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Last month a certain store purchased computers, some for \(\$600\) each and the rest for \(\$800\) each, and sold all these computers for a total of \(\$27,000\). Last Month, if the store purchases \(20\) computers for \(\$600\), how many computers did the store purchase for \(\$800\) each?
Let's break down what we're looking for: How many computers did the store purchase for \(\$\mathrm{800}\) each?
For this to be a sufficient answer, we need information that leads to exactly one possible value for the number of \(\$\mathrm{800}\) computers.
The critical insight here is that we're dealing with a cost-revenue puzzle. We know:
To find a unique answer, we need information that either:
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.
This gives us the profit from just the \(\$\mathrm{600}\) computers:
Now we can deduce:
Here's the critical problem: We know the \(\$\mathrm{800}\) computers generated \(\$\mathrm{11,000}\) in revenue, but we don't know:
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:
Statement 1 is NOT sufficient because multiple scenarios are possible.
This eliminates choices A and D.
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.
This is the key constraint! Statement 2 tells us:
Now we have a closed system:
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.
Statement 2 creates what we call a "closed system" - we know:
With total cost constrained and partial costs known, the remaining quantity is uniquely determined.
Statement 2 is sufficient because it uniquely determines that \(\mathrm{10}\) computers were purchased at \(\$\mathrm{800}\).
This eliminates choices A, C, and E.
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.