A Rectangular-Shaped Carpet Remnant That Measures x Feet GMAT Problem Solving

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)

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