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A store purchased coats from a manufacturer at \(\$40\) each and then sold all of the coats. The store's gross profit on the sale of the coats was what percent of the store's revenue from the sale of the coats?
Let's break down what we're being asked to find. The store purchases coats at \(\$40\) each and sells all of them. We need to determine the gross profit as a percentage of revenue.
In simpler terms: What percentage of the money collected from sales was profit?
Since every coat costs the same amount (\(\$40\)), if we know how the coats are priced for sale, we can determine the profit margin. The actual number of coats doesn't matter - what matters is the relationship between selling prices and the \(\$40\) cost.
For this question to be sufficient, we need information that allows us to calculate a single, definite percentage value.
Statement 1 tells us: \(20\%\) of coats sold at \(\$80\) each, and the remaining \(80\%\) sold at \(\$60\) each.
Here's the crucial insight: When all items have the same cost but are sold at specific price points in fixed proportions, the profit percentage depends only on that price mix - not on how many items you sell.
Think about it this way:
Whether we sell 10 coats or 1,000 coats with this distribution:
The beauty is that this percentage never changes regardless of quantity - both revenue and cost scale proportionally.
Since the profit percentage is fixed at \(37.5\%\) regardless of the number of coats sold, Statement 1 is sufficient.
[STOP - Sufficient!]
This eliminates choices B, C, and E.
Now let's forget Statement 1 completely and analyze Statement 2 independently.
Statement 2 tells us: Total revenue was \(\$6,400\).
Knowing only the total revenue and that each coat cost \(\$40\), can we determine the profit percentage? Let's test different scenarios to find out.
Scenario 1: 100 coats all sold at \(\$64\) each
Scenario 2: 80 coats all sold at \(\$80\) each
These two scenarios show that different combinations of quantity and selling price can produce the same \(\$6,400\) revenue but yield completely different profit percentages (\(37.5\%\) vs \(50\%\)).
Since we can get different profit percentages while maintaining the same revenue, Statement 2 is NOT sufficient.
This eliminates choices B and D.
Statement 1 alone provides the selling price distribution, which locks in a unique profit percentage regardless of quantity. Statement 2 alone allows multiple profit percentages for the same revenue.
Answer Choice A: Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.