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Aquafame Theme Park sells two types of tickets – for water park and fo

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EgmatQuantExpert
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Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   Updated on: 28 Mar 2019, 01:18
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E

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95% (hard)

Question Stats:

37% (02:35) correct 63% (02:40) wrong based on 115 sessions
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Aquafame Theme Park sells two types of tickets – for water park and for fun rides. On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets. If 33.33% of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets?

A. 20%
B. 33.33%
C. 40%
D. 66.67%
E. 80%

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Official Answer
E

Originally posted by EgmatQuantExpert on 13 Mar 2019, 01:40.
Last edited by EgmatQuantExpert on 28 Mar 2019, 01:18, edited 1 time in total.
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   14 Mar 2019, 02:17
EgmatQuantExpert wrote:
Aquafame Theme Park sells two types of tickets – for water park and for fun rides. On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets. If 33.33% of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets?

A. 20%
B. 33.33%
C. 40%
D. 66.67%
E. 80%



solved using 2x2 matrix

--------water park-------not wp------total
Funride--40--------------40--------80
notfr---20--------0---------20
total----60-------40--------100

let total =100
so 33.33% of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets
40+(40+x)*.33= 40+x
x= 19.7 ~ 20
so total water park tickets = 40+20 ; 60
rest we can solve
we get percentage of the total visitors bought fun rides tickets ; 80%
IMO E
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   Updated on: 19 Mar 2019, 01:43
EgmatQuantExpert wrote:
Aquafame Theme Park sells two types of tickets – for water park and for fun rides. On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets. If 33.33% of the visitors with water park tickets did not buy fun rides tickets, then what percentage of the total visitors bought fun rides tickets?

A. 20%
B. 33.33%
C. 40%
D. 66.67%
E. 80%


Let us assume the no. of water park ticket bought = x

again 33.33% or 1/3 of the visitors i.e x/3 with water park tickets did not buy fun rides tickets

So , 2x/3 bought water park tickets as well as fun ride tickets. this is 40% of the total number of visitors

So total visitors = 2x/3*100/40 = 5x/3

Number of visitors who bought fun ride tickets = 5x/3-x/3 = 4x/3

So percentage of fun ride tickets sold = (4x/3)/(5x/3)*100 = 80 . Answer (E)

Originally posted by shuvodip04 on 14 Mar 2019, 02:34.
Last edited by shuvodip04 on 19 Mar 2019, 01:43, edited 2 times in total.
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   14 Mar 2019, 05:55
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the question itself says 40 % of visitor bought both types of tickets.

hence, the Total number of visitor who purchased fun ride tickets must be more than 40%... then, A, B, and C are out.

with few mental calculations, anyone can say the answer is 80 %
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   14 Mar 2019, 07:17
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IMO C
OA E

Let total visitors be 100.
40 bought both Water park and Fun ride.
33.33% of water park ticket holders did not buy fun ride tickets means that 100-33.33=66.67% of water park ticket holders bought fun ride tickets as well.
that is, 66.67%WP=40
WP=60
therefore, FR=40
and FR=40%

EDIT:

FR=40 is the number of visitors that bought only fun ride ticket. It is asked - what % of total visitors bought fun ride ticket?
So total 80 visitors bought fun ride tickets, 40 visitors bought both and 40 visitors bought only fun ride.
Therefore %= 80%
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   18 Mar 2019, 22:44
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Solution


Given:
    • Aquafame Theme Park sells two types of tickets – for water park and for fun rides.
    • On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets.
    • 33.33% of the visitors with water park tickets did not buy fun rides tickets.

To find:
    • The percentage of the total visitors bought fun rides tickets.

Approach and Working:
Let us assume that the total number of visitors on the certain day was 100.
    • Number of visitors who had water park tickets as well as fun ride tickets = 40% of 100 = 40.

If n is the total number of visitors with water park tickets, then among them, \(\frac{n}{3}\) visitors did not have fun ride tickets.
    • Therefore, \((n – \frac{n}{3}) = \frac{2n}{3}\) visitors are there with water park tickets as well as fun ride tickets.

As per the given question, \(\frac{2n}{3} = 40\)
    • Or, \(n = 40 * \frac{3}{2} = 60\)

And, out of those 60 visitors, \(60 * \frac{1}{3} = 20\) visitors had only water park tickets.
    • Therefore, number of visitors with fun ride tickets = 100 – 20 = 80
    • Or, percentage of visitors with fun ride tickets = 80%

Hence, the correct answer is option E.

Answer: E
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   20 Mar 2019, 04:41
EgmatQuantExpert wrote:

Solution


Given:
    • Aquafame Theme Park sells two types of tickets – for water park and for fun rides.
    • On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets.
    • 33.33% of the visitors with water park tickets did not buy fun rides tickets.

To find:
    • The percentage of the total visitors bought fun rides tickets.

Approach and Working:
Let us assume that the total number of visitors on the certain day was 100.
    • Number of visitors who had water park tickets as well as fun ride tickets = 40% of 100 = 40.

If n is the total number of visitors with water park tickets, then among them, \(\frac{n}{3}\) visitors did not have fun ride tickets.
    • Therefore, \((n – \frac{n}{3}) = \frac{2n}{3}\) visitors are there with water park tickets as well as fun ride tickets.

As per the given question, \(\frac{2n}{3} = 40\)
    • Or, \(n = 40 * \frac{3}{2} = 60\)

And, out of those 60 visitors, \(60 * \frac{1}{3} = 20\) visitors had only water park tickets.
    • Therefore, number of visitors with fun ride tickets = 100 – 20 = 80
    • Or, percentage of visitors with fun ride tickets = 80%

Hence, the correct answer is option E.

Answer: E

Thank you , but why have you assumed that no one didn't bought neither ?
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink] New post   20 Mar 2019, 05:21
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foryearss wrote:
EgmatQuantExpert wrote:

Solution


Given:
    • Aquafame Theme Park sells two types of tickets – for water park and for fun rides.
    • On a certain day, 40% of the total visitors had water park tickets as well as fun rides tickets.
    • 33.33% of the visitors with water park tickets did not buy fun rides tickets.

To find:
    • The percentage of the total visitors bought fun rides tickets.

Approach and Working:
Let us assume that the total number of visitors on the certain day was 100.
    • Number of visitors who had water park tickets as well as fun ride tickets = 40% of 100 = 40.

If n is the total number of visitors with water park tickets, then among them, \(\frac{n}{3}\) visitors did not have fun ride tickets.
    • Therefore, \((n – \frac{n}{3}) = \frac{2n}{3}\) visitors are there with water park tickets as well as fun ride tickets.

As per the given question, \(\frac{2n}{3} = 40\)
    • Or, \(n = 40 * \frac{3}{2} = 60\)

And, out of those 60 visitors, \(60 * \frac{1}{3} = 20\) visitors had only water park tickets.
    • Therefore, number of visitors with fun ride tickets = 100 – 20 = 80
    • Or, percentage of visitors with fun ride tickets = 80%

Hence, the correct answer is option E.

Answer: E

Thank you , but why have you assumed that no one didn't bought neither ?


foryearss

The question stem says that Aquafame Theme Park sells two types of tickets – for water park and for fun rides.
So if you are visitor to the park you have to buy either of the ticket or both. If you dont buy any of the two ticket you can't be a visitor, since the park only sales only two type of tickets.

I hope I am able to clear the confusion you have.
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Re: Aquafame Theme Park sells two types of tickets – for water park and fo [#permalink]
20 Mar 2019, 05:21
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