A store purchased a Brand C computer for the same amount that it paid for a Brand D computer and...

Understanding the Question

Let's cut through the complexity here. We have two computers bought at the same cost and sold at different prices. We need to find: By what percent was the profit on Computer C greater than the profit on Computer D?

What We Need to Determine

This is a value question - we need a specific percentage. For sufficiency, we must be able to calculate one unique value for this percentage.

Given Information

• Both computers were purchased for the same amount
• Both were sold at higher prices (meaning both made a profit)
• We need the exact percentage by which C's profit exceeded D's profit

Key Insight

Here's the crucial realization: When two items have the same cost but different selling prices, the percentage difference in their profits depends on the markup percentage, not just the selling price difference. A 15% difference in selling prices could mean vastly different profit percentage differences depending on whether we're dealing with high-markup or low-markup items.

Analyzing Statement 1

Statement 1 tells us: The selling price of Computer C was 15% greater than the selling price of Computer D.

What This Means

Computer C sold for 15% more than Computer D, but both had the same cost. The key question: Does knowing the selling prices differ by 15% tell us by what percent the profits differ?

Testing with Concrete Examples

Let's test this with two scenarios to see if we get a unique answer:

High-markup scenario (like luxury goods):

• Cost for both: $100
• Computer D sells for: $1,000 (900% markup)
• Computer C sells for: $1,150 (15% more than $1,000)
• Profit on D: $900
• Profit on C: $1,050
• C's profit is greater by: \(\frac{\$1,050 - \$900}{\$900} = 16.7\%\)

Low-markup scenario (like commodity items):

• Cost for both: $900
• Computer D sells for: $1,000 (11% markup)
• Computer C sells for: $1,150 (15% more than $1,000)
• Profit on D: $100
• Profit on C: $250
• C's profit is greater by: \(\frac{\$250 - \$100}{\$100} = 150\%\)

Conclusion for Statement 1

The same 15% difference in selling prices creates dramatically different profit percentage differences (16.7% vs 150%) depending on the markup. Without knowing the cost-to-selling-price relationship, we cannot determine a unique answer.

Statement 1 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates 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 on Computer D was $300.

What This Provides

We now know the exact dollar amount of profit on Computer D. But we still don't know:

• The selling price of either computer
• The cost of the computers
• Any relationship between the two selling prices
• The profit on Computer C

The Missing Link

Without any information about Computer C's selling price or profit, we cannot determine by what percent C's profit exceeded D's profit.

For example:

• Computer C could have a profit of $301 (making it 0.33% greater)
• Computer C could have a profit of $600 (making it 100% greater)
• Computer C could have any profit above $300

Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Both Statements

Now let's use both statements together:

• From Statement 1: Computer C sells for 15% more than Computer D
• From Statement 2: Profit on Computer D = $300

The Critical Missing Piece

Here's the problem: We still don't know Computer D's selling price! And without that, we can't determine the percentage difference in profits.

Let me demonstrate with two possibilities:

Scenario 1: Computer D sells for $400

• \(\mathrm{Cost} = \$400 - \$300 = \$100\)
• Computer C sells for $460 (15% more than $400)
• \(\mathrm{Profit\,on\,C} = \$460 - \$100 = \$360\)
• C's profit is greater by: \(\frac{\$360 - \$300}{\$300} = 20\%\)

Scenario 2: Computer D sells for $1,300

• \(\mathrm{Cost} = \$1,300 - \$300 = \$1,000\)
• Computer C sells for $1,495 (15% more than $1,300)
• \(\mathrm{Profit\,on\,C} = \$1,495 - \$1,000 = \$495\)
• C's profit is greater by: \(\frac{\$495 - \$300}{\$300} = 65\%\)

Why Together They Still Aren't Sufficient

Even with both pieces of information, different selling prices for Computer D (all consistent with a $300 profit) lead to different percentage answers (20% vs 65%). We cannot determine a unique value.

The statements together are NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice C.

The Answer: E

The statements together are not sufficient because we cannot determine Computer D's selling price, which is necessary to calculate by what percent Computer C's profit exceeded Computer D's profit.

Answer Choice E: "The statements together are not sufficient."