Logical Reasoning – Set – Each visitor to an amusement park

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

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.

Q 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?
a) 38
b) 32
c) 36
d) 34

Q 2. 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

Q 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
Answer: 0

Q 4. Which of the following statements MUST be FALSE?
a) The numbers of Gold and Platinum tickets bought by Young visitors were equal
b) The numbers of Middle-aged and Young visitors buying Gold tickets were equal
c) The numbers of Old and Middle-aged visitors buying Economy tickets were equal
d) The numbers of Old and Middle-aged visitors buying Platinum tickets were equal

Solution: Let the number of old visitors = x so number of middle aged and young visitors will be 2x and 4x respectively. So x+2x+4x=140 or x=20
Let total number of platinum ticket sold = p (even)
Now on the basis of information given following table can be made:

	Old	Middle-aged	young	Total
Platinum			p/2	p
Gold	a	43 – p/2 – a	42 – p/2	85 – p
Economy	a	17 – a	38	55
Total	20	40	80	140

1. Given , the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Platinum tickets, So

	Old	Middle-aged	young	Total
Platinum	p/4	p/4	p/2	p
Gold	a	43 – p/2 – a	42 – p/2	85 – p
Economy	a	17 – a	38	55
Total	20	40	80	140

Now old = 40 so 2a + p/4 = 20
Or a + p/8 = 10
As p/8 must be an integer so p must be a multiple of 8. Thus option a) 38, c) 36 and d)34 get eliminated.
Only possible option is b) 32
2. Given, the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Economy tickets So

	Old	Middle-aged	young	Total
Platinum	x		p/2	p
Gold	a		42 – p/2
Economy	a	x	38	55
Total	20	40	80	140

So
2a + x = 20—–1) and
a+x + 38 =55——-2)
By solving above equations a = 3
So the number of Old visitors buying Gold tickets = 3
Answer: 3
3. The number of Old visitors buying Gold tickets was strictly greater than the number of Young visitors buying Gold tickets, so 42 – p/2 < a
Or a + p/2 > 42
So minimum value of a + p/2 = 43
Number of Middle-aged visitors buying Gold tickets = 43 – (p/2 +a) = 0
Answer: 0
4. Since Old – Economy + Middle age – economy = 17 which is odd so 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.
Answer: c) The numbers of Old and Middle-aged visitors buying Economy tickets were equal

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