Question: Do the diagonals of a quadrilateral ABCD bisect each other perpendicularly?
(1) AB=AD
(2) BC=DC
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- 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.
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