Question

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?

• A. 34
• B. 38
• C. 32
• D. 36
• A. The numbers of Old and Middle-aged visitors buying Economy tickets were equal
• B. The numbers of Old and Middle-aged visitors buying Platinum tickets were equal
• C. The numbers of Middle-aged and Young visitors buying Gold tickets were equal
• D. The numbers of Gold and Platinum tickets bought by Young visitors were equal

Answer 1

The Correct Option is C

The correct answer is (C):
Number of young visitors = 2 x number of middle age visitors
Number of middle age visitors = 2 x number of old visitors
Total number of tickets sold = total number of visitors = 140
Hence, the number of young visitors = 80, the number of middle age visitors = 40 and the number of old visitors = 20
The given data can be tabulated as follows.
Since half of the platinum tickets were purchased by young visitors, the remaining half were purchased by old and middle age visitors. Since these two are equal, half of total number of platinum tickets should be an even number. Among the given values, this is possible only for 32 and 36.
In case of 36, Old- Platinum = 9. In that case 2a = 11. But this is not possible. Hence, the total number of platinum tickets sold can only be 32.
Ans : 32

Answer 2

Number of young visitors = 2 x number of middle age visitors
Number of middle age visitors = 2 x number of old visitors
Total number of tickets sold = total number of visitors = 140
Hence, the number of young visitors = 80, the number of middle age visitors = 40 and the number of old visitors = 20
The given data can be tabulated as follows.
Let Old – platinum = Middle aged – Economy = x
We get x + 2a = 20 and a + x + 38 = 55
By solving these two equations we get x = 3.
Ans : 3

Answer 3

Number of young visitors = 2 x number of middle age visitors
Number of middle age visitors = 2 x number of old visitors
Total number of tickets sold = total number of visitors = 140
Hence, the number of young visitors = 80, the number of middle age visitors = 40 and the number of old visitors = 20
The given data can be tabulated as follows.
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
The maximum possible value of Young - gold = x – 1
Then young – platinum = 80 – (38 + x – 1) = 43 – x
Hence, Old – platinum + Middle age – Platinum = 43 – x
Total old + Middle age = 60
(Old – platinum + Middle age – platinum) + (Old – gold + Middle age – gold ) + (Old – economy + Middle age – economy) = 60
Hence, Old – gold + Middle age – gold = x
Thus, Middle age – gold = 0
Ans : Zero

Answer 4

The correct answer is (A):
Number of young visitors = 2 x number of middle age visitors
Number of middle age visitors = 2 x number of old visitors
Total number of tickets sold = total number of visitors = 140
Hence, the number of young visitors = 80, the number of middle age visitors = 40 and the number of old visitors = 20
The given data can be tabulated as follows.
Since Old – Economy + Middle age – economy = 17, these two can never be equal. Hence, the statement that “The numbers of Old and Middle-aged visitors buying Economy tickets were equal” is false.
Ans : “The numbers of Old and Middle-aged visitors buying Economy tickets were equal”