CAT 2018 Slot 2 — DILR Question 32
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:
- 140 tickets were sold.
- 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.
- 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.
- 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
- 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
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).