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Pls help~

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by tracyyahoo » Tue Oct 04, 2011 7:47 am
In planning for 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 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.
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Source: — Data Sufficiency |
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by GmatKiss » Tue Oct 04, 2011 8:13 am
IMO: E
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by Geva@EconomistGMAT » Tue Oct 04, 2011 8:29 am
tracyyahoo wrote:In planning for 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 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.
The answer is E. It all comes down to the question of "how significant are the +/- 5 miles and +/-10 MPH changes from the original estimate?"

If the numbers are great, then the changes are minor and will create a difference of less than 0.5 hour from the estimate.

Let's say that she planned on covering a distance of 10000 miles at a speed of 1000 miles per hour (I'm taking large numbers here, to make the difference insignificant).
estimate time: 10000/1000 = 10 hours

Now if she covers the same same at 10000 miles at 990 mph or at 1010 mph, the difference is minute - definitely less than 0.5 an hour. Likewise, if the distance changes by 5 miles here or there.

Use small numbers, and the differences become significant. If she estimated that she'll cover 30 miles at 15 mph (estimate of 2 hours), and then she travels at 5 mph (6 hours) or at 25 mph (1.16 hours), the difference from her estimate is definitely greater than 0.5 hours.
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Re: Pls help~

by Brent@GMATPrepNow » Sun Jan 19, 2020 12:28 pm
tracyyahoo wrote: ↑
Tue Oct 04, 2011 7:47 am
 In planning for 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 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.
Target question: Was Joan's ESTIMATE within 0.5 hour of the ACTUAL TIME that the trip took?

Statement 1: Joan’s ESTIMATE for the distance was within 5 miles of the ACTUAL distance.
Travel time = distance/speed

Statement 1 provides information regarding the accuracy of Joan's estimation of the travel distance, BUT it does not provide any information regarding her accuracy in estimating her speed.
As such, statement 1 is NOT SUFFICIENT

Statement 2: Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.
Statement 2 provides information regarding the accuracy of Joan's estimation of her average speed, BUT it does not provide any information regarding her accuracy in estimating the travel distance.
As such, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let's test some numbers.
There are several possible scenarios that satisfy BOTH statements. Here are two:
Case a: Joan's estimates were PERFECTLY accurate. In this case, her ACTUAL travel time was definitely WITHIN 0.5 hours of her ESTIMATED travel.

Case b: Joan's ESTIMATED distance and average speed were 8 miles and 8 miles per hour respectively, and the ACTUAL distance and average speed were 5 miles and 1 mile per hour respectively. So, Joan's ESTIMATED travel time = 8/8 = 1 hour, and her ACTUAL travel time = 5/1 = 5 hours. In this case, Joan's ACTUAL travel time was NOT WITHIN 0.5 hours of her ESTIMATED travel.

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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