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Ashley and Cassandra drove their cars along the same route for 400 miles and then stopped at a gasoline station, where each purchased exactly the amount of gasoline needed to fill her car's gasoline tank to capacity. If both cars began with full gasoline tanks, which person's car consumed more gasoline during the 400-mile trip?
Let's break down what we're being asked. Ashley and Cassandra each drove \(400\) miles, starting with full gas tanks. At the gas station, they each bought exactly enough gas to fill their tanks back to capacity. We need to determine which person's car consumed more gasoline during the trip.
Here's the key insight: Since both started with full tanks and filled back to capacity, the amount of gas purchased equals the amount consumed. This transforms our question into: "Who purchased more gas at the station?"
What makes this sufficient? We need to be able to definitively say either:
Statement 1 tells us: Ashley purchased \(10\%\) less gasoline by volume than Cassandra purchased.
Let me translate this: If Cassandra bought some amount \(\mathrm{C}\), then Ashley bought \(0.9\mathrm{C}\) (which is \(10\%\) less).
Since the amount purchased equals the amount consumed (remember, they started full and ended full), this directly tells us:
Since \(0.9\mathrm{C} < \mathrm{C}\), we know that Cassandra's car consumed more gasoline than Ashley's car.
[STOP - Sufficient!]
Statement 1 is sufficient to answer our question.
This eliminates choices B, C, and E.
Now let's forget Statement 1 completely and analyze Statement 2 independently.
Statement 2 tells us: The capacity of Ashley's gasoline tank is \(15\%\) less than the capacity of Cassandra's gasoline tank.
This tells us about tank sizes, but here's what we still don't know: How much gas was left in each tank when they stopped? Let me test some scenarios:
Scenario 1: Both tanks were nearly empty when they stopped
Scenario 2: Both tanks were still half full when they stopped
Wait, it might seem like Cassandra always consumes more because her tank is bigger. But what if their cars have dramatically different fuel efficiencies?
Scenario 3: Ashley's car is much more fuel-efficient
Scenario 4: Cassandra's car is much more fuel-efficient
Different scenarios lead to different answers about who consumed more gas. The key realization is that tank capacity alone doesn't tell us about actual consumption – we also need to know how efficient each car is.
Statement 2 is NOT sufficient.
This eliminates choices B and D.
Statement 1 alone tells us exactly who consumed more gas (Cassandra), while Statement 2 alone leaves us uncertain because tank capacity doesn't determine fuel consumption.
Answer Choice A: "Statement 1 alone is sufficient, but Statement 2 alone is not sufficient."