Three-fourths of the Area of a Rectangular Lawn 30 feet wide by 40 feet GMAT Problem Solving

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.

Suggested GMAT Problem Solving Sample

• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married to Each Other? GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
• If tu=xytu=xyand ty=uxty=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving
• A Farm has Chickens, Cows and Sheep. The Number of Chickens and Cows Combined is 3 Times the Number of Sheep. GMAT Problem Solving
• In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• The product of the first 10 prime numbers is closest to which of the following? GMAT Problem Solving
• There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5 GMAT Problem Solving
• An equilateral triangle ABC is inscribed in square ADEF, forming three right triangles GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B. The Selling Price of Model A is $120 GMAT Problem Solving
• A contractor combined x tons of a gravel mixture that contained 10 percent gravel G GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution GMAT Problem Solving
• Jug Contains Water And Orange Juice In The Ratio 5:7 . Another Jug Contains Water And Orange J GMAT Problem Solving
• The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated GMAT Problem Solving
• A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour GMAT Problem Solving
• The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. GMAT Problem Solving
• y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT Problem Solving
• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT Problem Solving
• How many factors does 36^2 have? GMAT Problem Solving
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively GMAT Problem Solving
• Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes GMAT Problem Solving
• A milkman cheats his customers by adding water to the milk he sells GMAT Problem Solving
• if 80 lamps can be lighted, 5 hours per day for 10 days for $21.25, then the number of lamps, GMAT Problem Solving
• Few of the corporate contributions to the earthquake relief fund, aside from Pterocom GMAT Problem Solving
• X is Older Than Y, Z Is Younger Than W And V Is Older Than Y GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• Find the Greatest Number That Will Divide 43,91 and 183 So as to Leave GMAT Problem Solving
• A Right Angled Triangle has its Sides in Arithmetic Progression and Being Integers GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 seconds Respectively GMAT Problem Solving
• A Man can Hit a Target Once with 4 Shots. If He Fires 4 Shots in Success GMAT Problem Solving
• A is twice as good a workman as B and together they finish a piece of GMAT Problem Solving
• Frances can complete a job in 12 hours, and Joan can complete the same GMAT Problem Solving
• The Average Age of Chief Executive Officers (CEO’s) in a Large Sample of Companies is 57 GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines can GMAT Problem Solving
• If a and b are positive integers such that a – b and a/b are both even GMAT Problem Solving
• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving