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16 Sep 2014, 01:50
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E
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Difficulty:
25%
(medium)
Question Stats:
77% (00:38) correct
23%
(00:34)
wrong
based on 44
sessions
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While motorcycling through the countryside, did Corrine ever exceed the posted 65-kilometer-per-hour speed limit?
(1) Corrine motorcycled for 3 hours through the countryside.
(2) Corrine motorcycled 180 kilometers through the countryside.
(1) Corrine motorcycled for 3 hours through the countryside.
(2) Corrine motorcycled 180 kilometers through the countryside.
16 Sep 2014, 01:50
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Official Solution:
We must determine if, at any time, Corrine violated the 65-kilometer-per-hour speed limit.
Statement 1 tells us that Corrine motorcycled for 3 hours through the countryside. However, it gives us no information regarding her speed. Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice must be B, C, or E.
Statement 2 tells us that Corrine motorcycled 180 kilometers through the countryside. This also tells us nothing about her speed. Statement 2 is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice is either C or E.
Taken together, we know the distance Corrine traveled and the time it took her to travel that distance. Recall that average speed can be computed according to the formula \(\text{rate} = \text{ distance } \div \text{ time}\). Thus, we can compute Corinne's average speed: \(180 \text{ kilometers } \div 3 \text{ hours } = 60 \text{ kilometers per hour}\). Nevertheless, knowing that Corinne's average speed was below the speed limit does not tell us whether or not she exceeded the speed limit at some point during her trip. For instance, she might have gone 40 kilometers per hour for the first hour, 40 kilometers per hour for the second hour, and then 100 kilometers per hour for the third hour. Since we can compute only her average speed, we cannot answer the question definitively. Together, the statements are NOT sufficient.
Answer: E
We must determine if, at any time, Corrine violated the 65-kilometer-per-hour speed limit.
Statement 1 tells us that Corrine motorcycled for 3 hours through the countryside. However, it gives us no information regarding her speed. Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice must be B, C, or E.
Statement 2 tells us that Corrine motorcycled 180 kilometers through the countryside. This also tells us nothing about her speed. Statement 2 is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice is either C or E.
Taken together, we know the distance Corrine traveled and the time it took her to travel that distance. Recall that average speed can be computed according to the formula \(\text{rate} = \text{ distance } \div \text{ time}\). Thus, we can compute Corinne's average speed: \(180 \text{ kilometers } \div 3 \text{ hours } = 60 \text{ kilometers per hour}\). Nevertheless, knowing that Corinne's average speed was below the speed limit does not tell us whether or not she exceeded the speed limit at some point during her trip. For instance, she might have gone 40 kilometers per hour for the first hour, 40 kilometers per hour for the second hour, and then 100 kilometers per hour for the third hour. Since we can compute only her average speed, we cannot answer the question definitively. Together, the statements are NOT sufficient.
Answer: E
