In planning for a trip, Joan estimated both the distance of the trip, in miles,

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri Jun 05, 2020 11:46 am

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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.

Answer: E
Source: Official guide

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 05, 2020 11:46 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: In planning for a trip, Joan estimated both the distance of the trip, in miles,

by Brent@GMATPrepNow » Sat Jun 06, 2020 8:24 am

BTGModeratorVI wrote: ↑
Fri Jun 05, 2020 11:46 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.

Answer: E
Source: Official guide

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: In planning for a trip, Joan estimated both the distance of the trip, in miles,

by deloitte247 » Sun Jun 07, 2020 7:49 am

There is a possible scenario of perfectly accurate estimates in which Joan's travel time will be equal to her estimated time and it will be within 0.5 hours
$$i.e\ \frac{5}{10}=\frac{1}{2}=0.5hrs$$
There is another possible scenario in which the estimates are NOT ACCURATE

If estimated distance and speed are 10miles and 8miles per hour and actual distance and speed are 7miles and 7miles per hour respectively
$$Estimated\ travel\ time\ =\ \frac{10}{8}=1.25$$
$$Actual\ travel\ time\ =\ \frac{7}{7}=1\ hour$$
The estimated travel time is still within 0.5hours of actual travel time as 1 - 1.25 = 0.25hours

But if estimated distance and speed are 10miles and 10miles per hour and actual distance and speed are 7miles and 3miles per hour respectively then
$$Estimated\ travel\ time\ =\frac{10}{10}=1hour$$
$$Actual\ travel\ time\ =\frac{7}{3}=2.3hours$$
The estimated travel time is no longer within 0.5hours of actual travel time. It is now within 2.3 - 1 = 1.5hours

Since the target question cannot be answered with certainty, both statements together are NOT SUFFICIENT

Answer = E

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: In planning for a trip, Joan estimated both the distance of the trip, in miles,

by deloitte247 » Sun Jun 07, 2020 8:26 am

Question => Was Joan's estimate within 0.5hour of the actual time that the trip took?

Statement 1 => Joan's estimate for the distance was within 5miles of the actual distance
$$Time\ taken\ =\ \frac{dis\tan ce}{speed}$$
This statement gives the estimate of Joan's distance but nothing regarding the estimate of her speed. Hence, statement 1 is NOT SUFFICIENT

Statement 2 => Joan's estimate of her average speed was within 10miles per hour of her actual average speed
This statement gives the estimate of her average speed but nothing regarding the estimate of the distance she covered. Hence, statement 2 is NOT SUFFICIENT

There is a possible scenario of perfectly accurate estimates in which Joan's travel time will be equal to her estimated time and it will be within 0.5 hours
$$i.e\ \frac{5}{10}=\frac{1}{2}=0.5hrs$$
There is another possible scenario in which the estimates are NOT ACCURATE

If estimated distance and speed are 10miles and 8miles per hour and actual distance and speed are 7miles and 7miles per hour respectively
$$Estimated\ travel\ time\ =\ \frac{10}{8}=1.25$$
$$Actual\ travel\ time\ =\ \frac{7}{7}=1\ hour$$
The estimated travel time is still within 0.5hours of actual travel time as 1 - 1.25 = 0.25hours

But if estimated distance and speed are 10miles and 10miles per hour and actual distance and speed are 7miles and 3miles per hour respectively then
$$Estimated\ travel\ time\ =\frac{10}{10}=1hour$$
$$Actual\ travel\ time\ =\frac{7}{3}=2.3hours$$
The estimated travel time is no longer within 0.5hours of actual travel time. It is now within 2.3 - 1 = 1.5hours

Since the target question cannot be answered with certainty, both statements together are NOT SUFFICIENT

Answer = E

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