Last month a certain store purchased computers, some for $600 each and the rest for $800 each, and sold all...

Understanding the Question

Let's break down what we're looking for: How many computers did the store purchase for \(\$\mathrm{800}\) each?

Given Information

• Store purchased computers at two prices: \(\$\mathrm{600}\) and \(\$\mathrm{800}\)
• Specifically purchased \(\mathrm{20}\) computers at \(\$\mathrm{600}\)
• Sold ALL computers for total revenue of \(\$\mathrm{27,000}\)
• Need to find: Number of computers purchased at \(\$\mathrm{800}\)

What We Need to Determine

For this to be a sufficient answer, we need information that leads to exactly one possible value for the number of \(\$\mathrm{800}\) computers.

Key Insights

The critical insight here is that we're dealing with a cost-revenue puzzle. We know:

• Total revenue (\(\$\mathrm{27,000}\))
• Partial purchase information (\(\mathrm{20}\) computers at \(\$\mathrm{600}\))
• But we're missing the connection between costs and revenues

To find a unique answer, we need information that either:

1. Tells us the selling prices (to work backwards from revenue)
2. Constrains the total costs (creating a closed system)

Analyzing Statement 1

Statement 1: The store made a total gross profit of \(\$\mathrm{4000}\) from the sale of the \(\mathrm{20}\) computers that it purchased last month for \(\$\mathrm{600}\) each.

What Statement 1 Tells Us

This gives us the profit from just the \(\$\mathrm{600}\) computers:

• Cost of these \(\mathrm{20}\) computers: \(\mathrm{20} \times \$\mathrm{600} = \$\mathrm{12,000}\)
• Profit from these computers: \(\$\mathrm{4,000}\)
• Therefore, revenue from these computers: \(\$\mathrm{12,000} + \$\mathrm{4,000} = \$\mathrm{16,000}\)

Now we can deduce:

• Revenue from \(\$\mathrm{800}\) computers = \(\$\mathrm{27,000} - \$\mathrm{16,000} = \$\mathrm{11,000}\)

What We Still Don't Know

Here's the critical problem: We know the \(\$\mathrm{800}\) computers generated \(\$\mathrm{11,000}\) in revenue, but we don't know:

• What price each \(\$\mathrm{800}\) computer sold for
• What profit margin was applied to \(\$\mathrm{800}\) computers

Think of it this way: If I tell you "some items generated \(\$\mathrm{11,000}\) total," can you tell me how many items there were? Not without knowing the price per item!

Example: The \(\$\mathrm{800}\) computers could have been:

• \(\mathrm{10}\) computers sold at \(\$\mathrm{1,100}\) each (profit of \(\$\mathrm{300}\) per computer)
• \(\mathrm{11}\) computers sold at \(\$\mathrm{1,000}\) each (profit of \(\$\mathrm{200}\) per computer)
• Many other combinations...

Conclusion

Statement 1 is NOT sufficient because multiple scenarios are possible.

This eliminates choices A and D.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2: The store made a total gross profit of \(\$\mathrm{7000}\) from the sale of all computers that it purchased last month.

What Statement 2 Provides

This is the key constraint! Statement 2 tells us:

• Total revenue: \(\$\mathrm{27,000}\) (given in question)
• Total profit: \(\$\mathrm{7,000}\)
• Therefore, total cost: \(\$\mathrm{27,000} - \$\mathrm{7,000} = \$\mathrm{20,000}\)

The Logical Path to Sufficiency

Now we have a closed system:

• We know exactly how much was spent in total: \(\$\mathrm{20,000}\)
• We know how much was spent on \(\$\mathrm{600}\) computers: \(\mathrm{20} \times \$\mathrm{600} = \$\mathrm{12,000}\)
• Therefore, amount spent on \(\$\mathrm{800}\) computers: \(\$\mathrm{20,000} - \$\mathrm{12,000} = \$\mathrm{8,000}\)

Since each \(\$\mathrm{800}\) computer costs exactly \(\$\mathrm{800}\), there's only one number that works:
\(\$\mathrm{8,000} \div \$\mathrm{800} = \mathrm{10}\) computers

[STOP - Sufficient!] We found a unique answer.

Why This Works

Statement 2 creates what we call a "closed system" - we know:

• Total money in (revenue)
• Total profit
• Therefore, total money out (cost)

With total cost constrained and partial costs known, the remaining quantity is uniquely determined.

Conclusion

Statement 2 is sufficient because it uniquely determines that \(\mathrm{10}\) computers were purchased at \(\$\mathrm{800}\).

This eliminates choices A, C, and E.

The Answer: B

Statement 2 alone provides the total profit, which allows us to determine total cost. Combined with the known partial costs, this uniquely determines the number of \(\$\mathrm{800}\) computers.

Answer Choice B: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."

Test-Taking Insight: In Data Sufficiency problems involving costs and revenues, look for information that "closes the system" - that is, information that constrains either total costs or individual selling prices. Statement 2 does exactly this by providing total profit.