Product sell

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