While motorcycling through the countryside, did Corrine ever exceed th

Statement 1:
Only time is given. We can't find speed.
Insufficient. Hence option A & D are out

Statement 2:
Only distance is given. We can't find speed.
Insufficient. Hence option B is out

By combining both the statements we can get the average speed as 60km/h. There is still no information about maximum or minimum speed.

Corrine can cover 180 km distance in 3 hours by constantly driving 60km/h speed. This confirms Corrine never exceeded the posted 65-kilometer-per-hour speed limit.
Corrine can cover 180 km distance in 3 hours by driving 70km/h for first 2 hours and 40km/h for 1 hour. This confirms Corrine exceeded the posted 65-kilometer-per-hour speed limit for 2 hours.

Combining both the statements is also Not Sufficient. Option C is out.

Hence E

Statement 1 : Corrine motorcycled for 3 hours through the countryside.
Clearly insufficient . Since we don't know the distance and whether she drove at a constant speed or not.

Statement 2 : Corrine motorcycled 180 kilometers through the countryside.
Clearly insufficient . Since we don't know the distance and whether she drove at a constant speed or not.and whether she drove at a constant speed or not.

Combining 1 and 2,
we can say that, the average speed = 180 / 3 = 60 hours
Therefore, if she traveled at this constant speed, then she wouldn't have exceeded the 65 km/hr mark
But, if her actual speed varied, then she could have exceeded the speed limit.

Therefore, E) should be the answer

Official Solution:

While motorcycling through the countryside, did Corrine ever exceed the posted 65-kilometer-per-hour speed limit?

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.

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