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In quadrilateral \(ABCD,\) is angle \(BCD\) a right angle?

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Source: — Data Sufficiency |

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Re: In quadrilateral \(ABCD,\) is angle \(BCD\) a right angle?

by Brent@GMATPrepNow » Mon Sep 14, 2020 8:59 am

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Gmat_mission wrote: ↑
Thu Sep 10, 2020 12:28 am
 In quadrilateral \(ABCD,\) is angle \(BCD\) a right angle?

(1) Angle \(ABC\) is a right angle.
(2) Angle \(ADC\) is a right angle.

Answer: E

Source: Official Guide
Target question: Is angle BCD a right angle?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Here are two quadrilaterals that satisfy BOTH statements:
CASE A: ABCD is a square
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In this case, the answer to the target question is YES, angle BCD is a right angle



CASE B: ABCD is not a square
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In this case, the answer to the target question is NO, angle BCD is not a right angle

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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