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If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?
  • a)
    8
  • b)
    9
  • c)
    16
  • d)
    23
  • e)
    24
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If (x # y) represents the remainder that results when the positive int...
The definition given tells us that when x is divided by y a remainder of (x # y) results.  Consequently, when 16 is divided by y a remainder of (16 # y) results.  Since (16 # y) = 1, we can conclude that when 16 is divided by y a remainder of 1 results.
Therefore, in determining the possible values of y, we must find all the integers that will divide into 16 and leave a remainder of 1.  These integers are 3 , 5, and 15.  The sum of these integers is 23.
The correct answer is D.
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