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

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Senior Manager
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17 Jul 2019, 09:09
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Explanation is in the attachment
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IMG_20190717_213452.JPG [ 888.59 KiB | Viewed 194 times ]

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Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 09:10
1
IMO-C

First 10# Movies= $50/movie From 11#- 20# movie=$45/movie
From 21#- 30# movie= $40/movie From 31#- 40# movie=$35/movie
From 41#- 50# movie= $30/movie From 51#-60# movie=$25/movie
61#- Any no.= $25/movie. Now , total movie watched= 95# Amount= 10 x (50+45+40+35+30+25) + (95-60) x 25 = 10 x 3 x 75 + (25 x 35) = 225 x 10 + (30-5)x(30+5) Manager Joined: 24 Jun 2019 Posts: 108 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 09:10 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? Movie # 1 -10 = 10 x 50 11-20 = 10 x 45 21-30 = 10 x 40 31-40 = 10 x 35 41-50 = 10 x 30 51-60 = 10 x 25 61-95 = 35 x 25.... no further discount after 25 Total dollar amount can be calculated by adding all results above. BUT, we dont want to do any calculations as the answers are not a single number. We will try to rewrite the answer in the format of the options: first 6 values have 10 as common so Total of all 7 terms could be written as (50+45+40+35+30+25) x 10 + 35 x 25 225 x 10 + 35 x 25 This matches with Option C 225 x 10 + (30+5)(30-5) Answer: C. 225×10+(30+5)(30−5) Senior Manager Joined: 13 Feb 2018 Posts: 448 GMAT 1: 640 Q48 V28 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 09:12 1 The price of: 1) first 10 movies: 10*50 2) second 10 movies: 10*45 3) third 10 movies: 10*40 4) fourth 10 movies: 10*35 5) fifth 10 movies: 10*35 6) sixth 10 movies: 10*25 Let's stop and calculate this part: Factor out 10 to get --> 10*(50+45+40+35+30+25)=10*225 As John has watched 95 movies and we have calculated the first 60 movies cost, we have to calculate 35 movies cost each costing$25 (per stem 25$is fixed and does not change after 60 movies) 35*25=(30+5)*(30-5) Let's sum both parts 10*225+(30+5)*(30-5) IMO Ans: C Manager Joined: 17 Apr 2018 Posts: 109 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 09:13 1 I was not able to figure out the series based on the option. So I quickly moved to solve. 1-10 --> 500 11-20 --> 450 21-30 --> 400 31-40 --> 350 41-50 --> 300 51-95 --> 45X25 = 1125 Adding all ==> 3125 Option C satisfies. Hence C is the answer. Intern Joined: 12 Aug 2017 Posts: 42 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 09:21 2 Sequences : (50*10) + (45*10) +(40*10) +(35*10) + (30*10) + (25*10) + (25*35) = 10 (50+45+40+35+30+25) + 25*35 = 10*225 + (30-5)(30+5) i.e. C _________________ The key is not the will to win, it's the will to prepare to win that is important !! Senior Manager Status: eternal student Joined: 06 Mar 2018 Posts: 290 Location: Kazakhstan GPA: 3.87 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 09:23 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? Attachment: movies.PNG [ 27.46 KiB | Viewed 141 times ] A. 200×10+35×25 =$2875
B. 60×25+45×35 = $3075 C. 225×10+(30+5)(30−5) =$3125
D. 225×10+(40+5)(30−5) = $3375 E. 225×10+(40+5)(40−5) =$3825

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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 09:26
1
Summation will be

500+400+350+300+250+250+250+250+125=3125

It option C matches this !!

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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 09:33
1
IMO C

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?

