Question: 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?
- $2,600
- $3,900
- $7,800
- $11,800
- $18,200
“Company C sells a line of 25 products with an average retail price of $1,200.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
There is only 1 approach for this question
The given scenario in the question states that a Company C sells a line of products that has an average retail price of $1200. However, none of the products are sold from the company at less than $420 and only 10 products could be sold for $1000.
To find out the greatest possible price for the products, it is important to understand the general rules that are required for solving the problem.
- to maximise one quantity, minimise the others;
- to minimise one quantity, maximise the others.
Accordingly, in order to maximise the price of the most expensive product it is important to minimise the prices of the remaining 24 products.
Accordingly, it can be presented that the average price of 25 products is $1,200 means that the total price of 25 products an be evaluated as
= 25*1,200=$30,000.
Further, taking into consideration the given scenario, then let the number of products sold at the minimum price for these 10 products be at $420 each
However, 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 that can be evaluated for the products is-
10*420+14*1,000=$18,200.
From this aspect, the greatest possible price for the product that could be sold by the company can be calculated as-
$30,000-$18,200=$11,800.
Hence, the correct answer $11,800
Correct Answer: D
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