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, Middleaged, or Young. The following facts are known about visitors and ticket sales on a particular day:
 140 tickets were sold.
 The number of Middleaged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middleaged visitors.
 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.
 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 Middleaged 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 Middleaged 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 Middleaged 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 Middleaged and Young visitors buying Gold tickets were equal
c) The numbers of Old and Middleaged visitors buying Economy tickets were equal
d) The numbers of Old and Middleaged 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 
Middleaged 
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 Middleaged visitors buying Platinum tickets, So

Old 
Middleaged 
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 Middleaged visitors buying Economy tickets So

Old 
Middleaged 
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 Middleaged 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 Middleaged visitors buying Economy tickets were equal” is false.
Answer: c)
The numbers of Old and Middleaged visitors buying Economy tickets were equal
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