In the Figure above, FGHI is Inscribed in the Circle with the Centre J GMAT Data Sufficiency

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.

Suggested GMAT Data Sufficiency Samples

• The Cardinality of a Finite Set is the Number of Elements in the Set., GMAT Data Sufficiency
• What is the Radius of the Circle above with Center O?, GMAT Data Sufficiency
• Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median?, GMAT Data Sufficiency
• If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?, GMAT Data Sufficiency
• If There are 78 People Working at an Office, How Many of Them are Women Older than 40?, GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• If L \(\neq\) 0, is \(\frac{18K}{L}\) an Integer?
• If 0 < x < 53, What is the Value of Integer x? GMAT Data Sufficiency
• If Vertices of a Triangle have Coordinates (-2,2) (3,2) GMAT Data Sufficiency
• Is P – 1 Even?, GMAT Data Sufficiency
• Buster Leaves the Trailer at Noon and Walks Towards the Studio at a Constant Rate of B Miles Per Hour., GMAT Data Sufficiency
• If ab = ac is b = 2?, GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency, GMAT Data Sufficiency
• Is Quadrilateral ABCD a Rectangle?, GMAT Data Sufficiency
• If \(x^2\)=\(2^x\), What is the Value of x ?, GMAT Data Sufficiency
• A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle, GMAT Data Sufficiency
• If m is a positive integer, is \(\sqrt{m}>25\) ? , GMAT Data Sufficiency
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle GMAT Data Sufficiency
• What is the Remainder when 333^222 is Divided by 7? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True? GMAT Data Sufficiency
• What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency
• If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency
• If m is a positive integer, is √m>25? GMAT Data Sufficiency
• If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency
• If ab = ac is b = 2? GMAT Data Sufficiency
• If x is a positive integer, what is the value of x? GMAT Data Sufficiency
• If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) And M101 GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour GMAT Data Sufficiency
• If sq rt{3+sq rt(x-1)} = 4, what is the value of x? GMAT Data Sufficiency
• What is the sum of a, b, and c? GMAT Data Sufficiency
• What is the value of \(6x^2+9y^2\)?, GMAT Data Sufficiency
• If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even?, GMAT Data Sufficiency
• If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
• S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency
• P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q?, GMAT Data Sufficiency