Question

In planning for a car trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?
(1) Joan's estimate for the distance was within 5 miles of the actual distance.
(2) Joan's estimate for her average speed was within 10 miles per hour of her actual average speed.

• 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.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

1. Given that Joan’s estimate for the distance was within 5 miles of the actual distance, it is not possible to determine whether her estimate for the time was within 0.5 hour without information about her estimated average speed. For example, if her estimated distance was 20 miles and was within 5 miles of the actual distance, then the actual distance would be between 15 and 25 miles. If her estimated speed was 20 miles per hour (mph) and was within, say, 10 mph of her actual speed, then her actual speed would be between 10 and 30 mph. Her estimated time would then be hour and the actual time would be between hour (least distance over greatest speed) and hours hours (greatest distance over least speed). Since 1.0 hour is between 0.5 hour and 2.5 hours, her estimate for the time could equal the actual time, and thus it is possible that her estimate of the time is within 0.5 hour of the actual time. However, her estimate for the time could be as much as 2.5 − 1.0 = 1.5 hours over the actual time, and thus it is possible that her estimate of the time is not within 0.50 hour; NOT sufficient.

• Given that Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed, the same examples used in (1) can be used to show that it cannot be determined whether her estimate for the time would be within 0.5 hour of the actual time; NOT sufficient.

• Taking (1) and (2) together is of no more help than either (1) or (2) taken separately because the same examples used to show that (1) is not sufficient also show that (2) is not sufficient.
• The correct answer is E; both statements together are still not sufficient.