Question: Do the diagonals of a quadrilateral ABCD bisect each other perpendicularly?

(1) AB=AD
(2) BC=DC

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.

Approach Solution : 1

Instead of asking whether the diagonals bisect, it would be preferable to ask whether they cut each other perpendicularly. It is important to not confuse it with the perpendicular bisector.

Given that two pairs of adjacent sides in both statements are equal, ABCD is a kite. Having two distinct pairs of equal adjacent sides, a kite is a quadrilateral.

Right angles form the intersection of the diagonals of the Kite

The diagonals cut one another in a perpendicular way.

Statement - 1 : AB=AD

From the explanation and the image, it is clear that this statement is true and therefore sufficient.

Statement - 2 : BC=DC

From the explanation and the image, it is clear that this statement is true and therefore sufficient.

Correct Answer: (C)

“Do the diagonals of a quadrilateral ABCD bisect each other” - is a subject covered in the GMAT quantitative reasoning section. There are 31 questions in the GMAT Quant section. A problem statement is followed by two factual statements in GMAT data sufficiency questions. Two-fifths of the total 31 GMAT Quant questions, or 15 questions, are devoted to the topic of data sufficiency.

Suggested GMAT Data Sufficiency Samples

• If |m + 4| = 2, what is the value of m? GMAT Data Sufficiency
• If a > b, how much greater than b is a? GMAT Data Sufficiency
• What is the radius of the circle above with center O? GMAT Data Sufficiency
• The cardinality of a finite set is the number of elements in the set. What is the cardinality of set A ? GMAT Data Sufficiency
• P and Q are prime numbers less than 70. What is the units digit of P*Q? GMAT Data Sufficiency
• Max purchased a guitar for a total of $624,which consisted of the price of the guitar and the sales tax GMAT Data Sufficiency
• In the figure shown, point O is the center of the semicircle and points B, C, D lie on the semicircle GMAT Data Sufficiency
• Is 500 the average (arithmetic mean) score on the GMAT? GMAT Data Sufficiency
• If 4x = 5y = 10z, what is the value of x + y + z ? (1) x - y = 6 (2) y + z = 36 GMAT Data Sufficiency
• Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters GMAT Data Sufficiency
• Can the Positive Integer p be Expressed as the Product of Two Integers GMAT Data Sufficiency
• A School Administrator will Assign each Student in a Group GMAT Data Sufficiency
• Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length GMAT Data Sufficiency
• A Certain Truck Uses 112+kv2 Gallons of Fuel Per Mile GMAT Data Sufficiency
• What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x > 0 GMAT Data Sufficiency
• What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Data Sufficiency
• For a Class of 50 Students, The Table Above Reports The Number of Students GMAT Data Sufficiency
• A Terminating Decimal is Defined as a Decimal GMAT Data Sufficiency
• A Rectangular Solid has Length, Width, and Height of L cm, W cm, and H cm, Respectively GMAT Data Sufficiency
• What is the circumference of circle C ? (1) The radius of circle C is 2π. (2) The center of circle C is located at point (7,8) in the xy-plane GMAT Data Sufficiency
• Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units GMAT Data Sufficiency
• If Each Side of Parallelogram P has Length 1, What is the Area of P? GMAT Data Sufficiency
• If g is an Integer and x is a Prime Number, Which of the Following Must be an Integer? GMAT Data Sufficiency
• Is the Positive Integer n a Multiple of 24? GMAT Data Sufficiency
• What is The Volume of the Right Circular Cylinder X ? GMAT Data Sufficiency
• If x>y^2>z^4, Which of The Following Statements Could Be True? GMAT Data Sufficiency
• A Clothing Manufacturer Makes Jackets That Are Wool or Cotton or a Combination of Wool and Cotton GMAT Data Sufficiency
• Is |x-1| < 1 ? 1. (x-1)^2 >1 2. x < 0 GMAT Data Sufficiency
• Is 2x - 3y < x^2 ? GMAT Data Sufficiency
• In Triangle PQR, if PQ = x, QR = x + 2, and PR = y GMAT Data Sufficiency
• In the Below Figure, O is The Centre of The Circle GMAT Data Sufficiency
• If p is the Perimeter of Rectangle Q, What is the Value of p? GMAT Data Sufficiency
• What is x? (1) x = 4y - 4 (2) xy = 8 GMAT Data Sufficiency
• Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0 GMAT Data Sufficiency
• What Is The Area Of Triangle ABC ? GMAT Data Sufficiency
• If n Is a Positive Integer And r Is The Remainder When n^2 - 1 is Divided By 8 GMAT Data Sufficiency
• If 0 < x < y, what is the value of (x+y)^2/(x−y)^2? GMAT Data Sufficiency
• If The Perimeter of Quadrilateral ABCD is 4, What Is Its Area? GMAT Data Sufficiency
• If Triangle ABC Is Isosceles, What Is The Length Of Side BC? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is x<5 ? (1)x^2 > 5 (2)x^2 + x < 5 GMAT Data Sufficiency
• Is x < y ? (1) 2x < 3y (2) xy > 0 GMAT Data Sufficiency
• Is c^(abcd) = 1? (1) |a|>|b|>|c|>|d| (2) c^d>3 GMAT Data Sufficiency
• If r and s are The Roots of The Equation x^2 + bx + c = 0 GMAT Data Sufficiency
• Equilateral triangle BDF Is Inscribed in Equilateral Triangle ACE GMAT Data Sufficiency
• What is the value of x if x^3 < x^2? GMAT Data Sufficiency
• If x ≠0, then what is the value of (|x|)x? 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