Miracle Walnut Company sells two products – bags of walnuts in their shells, for each of which the company charges $6, and bags of walnuts unshelled, for each of which the company charges $11. Last year the company sold fewer bags of walnuts in their shells and more bags of walnuts unshelled than it sold in the year before last year.
Which of the following is information provided by the statements above?
Compared with Miracle Walnut Company’s total revenue for the year two years ago, the company’s total revenue last year was greater.
Last year the average price Miracle Walnut Company received for a bag of walnuts was greater than the average price it received the year before last.
Last year, Miracle Walnut Company’s competitors sold walnuts in their shells at prices lower than that charged by Miracle Walnut Company for such walnuts.
Most of Miracle Walnut Company’s customers prefer unshelled walnuts over walnuts in their shells.
Last year, the number of bags of walnuts sold by Miracle Walnut Company was the same as the number it sold during the year before last year.
Scott Woodbury-Stewart
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Solution:
Analysis of the Information Given:
Effect of the First Statement: Defines that Miracle Walnut Company sells two products and provides descriptions of the products and the price of each. Products and Prices: Bags of Walnuts in Shells, $6. Bags of Walnuts Unshelled, $11.
Effect of the Second Statement: Defines only the directions of changes in the quantities of the two products sold in each of two years. Last year, fewer bags of walnuts in shells were sold than were in the year before last. Last year, more bags of walnuts unshelled were sold than were in the year before last.
To arrive at the correct answer to this question, we’ll have to be careful not to draw unwarranted conclusions from the information given. We know that the quantities sold of the two products changed, and we know the directions of the changes, but we don’t know the magnitudes of the changes. Each of the changes could have been large or small.
(A) Compared with Miracle Walnut Company’s total revenue for the year two years ago, the company’s total revenue last year was greater.
If one were to assume that the decrease in the number of bags of walnuts in shells sold matched the increase in the number of bags of unshelled walnuts sold, then one might believe that this statement is true. For example, if the number of bags of walnuts in shells sold decreased by 1000, then revenue decreased by $6000. If the number of bags of unshelled walnuts increased by 1000, revenue increased by $11,000. Since the increase would be greater than the decrease in this scenario, the net change would be an increase in revenue. However, since the passage does not tell us anything about the magnitudes of the decrease and the increase, it does not support this type of calculation. So, it does not support what this choice says.
CORRECT ANSWER(B) Last year the average price Miracle Walnut Company received for a bag of walnuts was greater than the average price it received the year before last.
No matter how many bags of walnuts in shells and bags of unshelled walnuts were sold in each of the two years, if the number of bags of walnuts in shells decreased from the first year to the second year, and the number of bags of unshelled walnuts increased, then the average price of a bag of walnuts sold by the company must have increased. To see why this increase in the average price must have occurred, you could consider the following. The first year’s average price would be calculated using a certain number of 6’s and a certain number of 11’s. Then the second year’s average would be based on fewer 6’s and more 11’s, as the number of bags sold for $6 decreased year over year, and the number of bags sold for $11 increased. So, from the first year to the second, the average price would move away from $6 and toward $11.
(C) Last year, Miracle Walnut Company’s competitors sold walnuts in their shells at prices lower than that charged by Miracle Walnut Company for such walnuts.
One might take the fact that fewer bags of walnuts in shells were sold last year than were the year before as an indication that competitors sold the same product at a lower price and, thus, took some business from Miracle Walnut Company. However, the passage does not give us a clear reason to believe that this specific factor caused the decrease.
(D) Most of Miracle Walnut Company’s customers prefer unshelled walnuts over walnuts in their shells.
One might take the fact that the price charged for a bag of unshelled walnuts is greater than the price charged for a bag of walnuts in their shells as an indication that customers prefer unshelled walnuts. However, it isn’t necessarily the case that customers prefer unshelled walnuts. It could be that the price for unshelled walnuts is higher because they cost more to produce, or for some other reason other than customer preference.
(E) Last year, the number of bags of walnuts sold by Miracle Walnut Company was the same as the number it sold during the year before last year.
What this choice says would be true only if the decrease in the number of bags of walnuts in shells sold exactly matched the increase in the number of bags of unshelled walnuts sold. Since the passage does not include information on the magnitudes of the changes in the number of bags sold, the passage does not provide support for the conclusion that the decrease matched the increase.
