When we perform a ‘digit slide’ on a number we move its unit digit’s to the front of the number. For example, the result of a ‘digit slide’ on 6471 is 1647. Let ‘z’ be the smallest positive integer with 5 as its unit’s digit such that the result of a ‘digit slide’ on number equals 4 times the number. How many digits will ‘z’ have?
a. 7
b. 6
c. 4
d. 3

• Letting X be the positive integer in question, 4X is the result of the digit slide on X.
  The units digit of X is 5, and 5• 4 = 20, so the units digit of 4X is 0, and the last two digits
  of X are 05.
  We can continue the argument as follows:
  05 • 4 = 20, so the last two digits of 4X are 20, and the last three digits of X are 205,
  205 • 4 = 820, so the last three digits of 4X are 820, and the last four digits of X are
  8205,
  8205 • 4 = 32820, so the last four digits of 4X are 2820, and the last five digits of X are
  28205,
  28205 • 4 = 112820, so the last five digits of 4X are 12820, and the last six digits of X are
  128205, and finally
  128205 • 4 = 512820, which just happens to be the result of a digit slide on 128205.
  Hence, 128205 is the smallest positive integer with 5 as its units digit such that the result
  of a digit slide on the number equals 4 times the number.
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