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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?
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 \(\frac{\mathrm{C}}{\mathrm{S}} \times 100\%\).
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:
Statement 1: At the same selling price, the retailer's gross profit would have been 15% greater if the cost had been 10% less.
This gives us a precise mathematical relationship between cost, selling price, and profit. Let's think through what this means:
Let's set up the equation:
\(\mathrm{S} - 0.9\mathrm{C} = 1.15(\mathrm{S} - \mathrm{C})\)
Solving step by step:
Therefore, cost is 60% of selling price.
Statement 1 gives us a unique value: C is exactly 60% of S.
[STOP - Sufficient!]
This eliminates choices B, C, and E.
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.
Again, we have a precise mathematical constraint that relates cost and selling price:
Setting up the equation:
\(\mathrm{S} - 1.02\mathrm{C} = 0.97(\mathrm{S} - \mathrm{C})\)
Solving:
Once again, cost is 60% of selling price.
Statement 2 also gives us the exact same unique value: C is 60% of S.
[STOP - Sufficient!]
This eliminates choices A, C, and E.
Since each statement independently gives us the exact percentage (60%), each statement alone is sufficient.
Answer Choice D: "Each statement alone is sufficient."