. 19
  15. 98
  16. 26
  17. 96
  18. 20
  19. 174
  20. 12
  21. 9
  22. 26
  23. 92
  24. 24
  25. 22
  26. 74
  27. 39
  28. 34
  29. 64
  30. 242
  31. 15
  32. 51
  33. 46
  34. 20
  35. 22
  36. 39
  37. 19
  38. 41
  39. 80
  40. 99

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