CAT 2018 LRDI Questions 162

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.

Question 1

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

Question 2

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

Question 3

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

Question 4

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”