Bunuel wrote:
Attachment:
Quadrilateral.png
If quadrilateral ABCD, pictured above, has a perimeter of 64, what is the length of line segment AD?
(1) The length of line segment AD is equal to the length of line segment BC
(2) Line segment AD is perpendicular to line segment BC
Kudos for a correct solution.Basically we want to know whether quadrilateral ABCD is a square.
1) I generally don't trust gmat's shapes, but this time I will give it a try. If the two diagonals have the same lenght and bisect each other the shape is a square. And thus this statement would be sufficient. If I chose to be wary, I still don't know whether the two diagonals bisect each other, opening the likelyhood to have a wonky shape that can resemble a rhombus. What makes me doubt about my second scenario is that all the quadrilateral's angles are 90 degrees, suggesting that the shape is a quare (it can't be a rectangle since the diagonals have the same lenght). If we move the diagonal as in scenario two the angles are goin to reflect that and won't be 90 degrees anymore.
2) AD is perpendicular to BC. Not sufficient. The shape can either be a square or be a rhombus.
Answer A.
Please correct me if I am wrong
thanks in advance,
_________________
learn the rules of the game, then play better than anyone else.