The table above shows quantities of the mobile phone models sold by a retailer. If prices did not change between 2003 and 2004, was the company’s total revenue from sales of these models in 2004 greater than its total revenue from sales of these models in 2003?
(1) Model A was the most expensive phone.
(2) Model C was the least expensive phone.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(A) In 2004, the retailer sold 15 fewer Model A phones and 15 more phones that were either model B or C.

Statement (1) tells us that Model A is the most expensive. Since the selling prices remained unchanged, the loss of revenue from selling 15 fewer of the most expensive phone must be greater than the increase in revenue from selling 15 more of the cheaper phone. So revenue must have decreased, and Statement (1) is sufficient.

Statement (2) tells us only that Model C is the least expensive phone. Since the retailer sold more Model B phones and fewer Model A phones, we need to know more information. If Model B phones were much more expensive than Model A phones, revenue might have increased. If Model A phones were much more expensive, revenue might have decreased.

Since Statement (1) is sufficient and Statement (2) is insufficient, the correct answer is choice (A).
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How do we know that the price of model B and model C put together is not more that the price of model A alone?

We do NOT need to know if the sum of the prices for the models B and C is greater than the price of model A.

In reasoning we rely on the fact given by the statement A, that model A is the most EXPENSIVE one. Therefore its price is greater than the price of model B and is greater than the price of model C.

Let us denote the prices of the models by a, b, c respectively.

In 2003 the revenue was:
190a + 200b + 210c.

In 2004 the revenue was:
175a + 205b + 220c.

The difference is:
175a + 205b + 220c – (190a + 200b + 210c) = (175 – 190)a + (205 – 200)b + (220 – 210)c =
= -15a + 5b + 10c

Since a>b and a>c, then
-15a + 5b + 10c < -15a + 5a + 10a = 0

The look similar on the face of it, but the key to solving this question are the differences in quantities sold.
A: -15
B: +5
C: +10

(1) If we know, that model A is the most expensive one, then
15 most expensive > 5 less expensive + 10 less expensive

(2) If we know, that model A is the cheapest one, then we do NOT know if
15 most expensive > 5 more expensive + 10 least expensive
or
15 more expensive < 5 most expensive + 10 least expensive

The solution is incorrect. The question stated that the prices of the mobile phones have not changed. How come then the writer arrived at the conclusion that This is nowhere stated in the question and cannot be logically decuced as well.

The logic here is quite simple.

1. The prices remained unchanged but quantities changed. So the change in quantities affects the change in revenue.
The revenue = price1 × quantity1 + price2 × quantity2 + price3 × quantity3.

2. 15 the most expensive phones cost more than 15 less expensive ones. So when we deduct the revenue from (the cost of) 15 the most expensive phones we loose more than we gain by adding the revenue from (the cost of) 15 less expensive phones.