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Company C sells a line of 25 products with an average retail

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Director
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Company C sells a line of 25 products with an average retail [#permalink] New post 21 Nov 2005, 19:18
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Question Stats:

74% (03:08) correct 26% (01:29) wrong based on 114 sessions
Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?

A. $2,600
B. $3,900
C. $7,800
D. $11,800
E. $18,200
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Dec 2012, 04:02, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 21 Nov 2005, 19:32
Cool Johnny!! You just lost your identity! :shock:

Min price of 10 products under $1000 = 420*10 = 4200
Since other products are $1000 or greater, let us say the next 14 products cost $1000 each = $14000

Total for 24 prod = 18200
Total for 25 prod = 25*1200 = 30000
25th product (most expensive) = 30000 - 18200 = 11800 (D)
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Re: PS- selling price [#permalink] New post 21 Nov 2005, 21:39
cool_jonny009 wrote:
Company C sells a line of 25 products with an average retail price of $1200. if none of these product sells for less than $420 and exactaly 10 of the products sell for less than $1000, What is the greatest possible selling price of the most expensive product?


a)2600
b)3900
c)7800
d)11,800
e)18,200


My answer is D

In order to find the greatest selling price, we have to minimize the 24 products.

Total price = $25*$1200 = $30,000

Min 10 of the products = 10*$420 = $4,200
Min the remaining 14 products = 14*$1000 = $14,000

$30,000 - $4,200 - $14,000 = $11,800
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 [#permalink] New post 21 Nov 2005, 22:36
25 products average at 1200 dollars, so total = 30,000 dollars

Assume 10 of the products that sell less than 1000 all sell for the minimum price of 420 dollars, then that's a total of 4200 dollars.

So we can have 14 products selling at 1000 dollars, so that's 14,000 dollars.

So the most expensive product can cost 11800 dollars.
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Re: PS- selling price [#permalink] New post 21 Nov 2005, 23:03
D - 11800.
Total price = 25*1200 = 30000
Min. price = 10 * 420 = 4200
=> Remaining 15 should sum to (30000 - 4200) = 25800
Let us assume that 14 of these cost 1000 each and they total to 14000
HEnce 25800 - 14000 = 11800 should be the greatest possible SP.
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 [#permalink] New post 22 Nov 2005, 01:10
yup got 11800 as well.

1200 * 25 - 420*10 - 1000*14 = 11800
so answer is D.
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 [#permalink] New post 22 Nov 2005, 18:48
Make 10 @420 = 4200

You have 15 left. You need to minimize 14, so make 14 @1000 = 14000

=(25*1200) - 14000 - 4200 = 11,800

Ans = D
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 [#permalink] New post 22 Nov 2005, 20:36
D. Say x-the most expensive product. Minimizing the value of 24 other products, x=1200*25-420*10-1000*14=11800
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Re: Company C sells a line of 25 products with an average retail [#permalink] New post 17 Dec 2012, 00:40
Sorry guys. Still feel like this question is missing something.
I understand why 10 products are priced at $420.
Why aren't the remaining 14 products also priced at $420 to maximize the final products price?
No where in the questions does it say that the other products must be priced at $1000.

Thanks in advance.


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Previous posted answer...
Min price of 10 products under $1000 = 420*10 = 4200
Since other products are $1000 or greater, let us say the next 14 products cost $1000 each = $14000

Total for 24 prod = 18200
Total for 25 prod = 25*1200 = 30000
25th product (most expensive) = 30000 - 18200 = 11800 (D)
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Re: Company C sells a line of 25 products with an average retail [#permalink] New post 17 Dec 2012, 04:27
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SFsubway wrote:
Sorry guys. Still feel like this question is missing something.
I understand why 10 products are priced at $420.
Why aren't the remaining 14 products also priced at $420 to maximize the final products price?
No where in the questions does it say that the other products must be priced at $1000.

Thanks in advance.


Because if the remaining 14 products are also priced at $420, then we'd have that 10+14=24 items are less than $1,000, and we are told that EXACTLY 10 of the products are priced less than $1,000,

Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?

A. $2,600
B. $3,900
C. $7,800
D. $11,800
E. $18,200

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So, to maximize the price of the most expensive product we should minimize the prices of the remaining 24 products.

The average price of 25 products is $1,200 means that the total price of 25 products is 25*1,200=$30,000.

Next, since exactly 10 of the products sell for less than $1,000, then let's make these 10 items to be at $420 each (min possible).

Now, the remaining 14 items cannot be priced less than $1,000, thus the minimum possible price of each of these 14 items is $1,000.

Thus the minimum possible value of 24 products is 10*420+14*1,000=$18,200.

Therefore, the greatest possible selling price of the most expensive product is $30,000-$18,200=$11,800.

Answer: D.

Hope it's clear.
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Re: Company C sells a line of 25 products with an average retail [#permalink] New post 17 Dec 2012, 07:29
Thanks Bunuel.
I guess "exactly 10" vs using say "only 10" through me off.
Thanks for the clarification.

Cheers!
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Re: Company C sells a line of 25 products with an average retail [#permalink] New post 25 Jun 2014, 08:29
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Re: Company C sells a line of 25 products with an average retail   [#permalink] 25 Jun 2014, 08:29
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