What is the Area of a Rectangular Field? GMAT Data Sufficiency

Question: What is the area of a rectangular field?

(1) The diagonal is twice the width.
(2) The length is 173 feet.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
The problem statement asks to find the area of the rectangular field.

As per the formula of the area of the rectangle, we know that:
Area of rectangular field = length * width

Statement 1 alone: The diagonal is twice the width.
Let the width of the rectangular field = d
Therefore, the diagonal of the rectangular field = 2d
Hence, the information is not enough to find the area of the rectangular field.
Therefore, statement one alone is not sufficient.

Statement 2 alone: The length is 173 feet
The statement does not provide any information about the width of the rectangular field.
So it will not be possible for us to find the area of the rectangular field without knowing both the length and width of the rectangle.
Therefore, statement two alone is not sufficient.
Combining both statement 1 and statement 2, we get:

We know from statement 1,
Width of the rectangular field = d
And the diagonal of the rectangular field = 2d
From statement two, we know that the length is 173 feet

Therefore, according to the Pythagoras theorem, we can say:
(2d)^2 = d^2 + 173^2
=>3*d^2 = 173^2
=>d = 173/(3^1/2)

Therefore, by combining the statement we can know both the length and width of the rectangular field.
Hence, both statements TOGETHER are sufficient to find the answer.

Approach Solution 2:
The problem statement asks to find the area of the rectangular field.

Statement 1 alone: The diagonal is twice the width.
Let the width of the rectangular field be x
Then, Diagonal = 2 * Width = 2x
=> Then the length of the rectangular field = √(4x^2 - x^2) [Since according to the Pythagoras theorem, diagonal^2 = length^2 + width^2 ]
=> L= x √3
Therefore, the length of the rectangular field = x √3.
However, we could not find the value of x from statement one alone.
Therefore, statement 1 alone is not sufficient to find the area of the rectangular field.

Statement 2 alone: The length is 173 feet
From this statement, we could not find the value of the width of the rectangular field.
Hence, statement 2 alone is not sufficient to find the area of the rectangular field.

Combining both statement 1 and statement 2, we get:
From statement 1, we get: L= x √3
From statement 2, we get: the length is 173 feet.

Therefore, we can say,
173= x√3
x = 173/√3
Therefore, we can find the width of the rectangular field i.e equals 173/√3.

Hence, from both statements, we know the length and width of the rectangular field.
Therefore, we could easily find the area of the rectangular field.

Hence, both statements TOGETHER are sufficient to find the answer.

“What is the area of a rectangular field?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2020”. The GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency includes 15 questions which are two-fifths of the total 31 GMAT quant questions.

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