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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 68% (02:23) correct 32% (03:08) wrong based on 207 sessions

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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. $$225 × 10 + (40 + 5)(40 - 5)$$ This question was provided by e-GMAT for the Game of Timers Competition _________________
SVP  D
Joined: 03 Jun 2019
Posts: 1877
Location: India
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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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)

Given: 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. John watched 95 movies in this movie theatre last year.

Asked: The dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

For first 10 movies, ticket price is $50/movie => Total ticket price for 10 movies =$500
For next 10 movies, ticket price is $45/movie => Total ticket price for next 10 movies =$450
For next 10 movies, ticket price is $40/movie => Total ticket price for next 10 movies =$400
For next 10 movies, ticket price is $35/movie => Total ticket price for next 10 movies =$350
For next 10 movies, ticket price is $30/movie => Total ticket price for next 10 movies =$300
For next 10 movies, ticket price is $25/movie => Total ticket price for next 10 movies =$250
For all other movies, ticket price is $25/movie => Total ticket price for next x movies =$25x

He watched 95 = 10 + 10 + 10 + 10 + 10 + 10 + 35 movies
Total ticket price = $( 500+450+400+350+300+250+25*35) = 50(5+6+7+8+9+10) + (30-5)*(30+5) = 45*50 + (30-5)*(30+5) = 225*10 + (30-5)*(30+5) IMO C ##### General Discussion Senior Manager  G Joined: 10 Aug 2018 Posts: 340 Location: India Concentration: Strategy, Operations WE: Operations (Energy and Utilities) Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 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? _________________ On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL" GMAT:[640 Q44, V34, IR4, AWA5] Director  P Joined: 16 Jan 2019 Posts: 507 Location: India Concentration: General Management WE: Sales (Other) Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 1 Movies 1-10 -$50*10
Movies 11-20 - $45*10 Movies 21-30 -$40*10
.
.
.
Movies 51-60 - $25*10 Movies 61-90 -$25*10 + $25*10 +$25*10
Movies 91-95 - $25*5 Total = 10*(50+45+40+35+30+25+25+25+25) + 125 = 3125 Since 3 out of 5 options b 3125=2250+875 = 225*10 + (25)(35) = 225*10 + (30-5)(30+5) Answer is (C) Intern  B Joined: 26 May 2018 Posts: 45 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 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
Manager  B
Joined: 27 Mar 2016
Posts: 116
GMAT 1: 590 Q44 V22 Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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1
Ist 10 tickets = 50*10 = 500
next 10 = 45*10=450
next 10 = 40* 10 = 400
next 10 =350
next 10 =300
next 10 = 250
next 10 = 250
next 10 = 250
next 10 = 250
next 5 = 125
total 3125
only 3rd equation satisfy this
hence C
Senior Manager  P
Joined: 27 Aug 2014
Posts: 368
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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1

total price can be written as follows:
50*10+45*10+40*10+35*10+30*10+25*10 + 35*25 = 225*10+35*25
which matches with C
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 615
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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1
Total Paid: 10 * (50 + 45 + 40 + 35 + 30) + 40*25 + 5*25
=> 10*(225) + 10*75 + 5*25
=>10*(225) + 25 * 35 C
Manager  G
Joined: 30 May 2018
Posts: 157
GMAT 1: 710 Q49 V36 GPA: 3.8
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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1
C.

Total 95 tickets are purchased.

Using the cost criterion discussed in the question, total amount paid should be: 10*50 + 10*45 +10*40 +10*35 +10*30 +10*25 +(95-60)*25 - note that ticket price remains same after it hits $25/ So, total price: 10*(50+45+40+35+30+25) + 35*25 = 225*10 + (30+5)*(30-5) Intern  B Joined: 05 Jun 2018 Posts: 31 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 1 Total price paid till he reaches 25 bucks per ticket = 50*10+ 45*10+40*10+35*10+30*10+25*10 = 225*10 Total tickets purchased till that time= 60 Rest, 35 tickets at 25 per ticket So answer C Posted from my mobile device Intern  B Joined: 10 May 2018 Posts: 17 A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 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... 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. Manager  G Joined: 28 Jan 2019 Posts: 127 Location: Peru A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 1 First we have to consider the starting price of$50 per movie for the first 10 movies.

