Retailer Z acquired a certain refrigerator and then sold it. Retailer Z's cost to acquire the refrigerator was what percent...
GMAT Data Sufficiency : (DS) Questions
Retailer Z acquired a certain refrigerator and then sold it. Retailer Z's cost to acquire the refrigerator was what percent of the selling price of the refrigerator?
- At the same selling price, the retailer's gross profit on the refrigerator would have been 15 percent greater if the cost to acquire it had been 10 percent less.
- At the same selling price, the retailer's gross profit on the refrigerator would have been 3 percent less if the cost to acquire it had been 2 percent greater.
Understanding the Question
Let's understand what we're being asked. The question wants us to find what percent the cost to acquire the refrigerator is of its selling price.
In simpler terms: If the selling price is S and the cost is C, we need to find \(\frac{\mathrm{C}}{\mathrm{S}} \times 100\%\).
What Makes This Sufficient?
Since this is a "value" question asking for a specific percentage, we need a definite numerical answer. We'll have sufficient information if we can:
- Determine the exact ratio C/S, or
- Find relationships that constrain C/S to a single value
Given Information
- Retailer Z acquired a refrigerator at cost C
- Retailer Z sold it at selling price S
- Gross profit = \(\mathrm{S} - \mathrm{C}\)
Analyzing Statement 1
Statement 1: At the same selling price, the retailer's gross profit would have been 15% greater if the cost had been 10% less.
What Statement 1 Tells Us
This gives us a precise mathematical relationship between cost, selling price, and profit. Let's think through what this means:
- Current profit = \(\mathrm{S} - \mathrm{C}\)
- If cost were 10% less (meaning \(0.9\mathrm{C}\)), the new profit would be: \(\mathrm{S} - 0.9\mathrm{C}\)
- This new profit equals \(1.15 \times\) (current profit)
The Calculation
Let's set up the equation:
\(\mathrm{S} - 0.9\mathrm{C} = 1.15(\mathrm{S} - \mathrm{C})\)
Solving step by step:
- \(\mathrm{S} - 0.9\mathrm{C} = 1.15\mathrm{S} - 1.15\mathrm{C}\)
- \(\mathrm{S} - 0.9\mathrm{C} = 1.15\mathrm{S} - 1.15\mathrm{C}\)
- \(-0.9\mathrm{C} + 1.15\mathrm{C} = 1.15\mathrm{S} - \mathrm{S}\)
- \(0.25\mathrm{C} = 0.15\mathrm{S}\)
- \(\frac{\mathrm{C}}{\mathrm{S}} = \frac{0.15}{0.25} = 0.6\)
Therefore, cost is 60% of selling price.
Conclusion for Statement 1
Statement 1 gives us a unique value: C is exactly 60% of S.
[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: At the same selling price, the retailer's gross profit would have been 3% less if the cost had been 2% greater.
What Statement 2 Provides
Again, we have a precise mathematical constraint that relates cost and selling price:
- Current profit = \(\mathrm{S} - \mathrm{C}\)
- If cost were 2% greater (meaning \(1.02\mathrm{C}\)), the new profit would be: \(\mathrm{S} - 1.02\mathrm{C}\)
- This new profit equals \(0.97 \times\) (current profit)
The Calculation
Setting up the equation:
\(\mathrm{S} - 1.02\mathrm{C} = 0.97(\mathrm{S} - \mathrm{C})\)
Solving:
- \(\mathrm{S} - 1.02\mathrm{C} = 0.97\mathrm{S} - 0.97\mathrm{C}\)
- \(-1.02\mathrm{C} + 0.97\mathrm{C} = 0.97\mathrm{S} - \mathrm{S}\)
- \(-0.05\mathrm{C} = -0.03\mathrm{S}\)
- \(\frac{\mathrm{C}}{\mathrm{S}} = \frac{0.03}{0.05} = 0.6\)
Once again, cost is 60% of selling price.
Conclusion for Statement 2
Statement 2 also gives us the exact same unique value: C is 60% of S.
[STOP - Sufficient!]
This eliminates choices A, C, and E.
The Answer: D
Since each statement independently gives us the exact percentage (60%), each statement alone is sufficient.
Answer Choice D: "Each statement alone is sufficient."