Hi Godot53,

One cardinal rule that will serve you well while solving Geometry questions on the GMAT is to

'never make assumptions'. While solving Ds questions, do not go by how the diagram looks to you, but instead look for definite pieces of information provided in the questions stem and the diagram.

The definite pieces of information provided here are

1. Angle ABD and BDC are 90 degrees

If we analyze this piece of information in depth, then we can definitely say that the lines AB and DC are parallel. When a transversal (in this case BD) cuts two lines (in this case AB and DC), the two lines are said to be parallel if

ONE of the three conditions are satisfied:

1. Alternate angles are equal

2. Corresponding angles are equal

3. Sum of the interior angles is 180 degrees

Attachment:

Screenshot.png [ 38.79 KiB | Viewed 1864 times ]
So here since we have angles ABD and BDC to be 90 degrees, the sum of interior angles will be 180 degrees. This makes lines AB and DC parallel.

ABCD is therefore a trapezoid whose bases are AB and CD and whose perpendicular height is BD=6.

Area of a trapezoid = (Sum of parallel sides)/2 * h Thus, area of trapezoid ABCD = (AB+CD)/2 * 6 = 3(AB+CD)Attachment:

Screenshot 2.PNG [ 14.34 KiB | Viewed 1864 times ]
In the figure above, since AO is perpendicular to CO, quadrilateral ABDO is a rectangle and ∆ACO is a right triangle

In rectangle ABDO, AO = BD =6 and DO = AB.

OC = OD+CD ------>

OC = AB + DC .

Since ∆ACE is a right triangle, AO^2 + OC^2 = AC^2 ------>

6^2 + OC^2 = AC^2. So here we just need the length of OC or the length of AB + DC.

Statement 1: The area of quadrilateral ABCD is 60 3(AB+CD) = 60

AB+CD = 20.

SUFFICIENT.

Statement 2: AD =10Using this information we can find out AB, but we still do not know the length of DC.

INSUFFICIENT. Answer : AHope this helps!

CrackVerbal Academics Team

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