Then, 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, so we have:

P*Q
45(we start from 45 since it is 50-5)*10
40*10
35*10
30*10
25*10

Quantity until now? 50 + 10 (of the first 10 movies priced at $50) = 60 And finally , the units to get 9 in total are going to be priced$25 per movie, so 95-60 = 35

Formula will be like this: (50+45+40+35+30+25)*10 + 35*25 = 225*10 + (30+5)*(30-5)

Originally posted by Mizar18 on 17 Jul 2019, 08:41.
Last edited by Mizar18 on 17 Jul 2019, 18:43, edited 1 time in total.
Manager  G
Joined: 26 Jan 2016
Posts: 181
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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Total spend = 50*10+45*10+35*10+30*10+25*45=3125

Only C = 3125

Hence C
Intern  B
Joined: 24 Mar 2019
Posts: 22
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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So first we calculate the total dollar amount that John paid. For the first 50 tickets John paid

10(50+45+40+35+30)
=2000
For the rest 45 tickets he paid
45*25
=1125

Total amount spent is 2000+1125
=3125

Then we calculate the amount from the options. If we can find the approx value first we can eliminate option a,b,e from c and d we calculate and get the answer as c

Posted from my mobile device
Senior Manager  G
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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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+35×25200×10+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.
Manager  S
Joined: 26 Mar 2019
Posts: 107
Concentration: Finance, Strategy
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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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?

Let us recap what we are given:
First 10 movies - price per movie is $50 2nd set of 10 movies - price per movie is $$50 - 5$$ n-th set of 10 movies - price per movie is $$50 - 5 * (n - 1)$$ until $$50 - 5 * n = 25$$ After price per movie is$25, all future tickets will remain at this price
John watched 95 movies T=95
What is the dollar amount he paid?

First, let us find what n is equal to:
$$50 - 5*(n-1) = 25$$ => $$50 - 5n + 5 = 25$$ => $$5n = 30$$ => $$n =6$$
Now, as we have n, we can write down what is the total amount of money for the movies:
For the first 10 movies set n=1 and the sum of money is $$10 * 50$$
For the second 10 movies n=2 and the sum of money is $$10 * (50 - 5 * (2 - 1))$$
For the 6th set of 10 movies n=6 and the sum of money is $$10 * (50 - 5 * (6 - 1))$$
For the movies after the 6th set of movies, the price is $$(95 - (n * 10) * 25)$$

The final formula is $$10 * 50 + 10 * (50 - 5) + 10 * (50 - 10) + 10 * (50 - 15) + 10 * (50 - 20) + 10 * (50 - 25) + (95 - 10 * 6) * 25 = 10 * (50 + 45 + 40 + 35 + 30 + 25) + (95 - 60) * 25 = 10 * 225 + 35 * 25$$

$$10 * 225 + 35 * 25 = 10 * 225 + (30 + 5) * (30 - 5)$$

Director  G
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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For 95 tickets John would have paid - 10*50+10*45+10*40+10*35+10*30+45*25 = 10(50+45+40+35+30)+45*25=200*10+45*25

Now go to answer options - PoE

A. 200×10+35×25 - Incorrect, As Option in same format as above but numbers are different
B. 60×25+45×35 - Incorrect, As Option in same format as above but numbers are different
C. 225×10+(30+5)(30−5) - Correct, First part has 200*10+25*10 that is is compensated by 25*(45-25) in the second part
D. 225×10+(40+5)(30−5) - Incorrect, as first part is excess by 250 which is not compensated
E. 225×10+(40+5)(40−5) - Incorrect as both first and second part have excess.

IMO C
Manager  G
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Booth, Berkeley Haas
GMAT 1: 730 Q50 V39 GPA: 3.95
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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1-10 50
11-20 45
21-30 40
31-40 35
41-50 30
51-95 25

I just calculated it
35*50+25*55=3125

First of all, I started with the last 3 options and substracted 225*10 from 3125
3125-2250=875
Then I just tried to divide it on 35 and got 25.
We could divide it on 25 or 45 and after all, we would got the answer ^^

So, The correct answer is C
Senior Manager  D
Joined: 30 Sep 2017
Posts: 450
GMAT 1: 720 Q49 V40 GPA: 3.8
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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John watched 95 movies last year, so the dollar he spent for all movie tickets is cumulative of the following:
$$1^{st}$$ ten movies: 10 x $50 $$2^{nd}$$ ten movies: 10 x$45
$$3^{rd}$$ ten movies: 10 x $40 $$4^{th}$$ ten movies: 10 x$35
$$5^{th}$$ ten movies: 10 x $30 $$6^{th}$$ ten movies: 10 x$25
$$61^{th} - 95^{th}$$ movies: 35 x $25 Thus, he spent in total $$(50+45+40+35+30+25)*10 + 25*35 = 225*10 + (30+5)*(30-5)$$ Answer is (C) $$: 225×10+(30+5)(30−5)$$ Manager  S Joined: 18 Feb 2017 Posts: 93 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 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. Re: A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 17 Jul 2019, 09:06

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