If quadrilateral ABCD, pictured above, has perimeter of 64, what is the length of the line segment AD?

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

The OA is B

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Re: If quadrilateral ABCD, pictured above, has perimeter of 64, what is the length of the line segment AD?

by Ian Stewart » Thu Jun 10, 2021 5:04 am

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I've never needed to know, in more than ten years of answering official GMAT Quant questions, that when a rectangle's diagonals are perpendicular, that rectangle is a square. But that's what this question is testing. If you know that, Statement 2 is clearly sufficient alone, and Statement 1 is not (the diagonals of any rectangle are equal in length by Pythagoras, so Statement 1 is always true and doesn't give any new information).

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