Is Quadrilateral ABCD a Square? GMAT Data Sufficiency

Question: 

Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

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.

“Is Quadrilateral ABCD a Square?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". 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.

Solution and Explanation:
Approach Solution 1:
(1) AB = BC = CD = DA --> both square and rhombus have all four sides equal in length. Not sufficient.

(2) AC = BD --> both square and rectangle have diagonals equal in length. Not sufficient.

(1)+(2) ABCD is a square. Sufficient.

Correct Answer: C

Approach Solution 2:
Statement 1: It can be either a square or rhombus. Insufficient.

Statement 2: It can be either a square or a parallelogram or a rectangle or any equidiagonal quadrilateral..

Combining St 1 and St 2, It has to be a square.

Correct Answer: C

Approach Solution 3:
The square has equal sides and equal diagonals.
The rhombus has equal sides but not equal diagonals.

So both together are sufficient

Correct Answer: C

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