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Three-fourths of the area of a rectangular lawn 30 feet wide

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by BTGModeratorVI » Tue Mar 03, 2020 6:54 am

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Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

A. 5/2
B. 5
C. 10
D. 15
E. 20

Answer: B
Source: Official Guide
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Re: Three-fourths of the area of a rectangular lawn 30 feet wide

by swerve » Tue Mar 03, 2020 9:48 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:54 am
 Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

A. 5/2
B. 5
C. 10
D. 15
E. 20

Answer: B
Source: Official Guide
Total area of lawn\(=30\cdot 40= 1200\)
area of fenced\(= 0.75\cdot 1200=900\)

dimensions of the fenced area when there is full width and reduced length-
width\(=30\)
length\(=\dfrac{900}{30}=30\)
length of fence\(= 2\cdot (30+30)=120\)

dimensions of the fenced area when there is full length and reduced width-
length\(= 40\)
width\(=\dfrac{900}{40}=22.5\)
length of fence\(= 2\cdot (40+22.5)=125\)

The difference in the length of fence in 2 Cases\(= 125-120=5\).
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Re: Three-fourths of the area of a rectangular lawn 30 feet wide

by Brent@GMATPrepNow » Mon Mar 09, 2020 6:12 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:54 am
 Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

A. 5/2
B. 5
C. 10
D. 15
E. 20

Answer: B
Source: Official Guide
Here's a diagram of the 30 x 40 lawn
Image

If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet
Image
So, the enclosure is a 30 by 30 square.
The PERIMETER = 30 + 30 + 30 + 30 = 120 feet


If we keep the full length (of 40 feet), then the width of the enclosure = 3/4 of 30 = 22.5 feet
Image
So, the enclosure is a 40 by 22.5 rectangle.
The PERIMETER = 40 + 40 + 22.5 + 22.5 = 125 feet

If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?
125 feet - 120 feet = 5

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Three-fourths of the area of a rectangular lawn 30 feet wide

by Scott@TargetTestPrep » Wed Mar 11, 2020 9:40 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:54 am
 Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

A. 5/2
B. 5
C. 10
D. 15
E. 20

Answer: B
Source: Official Guide
If the enclosure has full width and reduced length, then the width = 30 ft and the reduced length = 40 x 3/4 = 30 ft. So we need 2(30) + 2(30) = 60 + 60 = 120 feet of the fence for the enclosure.

On the other hand, if the enclosure has full length and reduced width, then the length = 40 ft and the reduced width = 30 x 3/4 = 22.5 ft. So we need 2(40) + 2(22.5) = 80 + 45 = 125 feet of the fence for the enclosure.

Therefore, we see that we save 5 feet of fence in the first option.

Answer: B

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