Three-fourths of the area of a rectangular lawn 30 feet wide by 40 fee

Question

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

PS98502.01
OG2020 NEW QUESTION

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

PS98502.01
OG2020 NEW QUESTION

BrentGMATPrepNow · Accepted Answer

Here's a diagram of the 30 x 40 lawn
 https://i.imgur.com/6dQyyQ5.png

If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet 
 https://i.imgur.com/nRkAVRU.png 
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 
 https://i.imgur.com/9mZNB8q.png 
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

nick1816 · Answer

Total area of lawn=30*40= 1200
 area of fenced= 0.75*1200=900

dimensions of the fenced area when there is full width and reduced length-
width=30
length=900/30=30
length of fence= 2*(30+30)=120

dimensions of the fenced area when there is full length and reduced width-
length= 40
width=900/40=22.5
length of fence= 2*(40+22.5)=125

Difference in the length of fence in 2 Cases= 125-120=5

ZoltanBP · Answer

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 \implies P_1=4\cdot 30=120

Case2:
 y\cdot 40=\frac{3}{4}\cdot 30\cdot 40

y=22.5 \implies P_2=2(40+22.5)=125

Finally, we determine the difference of the perimeters.

P_2-P_1=125-120=5

Answer: B

EgmatQuantExpert · Answer

Solution

Given:  
 • Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence.

To find:  
 • How much less fence will be needed if the enclosure has full width and reduced length rather than full length and reduced width.

Approach and Working:

• Area of lawn = 30 × 40
 o 3/4th of the area of lawn = ¾(30 × 40) = 30 * 30

Case-1)   When full width will be fenced, and reduced length will be fenced.

• Width = 30 feet
 o 30 * L = 30 * 30 
• Hence, length = 30 feet
• Length of fence needed = 2(30 +30) = 120 feet

Case-2)   When full length will be fenced, and reduced width will be fenced

• Length = 40 feet
 o 40 * W = 30 * 30
  W = 22.5 feet 
o Length of fence needed = 2(40 +22.5) = 125 feet

Difference in length of fence needed = 125- 120 = 5 feet.

Hence, option B is the correct answer.

Correct Answer: Option B

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

PS98502.01
OG2020 NEW QUESTION

Case 1: the enclosure has full width and reduced length
(40-2w)*30 = 3/4 * 30 * 40 
40 -2w = 30
w = 5
Dimensions = (30,30)
Perimeter = 120 feet

Case 2:the enclosure has full length and reduced width
40 * (30-2w) = 3/4 * 30 * 40
30 - 2w = 45/2 = 22.5
w = 3.75
Dimensions = (40,22.5)
Perimeter = 125 feet

Difference in perimeter = difference in fence needed = 125 - 120 = 5 feet

IMO B

Nipunh1991 · Answer

Area of the rectangle = 40* 30 =1200
3/4 * 1200 ( Area of Rectangle) = 900

Now to achieve 900 Sq ft, it can be done by two ways as mentioned in the question (Reducing Length or Reducing Width)
 Case 1: Reducing the Length to new length 'l'
30 * l = 900
l = 30
 Length of fence = Perimeter of fence = 30 + 30 +30 + 30 = 120

Case 2 : Reducing the width to new width 'w'
40 * w = 900
w = 22.5
 Length of fence = Perimeter of fence = 40*2 + 22.5*2 = 125

Difference in length , Case 2 vs Case 1 = 125 - 120 = 5

adkor95 · Answer

Is it just me, or is this a very poorly worded question?

From my understanding, this question had given us a defined scenario 'full width and reduced length' and asks us to find how much less fence is needed, but it does a poor job of clarifying the difference from what. I solved for how much less fence would be needed compared to the amount to enclose the entire rectangular lawn.

dave13 · Answer

BrentGMATPrepNow but 30 by 30 is not a rectangle but rather a square, and this contradicts information

see highlighted part

BrentGMATPrepNow · Answer

A square is a type of rectangle (it's also a type of rhombus) 
Likewise, a rectangle is a type of parallelogram. 
Likewise, a parallelogram is a type of quadrilateral.

So for example, if ABCD has four 90-degree angles and 4 equal sides, we can correctly say that: 
ABCD is a quadrilateral
ABCD is a parallelogram
ABCD is a rectangle
ABCD is a rhombus
ABCD is a square

Cheers, 
Brent

MBAB123 · Answer

I have a similar problem.  Bunuel   ScottTargetTestPrep   EgmatQuantExpert  or anybody else, could you please share some light on why it wasn't correct on my part to find the difference compare to the entire lawn. I realise it's wrong, but how do you make sure here?

ScottTargetTestPrep · Answer

Response:
 
This is actually an official question, so one can expect a question with a similar wording to this one in the real exam. I agree that this is not a straightforward question which requires to be read multiple times before it starts to make sense, I don’t think there is anything wrong with the wording of this question.

The question tells us nothing which could be interpreted as if the perimeter of the enclosure should be compared to the perimeter of the entire 30 by 40 lawn. If we fence the entire lawn, we are not fencing 3/4 the area of the lawn and that contradicts the question. A question which wants us to compare the amount of fencing for the full width, reduced length enclosure to the amount of fencing for the entire lawn would say something like “How much less fence will be needed if 3/4 the area of the lawn with full width and reduced length is fenced instead of the entire lawn?”. Notice that the question reads “If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?”. It is clear from this sentence that we need to compare full width-reduced length and full length-reduced width scenarios.

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=p-zI5sEKUEE

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=0WdJ0ZWHI5Q

ProKiller · Answer

For me, the trap here was of the language. I kept comparing 120 vs 140 ... hence went for option E. What we actually need to do is compare 120 vs 125 ... !! Damn!

100mitra · Answer

Correct option : B

Let L ft be the reduced length. 
Then from(30ft)(Lft)=3/4(30ft)(40ft)
it follows that L = 30, and hence in this case the amount of fence needed is 2(30ft+30ft) = 120 ft. 
Let W ft be the reduced width. 
Then from (Wft)(40ft)=3/4(30ft)(40ft) it follows that W = 22.5, and the amount of fence needed is 2
(22.5 ft + 40 ft) = 125 ft. 
Therefore, the former case requires 5 ft less fence than the latter case

Kratosthe1st · Answer

I thought the word  rather than  would signify we just work with one of the cases.

mcelroytutoring · Answer

Attached is a visual that should help.

https://www.drivecms.com/uploads/mcelroytutoring.com/Screen%20Shot%202023-09-20%20at%207.35.31%20PM.png

bumpbot · Answer

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Three-fourths of the area of a rectangular lawn 30 feet wide by 40 fee

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Three-fourths of the area of a rectangular lawn 30 feet wide by 40 fee

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