Threefourths 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) 2 1/2
B) 5
C) 10
D) 15
E) 20
B
Source: Official Guide 2020
Threefourths of the area of a rectangular lawn 30 feet wide
This topic has expert replies

 Master  Next Rank: 500 Posts
 Posts: 302
 Joined: 02 Jul 2017
 Thanked: 1 times
 Followed by:3 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Difficult
GMAT/MBA Expert
 Brent@GMATPrepNow
 GMAT Instructor
 Posts: 13576
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1256 members
 GMAT Score:770
Here's a diagram of the 30 x 40 lawnAbeNeedsAnswers wrote:Threefourths 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) 2 1/2
B) 5
C) 10
D) 15
E) 20
B
Source: Official Guide 2020
If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet
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
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
Use my video course along with Beat The GMAT's free 60Day Study Guide
Sign up for free Question of the Day emails
And check out all of these free resources
Use my video course along with Beat The GMAT's free 60Day Study Guide
Sign up for free Question of the Day emails
And check out all of these free resources
For each case, we determine the unknown dimension of the fence and calculate the perimeter of the fence.
Case 1:
\(30\cdot x=\frac{3}{4}\cdot 30 \cdot 40\)
\(x=30\,\Rightarrow\,P_1=4\cdot 120\)
Case 2:
\(y\cdot 40 = \frac{3}{4}\cdot 30 \cdot 40\)
\(y=22.5\,\Rightarrow\, P_2=2(40+22.5)=125\)
Finally, we determine the difference between perimeters
\(P_2P_1=125120=5\)
Therefore, the correct answer is __B__
Case 1:
\(30\cdot x=\frac{3}{4}\cdot 30 \cdot 40\)
\(x=30\,\Rightarrow\,P_1=4\cdot 120\)
Case 2:
\(y\cdot 40 = \frac{3}{4}\cdot 30 \cdot 40\)
\(y=22.5\,\Rightarrow\, P_2=2(40+22.5)=125\)
Finally, we determine the difference between perimeters
\(P_2P_1=125120=5\)
Therefore, the correct answer is __B__
GMAT/MBA Expert
 Scott@TargetTestPrep
 GMAT Instructor
 Posts: 4190
 Joined: 25 Apr 2015
 Location: Los Angeles, CA
 Thanked: 43 times
 Followed by:21 members
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.AbeNeedsAnswers wrote:Threefourths 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) 2 1/2
B) 5
C) 10
D) 15
E) 20
B
Source: Official Guide 2020
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
Scott WoodburyStewart
Founder and CEO
scott@targettestprep.com
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
 Rich.C@EMPOWERgmat.com
 Elite Legendary Member
 Posts: 10333
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:500 members
 GMAT Score:800
Hi All,
We're told that 3/4 of the AREA of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. We're asked if the enclosure has full width and REDUCED length rather than full length and REDUCED width, how much LESS fence will be needed. This question is built around some standard Geometry and Arithmetic rules  and you might find that a couple of drawings can help you to stay organized.
To start, the area of the FULL lawn is (30)(40) = 1200 squarefeet. Threequarters of that needs to be enclosed by a fence....
(3/4)(1200) = 3600/4 = 900 squarefeet
With full width, we would need the length to be 900/30 = 30 feet, meaning that we would have a 30 foot by 30 foot space. The length of THAT fence would be:
30 + 30 + 30 + 30 = 120 feet
With full length, we would need the width to be 900/40 = 90/4 = 22.5 feet, meaning that we would have a 22.5 foot by 40 foot space. The length of THAT fence would be:
22.5 + 22.5 + 40 + 40 = 125 feet
Thus, the difference in fence length would be 125  120 = 5 feet.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that 3/4 of the AREA of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. We're asked if the enclosure has full width and REDUCED length rather than full length and REDUCED width, how much LESS fence will be needed. This question is built around some standard Geometry and Arithmetic rules  and you might find that a couple of drawings can help you to stay organized.
To start, the area of the FULL lawn is (30)(40) = 1200 squarefeet. Threequarters of that needs to be enclosed by a fence....
(3/4)(1200) = 3600/4 = 900 squarefeet
With full width, we would need the length to be 900/30 = 30 feet, meaning that we would have a 30 foot by 30 foot space. The length of THAT fence would be:
30 + 30 + 30 + 30 = 120 feet
With full length, we would need the width to be 900/40 = 90/4 = 22.5 feet, meaning that we would have a 22.5 foot by 40 foot space. The length of THAT fence would be:
22.5 + 22.5 + 40 + 40 = 125 feet
Thus, the difference in fence length would be 125  120 = 5 feet.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich