A store purchased a computer for $800 and then sold it. Was the store's gross profit on the computer greater...

Understanding the Question

Let's break down what we're asking. The store bought a computer for \(\$800\) and sold it. We need to determine: Was the gross profit greater than \(\$200\)?

Since gross profit = \(\mathrm{Selling\ price} - \mathrm{Purchase\ price} = \mathrm{Selling\ price} - \$800\), we're really asking:
Is \((\mathrm{Selling\ price} - \$800) > \$200\)?

This simplifies to: Is the selling price \(> \$1000\)?

This is a yes/no question - we need a definitive answer about whether the selling price exceeded \(\$1000\). For sufficiency, we must be able to say either "Yes, definitely above \(\$1000\)" or "No, definitely not above \(\$1000\)."

Analyzing Statement 1

Statement 1 tells us: The store sold the computer for more than \(\$950\).

So we know: \(\mathrm{Selling\ price} > \$950\)

This gives us a range of possibilities. Let me test specific values to see if we can answer our question definitively.

Testing Different Scenarios

Case 1: Selling price = \(\$951\)

• Gross profit = \(\$951 - \$800 = \$151\)
• Is \(\$151 > \$200\)? NO

Case 2: Selling price = \(\$1050\)

• Gross profit = \(\$1050 - \$800 = \$250\)
• Is \(\$250 > \$200\)? YES

Both selling prices satisfy "more than \(\$950\)," but they give us different answers to our question. Since we can get both YES and NO outcomes, we cannot answer the question definitively.

Conclusion: Statement 1 is NOT sufficient.

This eliminates answer choices A and D.

Analyzing Statement 2

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

Statement 2 tells us: The store's gross profit was more than \(20\%\) of the selling price.

In other words: \(\mathrm{Gross\ profit} > 20\% \times \mathrm{Selling\ price}\)

Strategic Analysis

Here's the key insight: If the profit exceeds \(20\%\) of the selling price, then the cost (\(\$800\)) must be less than \(80\%\) of the selling price.

Think about it this way - the selling price is divided into cost and profit. If profit takes up more than \(20\%\), then cost must take up less than \(80\%\).

Let's find the boundary case:

• If cost (\(\$800\)) equals exactly \(80\%\) of selling price
• Then: \(\$800 = 0.80 \times \mathrm{Selling\ price}\)
• So: \(\mathrm{Selling\ price} = \$800 \div 0.80 = \$1000\)

Since we need the cost to be LESS than \(80\%\) of selling price (because profit is MORE than \(20\%\)), the selling price must be GREATER than \(\$1000\).

Therefore, the gross profit must be greater than \(\$1000 - \$800 = \$200\).

[STOP - Sufficient!] Statement 2 definitively tells us the answer is YES.

Conclusion: Statement 2 alone is sufficient.

The Answer: B

Statement 2 alone provides sufficient information to determine that the gross profit was indeed greater than \(\$200\), while Statement 1 alone does not.

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