Given, For the first 10 movies, cost = $10×50 For next 10 movies, cost =$10×45
For next 10 movies, cost = $10×40 For next 10 movies, cost =$10×35
For next 10 movies, cost = $10×30 For next 10 movies, cost =$10×25
Total dollar spent on first 60 movies = (500+450+400+350+300+250) = 2250 = 225×10
Total cost of last 35 movies = 35×25 = (30+5)(30−5)
So total amount spent for 95 movies = 225×10+(30+5)(30−5)
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 09:34
1
First 50 movies get charged at 50-5(n-1) where n is the set of ten movies John watched, e.g. movies 21-30 will be charged at 50-5(3-1)=40 and movies 41-50 at 50-5(5-1)=30 and any movie beyond the first 50 will be charged a ticket of 25 per movie.

If John watches 95 movies, the cost of movies will be given by:
$$50*10+45*10+40*10+35*10+30*10+25*45$$ ==>> $$10(200)+25*45$$. Now we can check to see which of the options give us the same result, we will refer to the portion of 10(200) as the "first part" and the 25*45 as the "second part" :

A. $$200×10+35×25$$ - Look at the expression, the first part i.e. $$200*10$$ is the same as our answer but the second part is $$35*25$$ which is not correct.
B. $$60×25+45×35$$ - If we factored out the original expression to get 25 in the first part we would have $$80*25+45*25$$, now this option is multiplying 20 less in the first part i.e. $$60*25$$ instead of $$80*25$$, now lets see if multiplying 45 by 35 instead of 25 makes up the difference: $$20*25=500$$ (the deficit from the first part) while $$45*10=450$$ (the excess from the second part of the expression) we are 50 short then, so this can't be correct either.
C. $$225×10+(30+5)(30−5)$$ - In the original expression the first part gave us a value of 2000 whereas first part in this option gives us a value of 2250 which is 250 higher, check to see if the second part is lower by 225, the second part in this option simplifies to $$35*25$$ which is 250 lower than $$25*45$$ ($$10*25=250$$). So it balances out and yields the same answer as the original expression. Lets check the other two options just to be sure.
D. $$225×10+(40+5)(30−5)$$ - First part is 250 higher than original, same as option C, but the second part is the same as the original expression, i.e. $$45*25$$ and thus answer will be 250 higher, incorrect.
E. $$225×10+(40+5)(40−5)$$ - First part is 250 higher just like options C and D, but second part is 450 higher than original expression, i.e. $$450*35$$ instead of $$450*25$$ which will be $$45*10=450$$ higher than the original answer, incorrect.

Correct option is C.
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 09:37
1
The dollar amount paid by John for the 95 movies =
= 1st 10 + 2nd 10 + 3rd 10 + 4th 10 + 5th 10 + 6th 10 + rest 35
$$= (10*50)+(10*45)+(10*40)+(10*35)+(10*30)+(10*25)+(35*25)$$
$$= 10(50+45+40+35+30+25)+(35*25)$$
$$=10*225 + (30+5)*(30-5)$$ --> C
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17 Jul 2019, 09:39
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)

its given: for each 10 movies price reduces from 50 to 25

so for first 60 movies prices are ( 10 x 50 ) + ( 10 x 45 ) +( 10 x 40 ) +( 10 x 35 ) +( 10 x 30 ) +( 10 x 25 )
= 10 x ( 50 + 45 + 40 + 35 + 30 + 25 )
= 10 x 225

