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A movie theatre rewards its loyal customers by offering them discounts

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New post 18 Jul 2019, 01:50
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Cost of 1st set of 10 movies = 10*50
Cost of next set of 10 movies = 10*45
Cost of next set of 10 movies = 10*40
Cost of next set of 10 movies = 10*35
Cost of next set of 10 movies = 10*30
Cost of next set of 10 movies = 10*25
So, cost of 60 movies = 10*(50 + 45 + 40 + 35 + 30 + 25) = 225*10

Cost of remaining 35 movies = 25$ each = 35*25

So, total cost of 95 movies = 225*10 + 35*25
= 225x10 + (30+5)x(30-5)

IMO Option C

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New post 18 Jul 2019, 03:12
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I manually counted and got C, 3125. (I counted every 10 tickets and multiplied by its price 50, 45,40,35,30,35,25,25,25. Last 5 movies also multiplied by 25)
Answer - C
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New post 18 Jul 2019, 03:26
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price reduces by $5 per movie till the point where the ticket price equals $25 per movie.

First 10 - $50
Next 10 - $45
10 - $40
10 - $35
10 - $30
Remaining - $25

First 50 tickets would cost - 10*50 + 10*45 + 10*40 + 10*35 + 10*30 = 2000
Remaining 45 at 25 = 45*25 = 1125
Total = 3125

Among the options,
C. 225×10+(30+5)(30−5)
is the only option which sums to 3125.

Option C.
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New post 18 Jul 2019, 03:42
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

A.
200×10+35×25
200×10+35×25

B.
60×25+45×35
60×25+45×35

C.
225×10+(30+5)(30−5)
225×10+(30+5)(30−5)

D.
225×10+(40+5)(30−5)
225×10+(40+5)(30−5)

E.
225×10+(40+5)(40−5)
225×10+(40+5)(40−5)

Solution:Now as per the statement
For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie,the follwoing situation arises:

10*50
10*45
10*40
10*35
10*30
10*25
sum of all above=10*225

Now if John watched 95 movies then as per above details given the remaining movies to be watched are 35 25 each.

Hence,the totl amount paid for total 95 movies=10*225+35*25
Therefore C is the answer IMO
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New post 18 Jul 2019, 03:54
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

A.200×10+35×25
B.60×25+45×35
C.225×10+(30+5)(30−5)
D.225×10+(40+5)(30−5)
E.225×10+(40+5)(40−5)

Solution:
The total number of movies that john watched is 95
For the First 10 movies , The cost is $50,
For the next 10, it will be 50+5 i.e 45
another 10, it's 40,
another 10, it's 35
another 10, it's 30
another 10, it's 25 so we have our final price of $25 per movie, note that the cost won't go down any further and $25 will be fixed. so till here, the total cost is 10 X 225
Hence for remaining 35 movies, the cost is going to be $25 per movie, i.e 35 X 25

Therefore, we can form the equation, 225 X 10 + 35 X 25 which is equal to option C

Answer is C
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New post 18 Jul 2019, 04:28
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Tickets => Price

0-10 => $50
11-20 => $45
21-30 => $40
31-40 => $35
41-50 => $30
51-60 => $25
61-95 => $25

{ 10*50 + 10*45 + 10*40 + 10*35 + 10*30 + 10*25 } + {35*25}
=10 (50+45+40+35+30+25) + (35*25)
= (10*225) + (35*25)
= Option (C)
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New post 18 Jul 2019, 04:53
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Question: A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

\[
\begin{matrix}
Set & Cost & = & (#Terms)(Cost) & = & Total Cost \\
1-10 & 50 & = & (10)(50)& = & $500 \\
11-20 & 45 & = & (10)(45)& = & $450\\
21-30 & 40 & = & (10)(40)& = & $400\\
31-40 & 35 & = & (10)(35)& = & $350\\
41-50 & 30 & = & (10)(30)& = & $300\\
51-60 & 25 & = & (10)(25)& = & $250\\
61-95 & 25 & = & (35)(25) & = & $875\\
\end{matrix}
\]

\(\text{Sum of tickets }1-60\):
\(= 500+450+400+350+300+250\)
\(= 2250 \implies (225)(10)\)

\(\text{Sum of tickets } 61-95\):
\(= (35)(25) \implies (30+5)(30-5)\)

Correct Answer: C. (225×10)+(30+5)(30−5)
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New post 18 Jul 2019, 05:07
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie.

Main question: If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

1. "For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie."
50*10
2. "For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie."
10*(45+40+35+30+25)
3. "The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. "
25*(95-60)= 25*35
4. SUM:
10*225+25*35

ASNWER C

A. 200×10+35×25
B. 60×25+45×35
C. 225×10+(30+5)(30−5)
D. 225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)
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New post 18 Jul 2019, 05:49
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IMO C.

Customer is charged at $50 for first 10 then 45,40,35,30 and the rest 40 at 25
The customer bought 95 tickets. This can be broken into:
1. First 10 tickets charged at $50 = 50*10=$500.
2. 10 tickets bought at 45,40,35, 30= $1500
3. Next 45 tickets at 25 = $1125
Hence, the total amount = 500 + 1500 + 1125 = $3125
The option which gives the same value is C.

