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by j_shreyans » Thu Aug 21, 2014 3:33 am
Guys ,

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

OAD

Thanks ,

Shreyans
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by Jim@StratusPrep » Thu Aug 21, 2014 5:14 am
If you want the maximum price for 1 item, all the other items must be priced as low as possible:

10 items @ $420 = $4,200
14 items @ $1,000 = $14,000

Lowest cost of the other 24 = $18,200

Total price of the 25 items = 25 x 1,200 = $30,000

30,000 - 18,200 = 11,800

D
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by Brent@GMATPrepNow » Thu Aug 21, 2014 7:03 am
j_shreyans wrote: 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
When it comes to averages, we know that average value = (sum of n values)/n
We can rewrite this into a useful formula: sum of n values = (average value)(n)

25 products with an average retail price of $1,200
So, the TOTAL VALUE of the 25 products = ($1200)(25) = $30,000

To MAXIMIZE the price for 1 item, we must MINIMIZE the prices of the other 24 items.

None of the 25 products sells for less than $420, and exactly 10 of the products sell for less than $1,000
To MINIMIZE the prices, we can have 10 items priced at $420 and 14 items priced at $1000
Value of the 24 items = (10)($420) + (14)($1000) = $4,200 + $14,000 = $18,200

If the TOTAL VALUE of the 25 products is $30,000, then the value of the last remaining item = $30,000 - $18,200 = [spoiler]$11,800[/spoiler]

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATinsight » Thu Aug 21, 2014 8:28 am
Answer: Option D
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