Question: The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

1. 2
2. 4
3. 16
4. 38
5. 40

Answer: E
Solution and Explanation:
Approach Solution 1:
This GMAT problem-solving question requires you to make use of the information supplied in the question. Many different branches of mathematics have contributed problems for this section. This one, in particular, may be
traced back to circles.
As a result of the format of the options offered, picking the correct answer can be difficult. It is incumbent upon the hopefuls to comprehend the best method to achieve the desired outcome. Only one of the five choices offered is correct.
Let x be the diagonal 21-degree square screen's length (and breadth).
The huge screen will have an x^2 larger area.
Let y be the diagonal 19-degree square screen's length (and breadth).
The mini screen's area will be y^2.
The value of x^2 - y^2 is what we're looking for.
Large TV: By using the Pythagorean Theorem, we can determine that x^2 + x^2 = 212 when we look at the right triangle formed by two sides (each with length x) and the diagonal.
This simplifies to 2x^2 = 441, which indicates that x^2 = 441/2.
Small TV: Using the Pythagorean Theorem, we can determine that y^2 + y^2 = 192 by looking at the right triangle formed by two sides (each with length y) and the diagonal.
This simplifies to 2y^2 = 361, which indicates that y^2 = 361/2.
Now, we can calculate the value of x^2 - y^2.
The result is x^2 - y^2 = 44 1/2 - 36 1/2 = 80/2 = 40.
E is the correct answer.

Approach Solution 2:
This GMAT problem-solving question requires you to make use of the information supplied in the question. Many different branches of mathematics have contributed problems for this section. This one, in particular, may be traced back to circles.
As a result of the format of the options offered, picking the correct answer can be difficult. It is incumbent upon the hopefuls to comprehend the best method to achieve the desired outcome. Only one of the five choices offered is correct.
Find the side of the 21-inch square display (i.e., the diagonal of the screen is 21 inches). Remember that a square's diagonal is equal to its second side.
21 = side√2
21/√2 = side
The area of the 21-inch screen is (21/\(\sqrt{2}\))^2 = 441/2 because the area is side^2.
Let's decide which side of the 19-inch square screen it is:
19 = side√2
19/√2 = side
The 19-inch screen has a surface area of (19/\(\sqrt{2}\))^2 = 361/2.
441/2 - 361/2 = 80/2, which equals 40.
E is the correct answer.

Approach Solution 3:
Here, we're working with squares.
When you divide a square diagonal in half, you get two isosceles triangles with the ratio x: x: x^2.
The hypotenuse is equal to x^2 because it is 21 inches long
. We set 21 = x\(\sqrt{2}\) to determine the length of the legs.
x = 21/√2
We divide 21/2 by 2, which yields 441/2, to find the area.
The same procedures are used for the 19-inch screen. The sides of the square screen, or the legs of the triangle, are measured to be 19/2 inches.
We square this to get 36 1/2 in order to get the area. Finally, take 441 / 2 - 361 / 2 to obtain 80/2, which equals 40.
E is the correct answer.

“The size of a television screen is given as the length of" - 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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