CAT 2018 Question Paper | CAT LR DI

CAT Questions

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CAT DILR : CAT 2018 Question Paper Slot 2

Set 5 : Amusement Park Tickets

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 : 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. 32
2. 38
3. 34
4. 36

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

From second constraint,
OLD Visitors = x, MID = 2x, Young = 4x.
7x = 140 or, x = 20 , 2x = 40 , 4x = 80.
Let us fill this in. and then go to constraint 3 and 4.

From constraint 3, Total Platinum = 2y, then YNG platinum should be y.
From constraint 4, Let us fill OLD-GOLD and OLD-ECO has z.

OLD-PT should be equal to MID-PT, OLD-PT and MID-PT add up to y.
So, each should be \\frac{y}{2}). Now, we know that \\frac{y}{2}) = 20 – 2z.
Total number of PT seats = 2y = 4 (20 – 2z) = 8 (10 – z). So, this number should be a multiple of 8.
The only possible answer is 32

The question is "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?"

Hence, the answer is 32

Choice A is the correct answer