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# A certain theater has 100 balcony seats. For every $2  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Senior Manager Status: May The Force Be With Me (D-DAY 15 May 2012) Joined: 06 Jan 2012 Posts: 291 Location: India Concentration: General Management, Entrepreneurship Followers: 2 Kudos [?]: 146 [2] , given: 16 A certain theater has 100 balcony seats. For every$2 [#permalink]  28 Apr 2012, 20:39
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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 _________________ Giving +1 kudos is a better way of saying 'Thank You'. Math Expert Joined: 02 Sep 2009 Posts: 30377 Followers: 5091 Kudos [?]: 57341 [3] , given: 8811 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  29 Apr 2012, 03:51
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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.

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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] 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. Intern Joined: 01 Mar 2012 Posts: 32 Concentration: Operations, Finance GMAT 1: 740 Q49 V41 GPA: 3.3 WE: Engineering (Manufacturing) Followers: 1 Kudos [?]: 4 [0], given: 46 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  01 May 2012, 06:54
The official answer given here is wrong, it is given E. Moderators please correct it, it'll be C.
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] 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. 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. @Bunuel, in this chart,$17*80 = 1360.
why should we avoid 'D' as answer.?
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] 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. 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. @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. _________________ Math Expert Joined: 02 Sep 2009 Posts: 30377 Followers: 5091 Kudos [?]: 57341 [0], given: 8811 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  31 May 2013, 05:22
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] 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
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] 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. 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.[/quote] 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
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink] 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 Intern Joined: 15 Jul 2012 Posts: 38 Followers: 0 Kudos [?]: 3 [0], given: 245 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  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.

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.

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+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$Math Expert Joined: 02 Sep 2009 Posts: 30377 Followers: 5091 Kudos [?]: 57341 [1] , given: 8811 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  16 Oct 2014, 06:51
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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.

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.

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. _________________ Intern Joined: 15 Jul 2012 Posts: 38 Followers: 0 Kudos [?]: 3 [0], given: 245 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  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.

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.

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!!! Manager Joined: 02 Jul 2012 Posts: 213 Location: India GMAT 1: 720 Q50 V38 GPA: 2.3 WE: Consulting (Consulting) Followers: 9 Kudos [?]: 138 [0], given: 82 Re: A certain theater has 100 balcony seats. For every$2 [#permalink]  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
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