In the morning, John drove to his mother's house

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Dec 02, 2017 3:47 am

In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

Can some experts find how the best Option become the correct answer?

OA A

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Source: Beat The GMAT — Data Sufficiency | Sat Dec 02, 2017 3:47 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Dec 04, 2017 9:44 pm

lheiannie07 wrote:In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

Can some experts find how the best Option become the correct answer?

OA A

Speed in the morning = 60 kmph;
Speed in the evening < 60 kmph

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.

Say the distance of the village = 120 kilometers (LCM of 60 and 40; ease to deal with)

Time taken in the morning = Distance/ Speed = 120 / 60 = 2 hours
Time taken in the evening = Distance/ Speed = 120 / 40 = 3 hours

Average speed = Total distance / Total time = (120+120) / 5 = 240/5 = 48 kilometers per hour. Sufficient

(2) John's morning drive lasted 2 hours.

We have no information about the speed in the evening. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8207; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jan 11, 2018 4:34 pm

lheiannie07 wrote:In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

We are given that John drives at a rate of 60 km per hour and drives at a lesser rate when driving again later. We also are given that the distances driven are the same and need to determine the average rate.
We can use the formula:

average speed = total distance/total time

Statement One Alone:

In the evening, John drove at a constant speed of 40 kilometers per hour.

Since the distance each way is d, we can let time 1 = d/60, and time 2 = d/40; thus:

average speed = 2d/(d/60 + d/40)

average speed = 2d/(2d/120 + 3d/120)

average speed = 2d/(5d/120)

average speed = 240d/5d = 48

Statement one alone is sufficient to answer the question.

Statement Two Alone:

John's morning drive lasted 2 hours.

Knowing only the total time is not enough to determine the average speed.

Answer: A

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Jan 12, 2018 3:29 am

lheiannie07 wrote:In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?

(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.

When the SAME DISTANCE on the GMAT is traveled at two different speeds, the average speed for the entire trip will be just a bit closer to the lower speed than to the higher speed.
The reason:
The journey at the lower speed takes LONGER than the journey at the higher speed.
Since more time is spent at the lower speed than at the higher speed, the average speed for the entire trip will be just a bit closer to the lower speed.
Put another way:
The average speed for the entire trip will be just a bit less than the AVERAGE of the lower speed and the higher speed.

Statement 1:
Since the same distance is traveled at 40 mph and at 60 mph, the average speed for the entire trip will be just a bit less than the average of 40 and 60:
(40+60)/2 = 50.
Thus, the average speed for the entire trip will be just a bit less than 50 mph.
SUFFICIENT.

Statement 2:
If the lower speed = 40 mph, then the average speed for the entire trip will be just a bit less than 50 mph, as in Statement 1.
If the lower speed = 50 mph, then the average speed for the entire trip will be just a bit less than 55 mph (the average of 50 and 60).
Since the average speed for the entire trip can be different values, INSUFFICIENT.

The correct answer is A.

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