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?

1. 5/2
2. 5
3. 10
4. 15
5. 20

Correct Answer: B
Solution and Explanation:

Approach Solution 1:

This is a GMAT problem-solving question in which you have to use the details given in the question to solve the problem. The problem in this category are coming from different areas of math topics. This one particularly is from area and volume.
The option is given in such a way that it is difficult to guess the correct answer. The candidates need to know the right approach to get the required answer. Only one of the given five choices is correct.

Given in question that a rectangular fence must surround three-fourths of a lawn that is 30 feet wide by 40 feet long. It has asked to find out how much less fence will be required if the enclosure is full width and reduced length rather from full length and reduced width.

Here's a diagram of the 30 x 40 lawn.

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

Approach Solution 2:

This is a GMAT problem-solving question in which you have to use the details given in the question to solve the problem. The problem in this category are coming from different areas of math topics. This one particularly is from area and volume.
The option is given in such a way that it is difficult to guess the correct answer. The candidates need to know the right approach to get the required answer. Only one of the given five choices is correct.

Given in question that a rectangular fence must surround three-fourths of a lawn that is 30 feet wide by 40 feet long. It has asked to find out how much less fence will be required if the enclosure is full width and reduced length rather from full length and reduced width.

From the question we can see that,
Total lawn area: 30 * 40 = 1200; total fence area: 0.75 * 1200 = 900

measurements of the gated space at full width and at a shorter length
width=30
length=900/30=30
Fence length = 2*(30+30) = 120

dimensions of the enclosed area at full length and decreased breadth: length = 40, width = 900/40, and the fence's length are 2*( 40 + 22.5), which equals 125.

The fence length differences in the two cases equal 125 - 120 = 5.

Approach Solution 3:

The problem statement states that:

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.
• The enclosure has full width and reduced length rather than full length and reduced width

Asked:

• How much less fence will be needed?

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

“Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”. To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The candidate can follow the GMAT Quant practice papers to practise several sorts of questions that will help them to improve their mathematical skills.

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