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Estimates questions

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Estimates questions

by jfranco23 » Thu Mar 12, 2009 3:16 pm
Planning a 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 hours of the actual time that the trip took?

1. Joan's estimated 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
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Source: — Data Sufficiency |
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by Alara533 » Thu Mar 12, 2009 4:08 pm
I think the answer is E.

1. Says Joan's estimated for the distance was within 5 miles of the actual distance. To cover this 5 miles difference in half an hour the average speed should be greater than or equal to 10 miles/hr. But we don't know the speed, hence insufficient.

2. Says Joan's estimate for her average speed was within 10 miles per hour of her actual average speed. Suppose the maximum difference was 10 miles/hour, then in half hour it will result in a maximum of 5 miles difference. Not sufficient since we don't have the difference in miles.

Now together they may look sufficient. But fails when the assumed speed is less than 10 miles/hour.

Suppose the total assumed dist was 100 miles and assumed avg speed was 10 miles per hour. Then the total journey would have taken 10 hrs.
Suppose the actual speed was 5 miles/hr (which is with the 10miles/hr range of the assumed speed). Then actual time will be 20 hrs, which is not in the half hour range of 10 hours.

Suppose the actual distance is 104 and actual speed is 8miles/hr. Both woth on the range provided. The time will be 13 hrs, which is still outside the half an hour range of 10.

hence not sufficient!
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