Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC

Question

https://gmatclub.com/forum/download/file.php?id=42504 Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC GMAT_DS_Magoosh_157.png

sudarshan22 · Answer

(1) ∠ADC = 90°
No information about sides, and other angle
  Insufficient

(2) AD = BC
No information about other sides, and angles
  Insufficient

Combining both :
Not much information to conclude that it is a rectangle
  Insufficient

Hence,   E  .

yoannnesme · Answer

Insufficient. Even if angle ADC=90º and AD=BC, angle DCB can take any value.

PKN · Answer

We need to determine whether all the four angles of the quadrilateral ABCD are 90 degree or not. Because a rectangle has all the four angles 90 (side lengths don't matter). When all the sides are equal then it is a square, otherwise it's a rectangle and every square is a rectangle.

St1:- ∠ADC = 90°. We don't know the measure of other three angles ,those sum to 360-90=270.
When they are equal, then each measures 90 degree and the quadrilateral becomes a rectangle. Otherwise, it's just a quadrilateral but not rectangle.
Insufficient.
St2:- AD = BC
Side doesn't help in determining type of quadrilateral specifically. Insufficient.

Combining, we have the same situation as mentioned in (1). We can draw rectangles with AD=BC and ∠ADC = 90°. And in the other case,it's not a rectangle.(See enclosed figure)
Insufficient.

Ans. (E)

bumpbot · Answer

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Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC

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