When a certain stretch of highway was rebuilt and

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

by BTGmoderatorDC » Wed Dec 25, 2019 6:09 pm

When a certain stretch of highway was rebuilt and straightened, the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent. By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit?

A. 16%
B. 36%
C. 37 1/2%
D. 45%
E. 56 1/4%

OA B

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Wed Dec 25, 2019 6:09 pm

SampathKp: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Nov 13, 2019 9:42 pm

by SampathKp » Thu Dec 26, 2019 3:17 am

BTGmoderatorDC wrote:When a certain stretch of highway was rebuilt and straightened, the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent. By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit?

A. 16%
B. 36%
C. 37 1/2%
D. 45%
E. 56 1/4%

Let the Initial Distance travel be 100 Units. Let the speed be in 100 units. So time taken is 1 unit (Distance = Speed * Time)

After highway has been rebuilt , The distance is 80 Units (decreased by 20%) and Speed is 125 units (Speed limit increased by 25%)

Time taken is 80/125 Units . 16/25 Units.

% by which the time taken reduce to drive after rebuilding the highway = (1-16/25)/1 *100 = 36%

Answer is B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: When a certain stretch of highway was rebuilt and

by Scott@TargetTestPrep » Mon Jan 13, 2020 2:23 pm

BTGmoderatorDC wrote: ↑
Wed Dec 25, 2019 6:09 pm
When a certain stretch of highway was rebuilt and straightened, the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent. By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit?

A. 16%
B. 36%
C. 37 1/2%
D. 45%
E. 56 1/4%

OA B

Source: Official Guide

We can let the original distance = 100 miles and the original speed limit = 100 mph, so the original time is 100/100 = 1 hour.

With the decreases and increases, the new distance is 80 miles, and the new speed limit is 125 mph, so the new time is 80/125 = 16/25 = 0.64 hour.

Thus, the percent decrease uses the formula:

(New - Old)/Old x 100 = (0.64 - 1)/1 = -0.36 = -36%

We see that the driving time is reduced by 36%.

Answer: B

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