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A certain theater has 100 balcony seats. For every $2 [#permalink] ### Show Tags 28 Apr 2012, 20:39 3 This post received KUDOS 11 This post was BOOKMARKED 00:00 Difficulty: 65% (hard) Question Stats: 64% (03:03) correct 36% (02:23) wrong based on 432 sessions ### HideShow timer Statistics A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ? A.$12
B. $14 C.$16
D. $17 E.$18

I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?
[Reveal] Spoiler: OA

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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] ### Show Tags 29 Apr 2012, 03:51 4 This post received KUDOS Expert's post 3 This post was BOOKMARKED boomtangboy wrote: A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ? A.$12
B. $14 C.$16
D. $17 E.$18

I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by$2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34. Answer: C. But the easiest way to solve this problem would be to write down a chart:$10*100=$1,000;$12*95=$1,140;$14*90=$1,260;$16*85=$1,360. Or do the other way around and plug the answer choices. Answer: C. _________________ Current Student Joined: 08 Jan 2009 Posts: 326 GMAT 1: 770 Q50 V46 Followers: 25 Kudos [?]: 136 [0], given: 7 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]

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30 Apr 2012, 02:53
Here's a long winded approach!

Think about a supply and demand chart, but put price along the x axis.

We are told:
Q = mP + C
(10,100)
(12,95)

Which is enough to work out the equation:

Work out m, m = (100-95) / (10 - 12) = -5 / 2
Solve for C

Hence Q = -5/2P + 125

Great. So for any given P, we now know Q seats were sold, but we are interested in total revenue

TR = Q * P = 1360, so

Q*P = -5/2P^2 + 125P
1360 = -5/2P^2 + 125P
2720 = -5P^2 + 250P
5P^2 - 250P + 2720 = 0
P^2 - 50P + 544 = 0

(P - 16)(P - 34) = 0
P = 16, P = 34

16.
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12 May 2012, 04:16
Bunuel wrote:
boomtangboy wrote:
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above$10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is$1,360 ?

A. $12 B.$14
C. $16 D.$17
E. $18 I solved it as follows: 10+2(x) = 100 -5(x) x= 12 Why is my approach wrong? Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

@Bunuel,

in this chart, $17*80 = 1360. why should we avoid 'D' as answer.? Math Expert Joined: 02 Sep 2009 Posts: 36566 Followers: 7079 Kudos [?]: 93182 [0], given: 10553 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]

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12 May 2012, 10:56
Expert's post
1
This post was
BOOKMARKED
kashishh wrote:
Bunuel wrote:
boomtangboy wrote:
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above$10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is$1,360 ?

A. $12 B.$14
C. $16 D.$17
E. $18 I solved it as follows: 10+2(x) = 100 -5(x) x= 12 Why is my approach wrong? Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

@Bunuel,

in this chart, $17*80 = 1360. why should we avoid 'D' as answer.? We can have ONLY one correct answer, so if C is correct then D is automatically wrong. Also, we are told that "for every$2 increase in the price 5 fewer seats will be sold" and from $16 to$17 there is only $1 increase, so you cannot write$17*80.

Hope it's clear.
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02 Jun 2013, 20:49
Hello Bunuel,
I solved it the following way. Let me know if I am correct in the logic and the approach.

R1 = 1000; revenue when price per seat = $10 and no. of seats are 100 R2 = 1360; revenue when price increase every time by$2 and 5 lesser no of seats sold that every time.

Hence, for R2,
x = no. of times price of each seat increase by $2 n = no. of times 5 lesser seats are sold when each time the price is increased by$2

Incremental revenue = $360 Now, essentially x = n (since everytime the price is increased, lesser no. of seats are sold) and this is attributed to the incremental revenue the number of times the price is increased by$2 = 2x
the number of times 5 lesser seats are sold = 5n

hence,
2x * 5n = 360
10xn = 360
xn = 36

now, as mentioned above, x = n
hence x^2= 36
giving, x = + / - 6

x cannot be -6 since the price is increased, thus making x = 6

hence the new price during R2 (1360) = 10+6 = $16 thanks, Rohan _________________ No looking back ! Intern Joined: 30 Jan 2012 Posts: 5 Followers: 0 Kudos [?]: 1 [0], given: 6 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]

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02 Jun 2013, 20:56
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above$10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is$1,360 ?

A. $12 B.$14
C. $16 D.$17
E. $18 I solved it as follows: 10+2(x) = 100 -5(x) x= 12 Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

Hello Bunuel,
I solved it the following way. Let me know if I am correct in the logic and the approach.

R1 = 1000; revenue when price per seat = $10 and no. of seats are 100 R2 = 1360; revenue when price increase every time by$2 and 5 lesser no of seats sold that every time.

