A store purchased coats from a manufacturer at $40 each and then sold all of the coats. The store's gross...

Understanding the Question

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?

What We Need to Determine

• Gross Profit = Revenue - Total Cost
• We want: (Gross Profit ÷ Revenue) × 100%

Key Insight

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.

Analyzing Statement 1

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.

Why This Works

Think about it this way:

• Each \(\$80\) coat generates \(\$40\) profit (\(100\%\) markup)
• Each \(\$60\) coat generates \(\$20\) profit (\(50\%\) markup)
• The mix is always \(20\%\) at the higher price, \(80\%\) at the lower price

Whether we sell 10 coats or 1,000 coats with this distribution:

• Average selling price = \((20\% × \$80) + (80\% × \$60) = \$16 + \$48 = \$64\) per coat
• Cost = \(\$40\) per coat
• Average profit = \(\$24\) per coat
• Profit percentage = \(\$24 ÷ \$64 = 37.5\%\)

The beauty is that this percentage never changes regardless of quantity - both revenue and cost scale proportionally.

Conclusion

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.

Analyzing Statement 2

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.

Testing Different Scenarios

Scenario 1: 100 coats all sold at \(\$64\) each

• Revenue: \(100 × \$64 = \$6,400\) ✓
• Cost: \(100 × \$40 = \$4,000\)
• Profit: \(\$6,400 - \$4,000 = \$2,400\)
• Profit percentage: \((\$2,400 ÷ \$6,400) × 100\% = 37.5\%\)

Scenario 2: 80 coats all sold at \(\$80\) each

• Revenue: \(80 × \$80 = \$6,400\) ✓
• Cost: \(80 × \$40 = \$3,200\)
• Profit: \(\$6,400 - \$3,200 = \$3,200\)
• Profit percentage: \((\$3,200 ÷ \$6,400) × 100\% = 50\%\)

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 \(50\%\)).

Conclusion

Since we can get different profit percentages while maintaining the same revenue, Statement 2 is NOT sufficient.

This eliminates choices B and D.

The Answer: A

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.