Amusement Park Tickets

CAT 2018 Slot 2 · DILR · Medium · Logical Reasoning

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Passage / data set

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.

Question 1 of 4

If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Platinum tickets, then which among the following could be the total number of Platinum tickets sold?

  1. A.

    32

  2. B.

    38

  3. C.

    34

  4. D.

    36

Answer

A

Explanation

Let Old = 2020, Middle-aged = 4040, Young = 8080 (Total = 140140). Let total Platinum tickets = 2P2P. Young bought PP Platinum tickets. Old + Middle-aged bought PP Platinum tickets. If Old buying Platinum = Middle-aged buying Platinum =x= x, then P=2xP = 2x, so total Platinum =4x= 4x (must be a multiple of 4). Testing options, 32 is a multiple of 4 and fits all constraints.

Question 2 of 4

If the number of Old visitors buying Gold tickets was strictly greater than the number of Young visitors buying Gold tickets, then the number of Middle-aged visitors buying Gold tickets was

Answer

0

Explanation

Setting up the 3x3 matrix for age groups vs ticket types with the given conditions forces the number of Middle-aged visitors buying Gold tickets to be 0.

Question 3 of 4

If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Economy tickets, then the number of Old visitors buying Gold tickets was

Answer

3

Explanation

Using the equality constraint between Old-Platinum and Middle-aged-Economy, solving the linear diophantine system yields Old visitors buying Gold tickets =3= 3.

Question 4 of 4

Which of the following statements MUST be FALSE?

  1. A.

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

  2. B.

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

  3. C.

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

  4. D.

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

Answer

C

Explanation

Total Economy tickets = 55. Young bought 38, leaving 17 Economy tickets for Old + Middle-aged. Since Old + Middle-aged Economy =17= 17, which is odd, the numbers of Old and Middle-aged visitors buying Economy tickets CANNOT be equal (as 2x=172x = 17 has no integer solution). Thus statement C MUST be FALSE.

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