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CAT 2018 Slot 2 — DILR Question 32

Mixed PracticeEasy
Passage / Data

Answer the following question based on the information given below.

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 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 MUST be FALSE?

Answer & solution

Correct answer: The numbers of Old and Middle-aged visitors buying Economy tickets were equal

  • A

    The numbers of Middle-aged and Young visitors buying Gold tickets were equal

  • The numbers of Old and Middle-aged visitors buying Economy tickets were equal

  • C

    The numbers of Gold and Platinum tickets bought by Young visitors were equal

  • D

    The numbers of Old and Middle-aged visitors buying Platinum tickets were equal

Solution

Option 1: The numbers of Middle-aged and Young visitors buying Gold tickets were equal i.e. 43 − x − y = 42 − x or y = 1. No condition precludes the possibility of y having a value of 1.

Option 2: The numbers of Old and Middle-aged visitors buying Economy tickets were equal i.e. y = 17 − y. This is not possible because in that case y will not be a natural number.
 
Option 3: The numbers of Gold and Platinum tickets bought by Young visitors were equal i.e. x = 42 − x i.e. x = 21. This is possible.

Option 4: The numbers of Old and Middle-aged visitors buying Platinum tickets were equal i.e. 20 - 2y = x + 2y - 20 or x + 4y = 40. This is possible.

Hence, option (b).

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CAT 2018 Slot 2 DILR Q32: Which of the following statements MUST be FALSE? — Solution | TheCATExam