A rectangular yard is 20 yards wide and 40 yards long. GMAT Problem-Solving

Question:A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width of the hedge?

         A. 160/120
         B. 170/120
         C. 180/120
         D. 191/120
         E. 800/120

Answer: C

Solution and Explanation:
Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.

The entire yard is 20 x 40 = 800 square yards;
Taking into account both the entire area and the area of the yard's portion that is covered by the hedge, the uncovered yard's area is 800-171=629 square yards;
The uncovered yard's area is equal to (20-2x)(40-2x)=629 because of its 20-2x width and 40-2x length. (20-2x)(40-2x)=17*37. Instead of trying to solve for x at this stage, it might be wiser to substitute values from the response options. The correct response is C, 3/2.
Correct answer: C

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
If the hedge grows uniformly and setting n as its breadth
40(20) - (40-2n)(20-2n) = 171
4n² - 120n +171 = 0
When n is solved, we get 1.5 or 28.5.
Of the options, (C) scores a 1.5.
There were no options that yielded n as 28.5, hence the answer is (C).
Correct answer: C

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Given: A tall hedge that grows on the property's edge but entirely inside the bounds of the yard surrounds a rectangular yard that is 20 yards wide and 40 yards long.
171 square yards are covered by the hedge.

• The hedge's width must be determined.

Working with the size of the entire yard: 40 x 20 = 800

• The area of the hedge is 171 square feet, so the yard's size without the hedge is 800 minus 171 feet, or 629.

If we assume that the hedge's width is w, then the yard's length and width are each equal to 40 - 2 w and 20 - 2 w, respectively.

• As a result, the size of the yard without a hedge is equal to (40 - 2w) (20 - 2w) = 629. Alternatively, (40 - 2w) x (20 - 2w) = 37 x 17 = (40 - 2 x 1.5) x (20 – 2 x 1.5)

We can state that w = 1.5 = 180/120 when comparing the two sides of the equation.
As a result, choice C is the right response.
Correct answer: C

“A rectangular yard is 20 yards wide and 40 yards long." - 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 problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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