Question

If Paula drove the distance from her home to her college at an average speed that was greater than 70 kilometers per hour, did it take her less than 3 hours to drive this distance? (1) The distance that Paula drove from her home to her college was greater than 200 kilometers. (2) The distance that Paula drove from her home to her college was less than 205 kilometers.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are not sufficient

Hint:

For distance, speed, and time problems, use the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \) to determine if the time is within the specified limits.

Answer 1

The Correct Option is C

Step 1: Analyze statement (1).
Statement (1) tells us that the distance is greater than 200 kilometers, but it does not give any information about the time it took to drive this distance, so statement (1) alone is insufficient.
Step 2: Analyze statement (2).
Statement (2) tells us that the distance is less than 205 kilometers, but it also does not tell us the time it took Paula to drive this distance, so statement (2) alone is insufficient.
Step 3: Combine both statements.
We now know that the distance is between 200 and 205 kilometers. Using the relationship \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \), we can check if it took less than 3 hours to drive. Since the speed is greater than 70 km/h, the time is: \[ \text{Time} = \frac{\text{Distance}}{70} \] For a distance of 200 kilometers, the time is: \[ \frac{200}{70} \approx 2.86 \text{ hours} \] For a distance of 205 kilometers, the time is: \[ \frac{205}{70} \approx 2.93 \text{ hours} \] Thus, in both cases, the time is less than 3 hours, and both statements together are sufficient to answer the question.
\[ \boxed{C} \]