Question: In quadrilateral ABCD, is AC longer than BD?

1. Angle ABC < Angle BCD
2. AB = BC = CD = DA

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.

“In quadrilateral ABCD, is AC longer than BD?”- 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.

Answer:

Approach Solution (1):

(1) Angle ABC < Angle BCD

This tells us that ABCD is not a square or a rectangle because naturally, both have four angles each equaling 90 degrees. With a triangle, the leg across from the largest angle is the longest but does it work like with a four sided figure, Apparently not because 1 is not sufficient.

(2) AB = BC = CD = DA

This tells us that ABCD is either a square or a rhombus. If the figure is a square, then both diagonals AC = BD. In the figure is a rhombus, then one diagonal will be longer than the other. Insufficient

1 + 2 this tells us that all four sides are equal and that one angle (or, in this case, pairs of angles) is greater than another. The only possible shape that has four equal sides and different interior angles is a Rhombus AC > BD. Sufficient.

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