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# A movie theatre rewards its loyal customers by offering them discounts

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Manager
Joined: 17 Jul 2014
Posts: 127
A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 20:15
1
----10 Movies-----||-------10 Movies----------||-------10 Movies------ ---||--||--|| -------10 Movies------||---------10 Movies---------||
ticket price = 50 || price reduces by 5=45 || price reduces by 5=40 ||--||--|| price until price =25 || lifetime price =25 ||

95 Movies
10 Movies = 10* 50 = 500
10 Movies = 10 *45 = 450
10 Movies = 10 *40 = 400
10 Movies = 10 *35 = 350
10 Movies = 10 *30 = 300
10 Movies = 10 *25 = 250
10 Movies = 10 *25 = 250
10 Movies = 10 *25 = 250
10 Movies = 10 *25 = 250
5 Movies = 5 *25 = 150

Then is the part to actually map it to the answer choice; only C matches
Manager
Joined: 29 Apr 2017
Posts: 56
Location: India
Concentration: Operations, Other
GMAT 1: 660 Q43 V38
GPA: 4
WE: Operations (Transportation)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 21:14
1
Given: Rate of first 10 movies=$50; Rate of next 10 movies(no.11 to no.20)=$45, Rate of next 10 movies(no.21 to no.30)= $40, Rate of next 10 movies(no.31 to no. 40)=$35, Rate of next 10 mobies(no.41 to no.50)=$30 and rate of movies afterwards=$25
Total no. of movies watched by John=95
Now,
Cost of first 10 movies= 10*$50 Cost of movies from no.11 to no.20(i.e next 10 movies)=10*$45
Cost of movies from no.21 to no.30(i.e next 10 movies)=10*$40 Cost of movies from no.31 to no.40(i.e next 10 movies)=10*$35
Cost of movies from no.41 to no.50(i.e next 10 movies)=10*$30 Cost of movies from no.51 to no.60(i.e next 10 movies)=10*$25
Cost of movies from no.61 onwards(i.e no.61 to no.95)= 30*$25 Toatl cost=10*$50+10*$45+10*$40+10*$35+10*$30+10*$25+35*$25
=10(50+45+40+35+30+25)+35*25
=225*10+35*25
=225*10+(30+5)(30-5)

Manager
Joined: 30 May 2019
Posts: 108
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 21:16
1
Customer paid for 95 movies:

First 10 movies - 10*$50 Second 10 movies - 10*$45
Third 10 movies - 10*$40 Fourth 10 movies - 10*$35
Fifth 10 movies - 10*$30 Sixth 10 movies - 10*$25
Seventh 10 movies - 10*$25 Eighth 10 movies - 10*$25
Ninth 10 movies - 10*$25 Last 5 movies - 5*$25
Total: 45*$25+50*$40(average of $30,$35, $40,$45, $50)=$3125, customer paid for 95 movies. Let's see which answer yields 3125.

A. 200×10+35×25 = 2875 NO
B. 60×25+45×35 = 3075 NO
C. 225×10+(30+5)(30−5) = 3125 YES
D. 225×10+(40+5)(30−5) = 3375 NO
E. 225×10+(40+5)(40−5) = 3825 NO

Manager
Joined: 08 Jan 2018
Posts: 129
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 21:24
1
Let us see the pattern of pricing of movie tickets:

First 10 - $50 each -> 10 *$50
Next 10 - $45 each -> 10 *$45
Next 10 - $40 each -> 10 *$40
Next 10 - $35 each -> 10 *$35
Next 10 - $30 each -> 10 *$30
Next 10 - $25 each -> 10 *$25
Next N - $25 each -> N *$25

John watches 95 movies: 10 + 10 + 10 + 10 + 10 + 10 + N = 95 => N = 35

Total price of tickets = 10*($50 +$45 + $40 +$35 + $30 +$25) + N*$25 =>10*(225) + 35*25 =>225 * 10 + (30 + 5)*(30-5) Answer C Intern Joined: 28 Feb 2018 Posts: 17 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 21:41 1 first set of 10 tickets :- 10*50 second set of 10 tickets :- 10*45 third set of 10 tickets :- 10*40 fourth set of 10 tickets :- 10*35 fifth set of 10 tickets :- 10*30 sixth set of 10 tickets :- 10*25 Total sum of 6 set (60 movies) of tickeys:-2250 for next 35 movies , the cost will be :- 35*25 Total cost :- 2250+35*25 Intern Joined: 22 Jun 2019 Posts: 41 Location: Canada Concentration: Operations, Organizational Behavior A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 21:44 1 See the picture Attachments IMG_20190717_222632.jpg [ 2.41 MiB | Viewed 220 times ] Manager Joined: 12 Jan 2018 Posts: 112 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 22:35 1 1-10 :$50
11-20:$45 21-30:$40
31-40:$35 41-50:$30
>50:$25 Since, John watched 95 movies, his total expenses= 45*25+ 10(30+35+40+45+50) =45*25+10*200=$3125

Verify options,

A. 200×10+35×25 =2000+875, Incorrect
B. 60×25+45×35= 1500+1575,Incorrect
C. 225×10+(30+5)(30−5)= 2250+875=3125, Correct

Correct Ans: C
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Manager
Joined: 24 Jan 2019
Posts: 104
Location: India
Concentration: Strategy, Finance
GMAT 1: 730 Q51 V38
GPA: 4
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 22:58
1
John has watched 95 movies till now.

