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?**