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New post 18 Jul 2019, 05:49
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In total, John watched 95 movies:

For the first 10 movies, he paid $50 each--> 10*$50
For the second 10 movies, He paid 10*$45
... third 10 movies, ... 10*$40
... fourth 10 movies,... 10*$35
... fifth 10 movies,... 10*$30
... sixth 10 movies,... 10*$25

For the subsequent movies, he paid $25 per movie (95-10-10-10-10-10-10=35 )

The amount of money he paid for 95 movies was:
10*50+10*45+10*40+10*35+10*30+10*25+35*25=10(50+45+40+35+30+25)+35*25=10*225+35*25

Only C satisfies this answer. 225*10+(30+5)*(30-5)
The answer choice is C
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New post 18 Jul 2019, 07:29
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Amount paid for 95 movies is
(10x50)+(10x45)+(10x40)+(10x35)+(10x30)+(10x25)+(35x25)
= 10(50+45+40+35+30+25)+(35x25)
=(10x225)+(30+5)(30-5)

Option (C)
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New post 18 Jul 2019, 07:44
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Answer C
Each lot of 10 movies cost decreases by 5$ and after 25$ remains constant

50*10+45*10+40*10+35*10+30*10+25*10+25*35
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New post 17 Jul 2019, 08:15
I applied the brute force method.

C has to be the right answer. 10(50+45+40+35+30+25)+35x25

Is there any other fast method?
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New post 17 Jul 2019, 08:26
Answer is D.

A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

First 10 movies = 10(50)
Following 5 movies until it reaches 25
45-5=40-5=35-5=30-5=25 total of 5 movies
the remaining movies= 90-10-5=80 @ $25
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New post Updated on: 18 Jul 2019, 08:35
Assuming that the first of 95 movies John has watched is the first he's watched at the theater:
(10*$50)+(10*$45)+(10*$40)+(10*$35)+(10*$30)+(10*$35)+(45*25)
Once John has watched 50 movies, the price is set at 25. So the remaining 45 (of the 95) would be 45*35
Take the 10 out
(10*(50+45+40+35+30+25)+(45*25)
(10*225)+(45*25)
The answers further divide out the (45*25) piece which is equivalent to (40+5)(30−5)


*Edit* Messed up the math on number of movies remaining... :cry:

Originally posted by coloredflash on 17 Jul 2019, 08:38.
Last edited by coloredflash on 18 Jul 2019, 08:35, edited 1 time in total.
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New post 17 Jul 2019, 08:45
A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

A. 200×10+35×25200×10+35×25
B. 60×25+45×3560×25+45×35
C. 225×10+(30+5)(30−5)225×10+(30+5)(30−5)
D. 225×10+(40+5)(30−5)225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)


Pure calculation question. Highly unlikely that you will see this type of question on the GMAT.
The answer is A.
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New post 17 Jul 2019, 09:06
IMO B.

Customer is charged at $50 for first 10 then 45,40,35,30 and the rest 6 at 25 in batches of 10.
The customer bought 95 tickets. This can be broken into:
1. First 10 tickets charged at $50 = 50*10=$500.
2. Next 8 batches of 10 tickets charged at $300 = 300*8 = $2400.
3. Next 5 tickets according to the batch of 10, will be charged as - 45,40,35,30 and 25 = $175.
Hence, the total amount = 500 + 2400 + 175 = $3075.
The option which gives the same value is B.
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New post Updated on: 18 Jul 2019, 09:14
Quote:
A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

A. 200×10+35×25
B. 60×25+45×35
C. 225×10+(30+5)(30−5)
D. 225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)


given: after first 10, each subsequent set of 10 get price reduced by 5, limited to $25 life-time
n=95… amount={10*50+10*45+10*40+10… (notice the pattern)}:
{50(10+9+8+7+6+5)+25(35)}=50(45)+25(35)=2250+25(35)

Answer (C).

Originally posted by exc4libur on 17 Jul 2019, 09:44.
Last edited by exc4libur on 18 Jul 2019, 09:14, edited 1 time in total.
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 10:07
For first 10 movies price is 50 x 10 = 500
For next 10 movies price is 45+40+35+30+25+ 25*5 = 300
Price for 80 movies (after first 10 movies) = 300*8 = 2400
Price of last 5 movies = 45+40+35+30+25 = 175

Total price of 95 movies = 500+2400+175 = 3075

B. 60×25+45×35 = 1500 + 1575 = 3075

B is correct.
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New post 17 Jul 2019, 11:56
Given,

1. Total movies watched by John in the year = 95

2. Cost of first 10 movies for John = 10 * 50 = 500 .... 1

3. Cost of subsequent sets of 10 movies for John = (45 + 40 + 35 + 30 + 25 + 5 * 25)

4. Total number of subsequent sets of 10 movies = 8

5. Cost of subsequnt 8 sets of 10 movies each = 8 * (45 + 40 + 35 + 30 + 25 + 5 * 25)
=> 8 * (5 * (9 + 8 + 7 + 6 + 5) + 5 * 25)
=> 40 * (35 + 25)
=> 40 * 60
=> 2400 .... 2

6. Cost of remaining set of 5 movies as total is 95 = (45 + 40 + 35 + 30 + 25) = 175 .... 3

Adding 1, 2, 3 we get,

=> 500 + 2400 + 175
=> 3075

Now let us check the options,

A. 200×10+35×25 => 2875 => Wrong.

B. 60×25+45×3560×25+45×35 => 3075 => Correct.

C. 225×10+(30+5)(30−5)225×10+(30+5)(30−5) => 3125 => Wrong.

D. 225×10+(40+5)(30−5)225×10+(40+5)(30−5) => 3375 => Wrong.

E. 225×10+(40+5)(40−5) => 3825 => Wrong.

----------------------------------------------------------------------------------------------------------------------

P.S: I found this to be a very poorly worded question.
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Re: A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 17 Jul 2019, 11:56

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