Julian bought 6 kilograms of cheese from each of Deli A and Deli B. At the prices given in the table above, did he spend more money on cheese at Deli A or at Deli B?
(1) The ratio of American to Provolone to Swiss purchased at Deli A was 6 : 2 : 1.
(2) The ratio of American to Provolone to Swiss purchased at Deli B was 2 : 7 : 2.

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) Statement (2) tells us the ratio of purchases at Deli B. Since equal amounts of American and Swiss cheese were purchased, the average price of the cheese purchased at Deli B was $18 per kilogram. From here, we can calculate the total amount of money spent at Deli B, but we still know nothing about the distribution of purchases at Deli A. Since the American cheese at Deli A is less expensive than any cheese at Deli B, we would need to know the breakdown of cheeses at Deli A to answer the question. So Statement (2) alone is insufficient.

Using Statement (1), we can determine the average price per kilogram of cheese at Deli A:
= ((15 × 6) + (17 × 2) + (19 × 1)) / 9 = (90 + 34 + 19) / 9 = 143/9 = $15 8/9.
So the average price of the cheese bought at Deli A is less than $16/kilogram. Notice that the least expensive cheese at Deli B costs $16 per kilogram. Because Julian bought the same amount of cheese in each store, and the least expensive cheese at Deli B costs $16/kilogram, he must have spent less money in Deli A. Therefore, Statement (1) is sufficient alone.

Since Statement (2) is insufficient and Statement (1) is sufficient, the correct answer is choice (A).

*Note, that the sing of division can be either ÷ or /.
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Why is statement (1) sufficient?

Statement (1) is sufficient. Let me explain why.

We know that (1) The ratio of American to Provolone to Swiss purchased at Deli A was 6 : 2 : 1. So if we denote by x kg the amount of Swiss cheese bought at Deli A then we can write the amount of American and Provolone cheese bought at the Deli A:
6x, 2x respectively. Overall he bought 6 kg at Deli A, so we can write an equation:
6x + 2x + x = 6
9x = 6
x = 6/9 = 2/3, 6x = 4, 2x = 4/3

So he spent:
4 × 15 + 4/3 × 17 + 2/3 × 19 = 60 + 68/3 + 38/3 = 180/3 + 68/3 + 38/3 = 286/3 = 95,333...

The least amount of money he could have spent at Deli B is if he bought all 6kg of American cheese (cheapest) and it is:
6 × 16 = 96

96 > 95,333... so in any case he would spend more at deli B. Since we can give a definite answer the statement (1) is sufficient alone.

There are just several calculations in this question, they are NOT complicated and they CANNOT be avoided.

When we analyze the statement (2), we find the average price of cheese that was bought in the Deli B without calculations. And then we even do NOT need to conduct a simple multiplication of 2 numbers to get to the conclusion that the statement (2) by itself is NOT sufficient:
19 × 6 > 18 × 6
15 × 6 < 18 × 6

When we analyze the statement (1), you need to calculate either the average price or the overall sum spent at the Deli A:
($15 8/9) × 6 < $16 × 6
You see how close the numbers are, so a rough approximation is NOT possible in this case.

He bought 6 kg of cheese in B in total, while the ratio of American to Provolone to Swiss purchased at Deli B was 2 : 7 : 2. (base statement + statement 2).
If he had bought 6 kg of the cheapest cheese (American) in B, then, considering the ratio, he would also have bought 6 kg of the Swiss cheese and (7/2) × 6 = 21 kg of the Provolone cheese. The total amount would have been 6 + 21 + 6 = 33 kg, NOT 6kg. So the proposed amount of the cheapest cheese, bought in B, is impossible.

We also know that he bought 6 kg of cheese in each of the delis. That's why knowing an average gives us the total amount of money he spent in a deli.

Furthermore, even if we didn't know the exact amount of cheese (6kg) bought in each deli, but just knew that he bought the same amount of cheese in total in each deli, that still would be enough.