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

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.