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555-605 (Medium)|   Geometry|      
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Bunuel
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Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC 02 Aug 2018, 01:33
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E
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25% (medium)

Question Stats:

63% (00:53) correct 37% (00:58) wrong based on 156 sessions

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Is ABCD a rectangle?


(1) ∠ADC = 90°

(2) AD = BC


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GMAT_DS_Magoosh_157.png
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E
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Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC 02 Aug 2018, 02:29
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(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.
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Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC 02 Aug 2018, 02:30
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Insufficient. Even if angle ADC=90º and AD=BC, angle DCB can take any value.
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Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC 02 Aug 2018, 09:01
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Bunuel

Is ABCD a rectangle?


(1) ∠ADC = 90°

(2) AD = BC


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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)
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Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC 03 Sep 2019, 06:32
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