Question: In the figure above, FGHI is inscribed in the circle with the centre J. What is the ratio of the area of FGHI to the area of the circle?

1. FGHI is a square
2. The area of the circle is

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.

Answer:

Approach Solution (1):

(1) FGHI is a square

The radius of the circle is R
Side length of square = \(R\sqrt{2}\)

Can calculate the area of the square and the area of the circle in terms of R and then calculate the ratio
Sufficient

(2) The area of the circle is \(8\pi\)

Don’t know if the figure inscribed in the circle is which kind of the quadrilateral
Can’t calculate the area of FGHI
Insufficient

Correct Option: A

Approach Solution (2):

S1- Suppose the radius of the circle is R, then the diagonal of the square (diameter of circle) is 2R.
We can find the sides of the square, hence the area too in terms of R and the area of the circle in terms of R too.
S1 is sufficient.

S2- We doesn’t know if the figure inscribed in the circle is a square or a rectangle, if it’s a rectangle then we can visualize many rectangles of different lengths and breadths. We will basically get multiple ratios and hence the statement is insufficient.

Correct Option: A

“In the figure above, FGHI is inscribed in the circle with the centre J. What is the ratio of the area of FGHI to the area of the circle?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". 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 comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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