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Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day:

  1. $140$ tickets were sold.
  2. The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.
  3. Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.
  4. The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.

Which of the following statements $\text{MUST}$ be $\text{FALSE}?$

  1. The numbers of Old and Middle-aged visitors buying Economy tickets were equal
  2. The numbers of Old and Middle-aged visitors buying Platinum tickets were equal
  3. The numbers of Middle-aged and Young visitors buying Gold tickets were equal
  4. The numbers of Gold and Platinum tickets bought by Young visitors were equal
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