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OG question 134 - estimated avg speed

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by NadineKh » Tue Aug 15, 2017 1:00 am

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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.

Answer: E

How would you rephrase the problem and how would you solve it?
I'm trying to find a more systematic way to solve this type of problem than trying numbers.

Thank you!
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Tue Aug 15, 2017 9:38 am
NadineKh wrote: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.

Answer: E

How would you rephrase the problem and how would you solve it?
I'm trying to find a more systematic way to solve this type of problem than trying numbers.

Thank you!
Well, I'm not sure I'd bother rephrasing this one. Here's how I think about it: you can dismiss each statement on its own almost immediately. The first statement tells you nothing about speed and the second tells you nothing about distance.

Together, we want to see if we can get a YES and a No to the original question. Well, we can obviously get a YES - it's possible that Joan estimated the distance and the speed with uncanny precision, getting both on the nose, and so she'd have gotten the time on the nose as well. So in this case, YES, her estimate would be within .5 hours of the actual time.

So all we need is a NO.
Actual distance = 5
Joan's estimate = 10

Actual speed = 20mph
Joan's estimate = 10mph

Actual Time = 5/20 = .25 hours
Joan's estimate = 10/10 = 1 hour
1 - .25 = .75, so NO, her estimate is not within .5 hours. Together the statements are not sufficient. The answer is E
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by DavidG@VeritasPrep » Tue Aug 15, 2017 10:00 am
Come to think of it, we don't have to think about this one very hard.

Together:
Scenario 1: She gets the distance and the rate exactly right - YES, she's within 5. hours of the actual time.

Scenario 2: actual rate = 0; estimated rate = 10. Clearly, NO, she's not within .5 hours of the actual time, no matter the distance. She's not moving.

Answer is E
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by NadineKh » Tue Aug 15, 2017 10:19 am
Thank you very much!!

It also helped me interpreting it more intuitively: since we have delta (differences between estimation and reality) in both numerator and denominator, we can't have an idea of the % deviation without knowing the value of the ratio.
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by Brent@GMATPrepNow » Wed Nov 15, 2017 4:35 pm
NadineKh wrote: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.
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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