Ticket price for movies are as per following:

1-10 movies : 50*10 = 500 (ticket price starts from 50per movie and it will reduce by 5 per movies for each subsequent set 10 movies.)
11-20 movies : 45*10 = 450
21-30 movies : 40*10 = 400
31-40 movies : 35*10 = 350
41-50 movies : 30*10 = 300
51-60 movies : 25*10 = 250
61-95 movies : 25*35 = (30+5)(30-5)

If we add all of these : 2250 + (30+5)(30-5) = 225*10 + (30+5)(30-5)

Intern
Joined: 09 May 2019
Posts: 21
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 23:24
1
Price of first 10 movie tickets @ 50 ,Total Cost 50 *10 = 500
Price of next 10 movie tickets 45 ,Total Cost 45 *10 = 450
Price of next 10 movie tickets @ 40 ,Total Cost 40 *10 = 400
Price of next 10 movie tickets @ 35 ,Total Cost 35 *10 = 350
Price of next 10 movie tickets 30 ,Total Cost 30 *10 = 300
Total price of 50 tickets = 2000

Rest all 45 tickets will cost 25, Total cost - 25 * 45 = 1125
Total Cost - 1125 + 2000 = 3125

Option C is same as this - 225 *10 + 35 *25 = 3125
Manager
Joined: 06 Jun 2019
Posts: 116
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 23:58
1
The initial price of the ticket for the first 10 movies is $50. For the next 10 movies the price will drop by$5. We will have have 5 such drops untill we pay $25. So $$10*50+10*45+10*40+10*35+10*30+10*25$$ is the price for the first $$60$$ tickets, if simplified $$10*(50+45+40+35+30+25)$$ or $$225*10$$ For the rest 35 tickets we pay by $$25$$ or $$35*25$$. Is summed $$225*10+35*25$$ Hence C _________________ Bruce Lee: “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.” GMAC: “I fear not the aspirant who has practiced 10,000 questions, but I fear the aspirant who has learnt the most out of every single question.” Intern Joined: 09 Jul 2019 Posts: 38 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 00:19 1 0-10 movies 10*50=500 11-20 movies 10*45=450 21-30 movies 10*40=400 31-40 movies 10*35=350 41-50 movies 10*30=300 51-95 movies 45*25=1125, all added 3125 (C) Manager Joined: 08 Jan 2018 Posts: 98 Location: India GPA: 4 WE: Information Technology (Computer Software) Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 00:55 1 For the 95 movies, we can break down the logic as follows: 10*50 + 10*45 + 10* 40 + 10*35 + 10*30 + 10*25 => 2250 So till now 60 movies got completed. For the remaining 35 movies: 35*25 => 875 Adding all the values=> 3125 We get that only option C is equal to 3125. IMO the answer is C. Please hit kudos if you like the solution. Intern Joined: 08 Jul 2019 Posts: 37 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 01:33 1 For every 10 movies watched, a loyal customer gets discount of 5$ until ticket price reaches 25$. First set of 10 movies cost 50$ each (500 in sum), second set 45$per each out of 10 movies watched (450), ....... 350+300+250 (50 movies were watched so far). Other 45 movies will be charged 25$. Total sum paid 500+450+400+250+300+250*55=3125.
It is C
Director
Joined: 20 Jul 2017
Posts: 661
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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18 Jul 2019, 01:50
1
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 Pls Hit kudos if you like the solution Posted from my mobile device Manager Joined: 07 Jul 2019 Posts: 54 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 03:12 1 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 Manager Joined: 27 May 2010 Posts: 200 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 03:26 1 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. _________________ Please give Kudos if you like the post Manager Joined: 22 Oct 2018 Posts: 73 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 03:42 1 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
Senior Manager
Joined: 25 Sep 2018
Posts: 403
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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18 Jul 2019, 03:54
1
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

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Manager
Joined: 07 Dec 2018
Posts: 112
Location: India
Concentration: Technology, Finance
GMAT 1: 670 Q49 V32
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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18 Jul 2019, 04:28
1
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) Intern Joined: 14 Mar 2017 Posts: 40 Location: United States (MD) GPA: 2.9 WE: Science (Other) A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 18 Jul 2019, 04:53 1 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?

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

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

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

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A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 18 Jul 2019, 04:53

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