for next 35 ( 95 - 60) movies price = 25 X 35

so total price = 10 x 225 + 25 X 35 . Thus ans C
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Senior Manager
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A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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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 $25 life-time n=95… amount={10*50+10*45+10*40+10… (notice the pattern)}: {50(10+9+8+7+6+5)+25(35)}=50(45)+25(35)=2250+25(35) Answer (C). Originally posted by exc4libur on 17 Jul 2019, 09:44. Last edited by exc4libur on 18 Jul 2019, 09:14, edited 1 time in total. Intern Joined: 13 Mar 2019 Posts: 28 Location: India Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 09:51 1 so the rates will be like below for the 95 days: 10 days-50$
10 days 45$10 days 40$
10 days 35$10 days 30$
Remaining days 25$=> 45 days so total=500+450+400+350+300+25*45 =2000 + 45*25 Option A/D &E goes out of picture immediately as they are greater than above. B is less than the 2000$ + 45*25 $so answer is option C. Senior Manager Joined: 31 May 2018 Posts: 306 Location: United States Concentration: Finance, Marketing Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 10:02 1 For the first 10 movies, ticket price = 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. after that, each movie price = 25 per movie john watch 95 movies first 10 movies cost = 10*50 = 500 from now on each set of 10 movies reduces by 5 till ticket price equals 25 per movie set--1 10 movies cost = 10*45 set--2 10 movies cost = 10*40 set--3 10 movies cost = 10*35 set--4 10 movies cost = 10*30 set--5 10 movies cost = 10*25 now 35 movies left each cost 25 per movie = 35*25 = (30+5)(30-5) cost of above 60 movies = 10(25+30+35+40+45+50) = 10*225 the total cost of 95 movies that he paid = 225*10 + (30+5)(30-5) C is the answer Manager Joined: 28 Feb 2014 Posts: 146 Location: India Concentration: General Management, International Business GPA: 3.97 WE: Engineering (Education) Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 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. Manager Joined: 24 Jun 2017 Posts: 71 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 10:30 1 First 10 movies -$50
Next10 Till 20 - $45 " Till 30 -$40
" Till 40 - $35 " Till 50 -$30
" Till 60 - $25 and after this no more reductions So 95 movies implies = 10*(50+45+40+35+25) + 25*35(remaining 35 movies in 25$) = 225*10 + 25*35 --> C
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 10:31
1
Given that;

1 - 10 tickets = 50 x 10 = 500
11 - 20 tickets = 45 x 10 = 450
21 - 30 tickets = 40 x 10 = 400
31 - 40 tickets = 35 x 10 = 350
41 - 50 tickets = 30 x 10 = 300
51 - 60 tickets = 25 x 10 = 250

Total cost here = 2250 = 225 x 10

From this point on, the tickets remain constant at $25 therefore, 61 - 95 = 25 x 35 = 1125 Thus, total cost = 225 x 10 + (25 x 35) This can be re-written as: 225 x 10 + (30 + 5)(30 - 5) Hence answer choice C. _________________ Be Braver, you cannot cross a chasm in two small jumps... Senior Manager Joined: 12 Dec 2015 Posts: 427 Re: A movie theatre rewards its loyal customers by offering them discounts [#permalink] ### Show Tags 17 Jul 2019, 10:32 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?
Solution:
1st 10 tkts: 10*50
2nd 10 tkts: 10*(50 - 1*5)
3rd 10 tkts: 10*(50 - 2*5)
............................
6th 10 tkts: 10*(50 - 5*5)

Total paid for 6*10 i.e 60 tickets = 10*50 + 10*45 + 10 *40 + .....+ 10 * 25 = 10 * 5 ( 10 + 9 +.....+ 5 ) = 10 * 5 * 6*(10+5)/2= 50*45 = 225 * 10 --(i)
money paid for last 95-60 i.e. 35 tickets = 25 * 35 = (30+5) * (30-5) --(ii)
Total paid for 95 tickets = 225*10 + (30+5) * (30-5) .... adding (i) & (ii)

A. 200×10+35×25
B. 60×25+45×35
C. 225×10+(30+5)(30−5) --> correct
D. 225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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17 Jul 2019, 11:19
1
First 10 moviest at price 50 = 50*10
Second 10 at price 45 = 45*10
.. so it goes till price reaches 25: 10*50+10*45+10*40+10*35+10*30
we are left with 95-50 = 45 movies at price 25. We can rewrite $$45*25$$ as $$10*25+35*25$$ and as $$10*25 + (30+5)*(30-5)$$.

Total equation is therefore as following:
$$10*50+10*45+10*40+10*35+10*30+10*25+35*25 = 10*(50+45+40+35+30+25)+(30+5)*(30-5) = 10*225 + (30+5)*(30-5)$$, which is C
Re: A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 17 Jul 2019, 11:19

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