Hence, for R2,
x = no. of times price of each seat increase by $2 n = no. of times 5 lesser seats are sold when each time the price is increased by$2

Incremental revenue = $360 Now, essentially x = n (since everytime the price is increased, lesser no. of seats are sold) and this is attributed to the incremental revenue the number of times the price is increased by$2 = 2x
the number of times 5 lesser seats are sold = 5n

hence,
2x * 5n = 360
10xn = 360
xn = 36

now, as mentioned above, x = n
hence x^2= 36
giving, x = + / - 6

x cannot be -6 since the price is increased, thus making x = 6

hence the new price during R2 (1360) = 10+6 = $16 thanks, Rohan _________________ No looking back ! Intern Joined: 02 Jul 2014 Posts: 12 Concentration: Marketing, Strategy Followers: 0 Kudos [?]: 8 [0], given: 34 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]

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06 Jul 2014, 20:46
(final price)*(final seats sold) = 1360

so either (final price) or (final seats sold) should be a factor of 1360

A. 1360/12 indivisible
B. 1360/14 indivisible
C. 1360/16 = 85 (final seats sold) divisible, correct
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] ### Show Tags 16 Oct 2014, 04:42 Bunuel wrote: boomtangboy wrote: A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ? A.$12
B. $14 C.$16
D. $17 E.$18

I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by$2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34. Answer: C. But the easiest way to solve this problem would be to write down a chart:$10*100=$1,000;$12*95=$1,140;$14*90=$1,260;$16*85=$1,360. Or do the other way around and plug the answer choices. Answer: C. Hey Bunuel, What should we do with this piece of information? If all the balcony seats are sold when the price of each seat is$10
shouldn't it be included in the total revenue from sale of tickets? something like
10y+(10+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] ### Show Tags 16 Oct 2014, 06:51 1 This post received KUDOS Expert's post saggii27 wrote: Bunuel wrote: boomtangboy wrote: A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ? A.$12
B. $14 C.$16
D. $17 E.$18

I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by$2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34. Answer: C. But the easiest way to solve this problem would be to write down a chart:$10*100=$1,000;$12*95=$1,140;$14*90=$1,260;$16*85=$1,360. Or do the other way around and plug the answer choices. Answer: C. Hey Bunuel, What should we do with this piece of information? If all the balcony seats are sold when the price of each seat is$10
shouldn't it be included in the total revenue from sale of tickets? something like
10y+(10+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$

No. The number of tickets sold at $10 is 100. We are told that the theater has 100 balcony seats and all the balcony seats are sold when the price of each seat is$10. Check the red portion of my solution above.
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] ### Show Tags 16 Oct 2014, 09:46 Bunuel wrote: saggii27 wrote: Bunuel wrote: A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ? A.$12
B. $14 C.$16
D. $17 E.$18

I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by$2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34. Answer: C. But the easiest way to solve this problem would be to write down a chart:$10*100=$1,000;$12*95=$1,140;$14*90=$1,260;$16*85=$1,360. Or do the other way around and plug the answer choices. Answer: C. Hey Bunuel, What should we do with this piece of information? If all the balcony seats are sold when the price of each seat is$10
shouldn't it be included in the total revenue from sale of tickets? something like
10y+(10+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$

No. The number of tickets sold at $10 is 100. We are told that the theater has 100 balcony seats and all the balcony seats are sold when the price of each seat is$10. Check the red portion of my solution above.[/quote]

got it thanks.

kudos!!!
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] ### Show Tags 16 Oct 2014, 22:15 boomtangboy wrote: A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ? A.$12
B. $14 C.$16
D. $17 E.$18

This seems to be another brilliant question, which seems easy, but has a small trap. If we start from option E, we would realize that even 17 divides 1360. But, that can not be the correct choice, since the increase in price d be $2 _________________ Give KUDOS if the post helps you... SVP Joined: 17 Jul 2014 Posts: 2187 Location: United States (IL) Concentration: Finance, Economics Schools: Stanford '19 (S) GMAT 1: 560 Q42 V26 GMAT 2: 550 Q39 V27 GMAT 3: 560 Q43 V24 GMAT 4: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Followers: 20 Kudos [?]: 270 [0], given: 140 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]

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09 Dec 2015, 19:14
solved it as everyone else:
1360=1000+150x-10x^2
or (x-3)(x-12)

now, either x is 3 or 12. if 12, then the price would be 12*2+10 => 34$. Since we don't have it in our answer choices, it must be the other case, when x is 3. if x is 3, then the price is 3*2+10 = 16. Senior Manager Joined: 07 Dec 2014 Posts: 491 Followers: 3 Kudos [?]: 81 [0], given: 2 A certain theater has 100 balcony seats. For every$2 [#permalink]

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20 Jan 2016, 14:37
let 10+x=seat price
100-2.5x=number of seats sold
(10+x)(100-2.5x)=1360
x=6
10+x=$16 Manager Joined: 22 Feb 2015 Posts: 80 Followers: 0 Kudos [?]: 8 [0], given: 9 A certain theater has 100 balcony seats. For every$2 [#permalink]

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21 Jan 2016, 04:09
Suppose the price of a balcony seat = $x So, seats sold = 100 - [(x-10)/2]*5 But x*{100 - [(x-10)/2]*5} = 1360 -> x*{100 - (x/2 - 5)*5} = 1360 -> x*{100 - 5x/2 + 25} = 1360 -> x*{125 - 5x/2} = 1360 -> 125x - 5*x^2/2 = 1360 -> 250x - 5*x^2 = 2720 -> 50x - *x^2 = 544 -> x^2 - 50x + 544 = 0 -> x^2 - 34x - 16x + 544 = 0 -> x(x - 34) - 16(x - 34) = 0 -> (x - 34)(x - 16) = 0 So, x could be 34 or 16 Since 16 is given in the answer choices, answer = C A certain theater has 100 balcony seats. For every$2   [#permalink] 21 Jan 2016, 04:09
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