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A word-and-number arrangement machine works on an input line of words and two-digit numbers in steps, and in this machine nothing ever changes place. In each step the leftmost number it has not already dealt with is rubbed out and the difference of its two digits — the larger digit minus the smaller — is written in that same position. Words are never touched, and the machine stops once every number of the line has been dealt with.
Input: 74 shirt 39 scarf 62 jacket.
Which of the following is the last step of the above arrangement?

Competition practiceInput-Output
  • A3 shirt 6 scarf 62 jacket
  • B11 shirt 12 scarf 8 jacket
  • C47 shirt 93 scarf 26 jacket
  • D3 shirt 6 scarf 4 jacket

Step-by-Step Solution

Step 1 turns 74 into 7 minus 4, that is 3: 3 shirt 39 scarf 62 jacket. Step 2 turns 39 into 9 minus 3, that is 6: 3 shirt 6 scarf 62 jacket. Step 3, the last, turns 62 into 6 minus 2, that is 4: 3 shirt 6 scarf 4 jacket. "3 shirt 6 scarf 62 jacket" is Step 2, one step short. "11 shirt 12 scarf 8 jacket" adds the digits instead of subtracting them. "47 shirt 93 scarf 26 jacket" writes each number backwards, which is a different machine altogether.
Answer: D) 3 shirt 6 scarf 4 jacket

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