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A certain movie depicted product A in 21 scenes, product B in 7 scenes

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A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 02 May 2011, 18:19
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

85% (01:55) correct 15% (00:57) wrong based on 33 sessions
A certain movie depicted product A in 21 scenes, product B in 7 scenes, product C in 4 scenes, and product D in 3 scenes. The four product manufacturers paid amounts proportional to the number of scenes in which their product was depicted in the movie. If each manufacturer paid x dollars per scene, how much did the manufacturer of product D pay for this advertising?

(1) The manufacturers of product A and B together paid a total of $560,000 for this advertising.
(2) The manufacturer of product B paid $60,000 more for this advertising than the manufacturer of product C paid.

[Reveal] Spoiler:
Presumably, the equation to find the total amount would be: A + B + C + D = $total

Based on what was provided I decided to pick E because I thought:
(1) Only provided the amount that A and B together paid and even if you figure out what A and B individually paid based on that number, you're still missing the total amount paid by ALL product manufacturers (in order to get D's amount).
The equation I came up with was A + B = $560,000

(2) Based on that, you can figure out what C would be but none of the other values are given so you still can't get D.
The equation I came up with was A + (C + 60,000) + C + D = $?

When you put (1) and (2) together, you can get:
560,000 + (560,000/28)*4 + D = $?
but without knowing the total amount, you still can't subtract out D. (Or can you??)

Am I missing something really obvious here...? I don't see how the answer can be D. :? Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jan 2015, 23:56, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 02 May 2011, 18:30
Not sure where "D" comes from, but I think both scenarios can work.

Essentially it comes down to multiples. The total pot of money is 35x if you add up all the shares. In the first case, 28x potentially equalled $560M >> that can work if x = $20M. In the second case, 7x = 4x + $60M >> that can work too if x = $20M too.

So IMHO both are the same answer. If there's any hole in my reasoning, I welcome comments. As I can benefit from it too :-)
(Thanks in advance.)
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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 02 May 2011, 18:34
Ohhh...I got that. I guess what I was thinking though was that each amount was different. Then again, I guess if you read the question very carefully, it does say the amounts are "proportional." I think I was continuing to try to solve it because I thought A was different from B was different from C and so on.

I already came up with $20,000 by working the problem... :(

I think I'm having "one of those nights"...
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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 02 May 2011, 19:17
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(1)

21x + 7x = $560,000

=> x = 560000/28 = 20000

So D paid -> 200000 * 3 = 60000

Sufficient


(2)

7x - 4x = 60000

=> x = 20000


So D paid -> 200000 * 3 = 60000
Sufficient.

Answer- D
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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 02 May 2011, 19:39
let the proportionality constant be k such that the amount paid are in the ratio 21k:7k:4k:3k

we need to find k for this.

a 21k + 7k = 60 * 10^3 k's value can be found. Hence 3k will be D's amount.
b 7k- 60000 = 4k k's value can be found. Hence 3k will be D's amount.

Thus D.
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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 20 Jan 2015, 17:21
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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes [#permalink] New post 20 Jan 2015, 19:06
Expert's post
Hi All,

GMAT questions are always carefully worded, so you really have to pay attention to the details (and take the necessary notes) so that you don't miss anything.

In this question, we're told that EACH manufacturer paid X dollars PER SCENE. That is a "fixed" rate that is the same for everyone.

So....
1 scene = X dollars
2 scenes = 2X dollars
3 scenes = 3X dollars
Etc.

We're also told the number of scenes that each manufacturer advertised in (21 for A, 7 for B, 4 for C and 3 for D). The question asks how much was paid by D. From here, the real question is "what is X?" If we know the price per scene, then we can figure out what D paid (3X = the answer). When dealing with the 2 Facts, we're really just doing simple algebra.

Fact 1: A and B paid a total of $560,000

A and B had a combined total of 28 scenes, so...

28X = 560,000
X = 20,000
Fact 1 is SUFFICIENT

Fact 2: B piad $60,000 more than C

7X = 4X + 60,000
3X = 60,000
X = 20,000
Fact 2 is SUFFICIENT

Final Answer:
[Reveal] Spoiler:
D


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Re: A certain movie depicted product A in 21 scenes, product B in 7 scenes   [#permalink] 20 Jan 2015, 19:06
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