Question: A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

1. 50xy
2. 450xy
3. xy/9
4. xy/50
5. 450/(xy)

“A rectangular-shaped carpet remnant that measures x feet ''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section tests the calculative aptitudes of the candidates to solve quantitative problems. The candidates must choose the correct option by properly analyzing the problem with mathematical understanding. The candidates must have knowledge of highly calculative mathematics to solve GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part cites mathematical problems that can only be solved with appropriate quantitative skills.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• A rectangular-shaped carpet remnant measures x feet by y feet.
• The price of the carpet is $50
• 9 square feet = 1 square yard

Find Out:

• The cost of the carpet per square yard.

The dimension of the carpet is x feet and y feet.
Therefore, the area of the carpet= xy square feet (Since the area of a rectangle=length*breadth)
Cost of the carpet per square foot = $50/xy
Therefore, the cost of the carpet per square yard = $50/(xy/9) = $450/xy square yard.

Correct Answer: (E)

Approach Solution 2:

The problem statement suggests that:

Given:

• A rectangular-shaped carpet remnant measures x feet by y feet.
• The cost of the carpet is $50
• 9 square feet = 1 square yard

Find Out:

• The cost of the carpet per square yard.

Since rectangular-shaped carpet remnant of dimensions x feet by y feet is priced at $50, we can write it as, xy sq ft = $50
Therefore, 1 sq ft = $50/xy

By multiplying 9 on both sides, we get,
9 sq ft = $450/xy
or 1 sq yard = $450/xy
Therefore, the cost of the carpet per square yard= $450/xy

Correct Answer: (E)

Approach Solution 3:

The problem statement suggests that:

Given:

• A rectangular-shaped carpet remnant measures x feet by y feet.
• The cost of the carpet is $50
• 9 square feet = 1 square yard

Find Out:

• The cost of the carpet in dollars per square yard.

Area of rectangular-shaped carpet = x feet * y feet = xy square feet

It is asked to find the cost in dollars per square yard

The question states that 9 square feet = 1 square yard
Therefore, we can say, 1 square foot = 1/9 square yard
Then, xy square feet = (1/9) * xy square yard
                                      = xy/9 square yard
Therefore the cost of the carpet in dollars per square yard = $50 / (xy/9) square yard
                                                                                                = (450/xy) dollars per square yard

Correct Answer: (E)

Suggested GMAT Problem Solving Questions

• The Sum of 5 Numbers in the Geometric Progression is 24 GMAT Problem Solving
• Two Students Appeared At An Examination. One of Them Secured 9 Marks GMAT Problem Solving
• x' is a Positive Integer and x^3 is Divisible by 27 GMAT Problem Solving
• Which of the Following Equation is NOT Equivalent to 25x^2 = y^2 - 4? GMAT Problem Solving
• The Variable x is Inversely Proportional to the Square of the Variable GMAT Problem Solving
• 16 Ounces of Fresh Orange Juice Contains 216 Calories GMAT Problem Solving
• An Urn Contains 6 Red, 4 Blue, 2 Green and 3 Yellow marbles GMAT Problem Solving
• The Price of Raw Materials Has Gone up by 15% GMAT Problem Solving
• In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics GMAT Problem Solving
• If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
• Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
• Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45
• How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
• 16 Ounces of Birdseed Mix Contains 10% Sesame Seed by Weight GMAT Problem Solving
• The Diameter of Circle S is Equal in Length to a Side of a Certain Square 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
• If The Sum of 9 Consecutive Integers is 90 GMAT Problem Solving
• If a Carton Containing a Dozen Mirrors is Dropped GMAT Problem Solving GMAT Problem Solving
• The Number 2 - 0.5 is How Many Times the Number 1 - 0.5? GMAT Problem Solving
• If n = 3, What is The Value of 2^2n+1? GMAT Problem Solving