In quadrilateral ABCD, is angle BCD a right angle?

Question

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

DS88111.01

shridhar786 · Accepted Answer

In quadrilateral ABCD, is angle BCD a right angle?

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

BrentGMATPrepNow · Answer

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
 https://i.imgur.com/ponS7yG.png 
In this case, the answer to the target question is  YES, angle BCD is a right angle

CASE B : ABCD is not a square
 https://i.imgur.com/fk1AbH3.png 
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

brains · Answer

Each statement is definitely insufficient. The trap lies in the idea that when two right angles opposite to each other is given, there is a general tendency to think that the quadrilateral is either a square or rectangle.

However if you can trace back to childhood, you must have used a typical shaped  Kite . This is perfect case of that example. A kite can have two right angles opposite however the other two need not be necessarily right angles. If its difficult to imagine, try to draw a circle first. And then take any point(P) outside the circle(preferably a little far for better visualisation). This is obvious fact that from point P, you can draw two tangents to the circle . And we also know that radius from the centre to that tangent points will be perpendicular at the point of tangency. Now try to join all four sides and make a quadrilateral. You can visualise that angles are not right angles.

Hence the answer is E

SkyCot · Answer

i cannot view the full question with diagram also cant see options

Bunuel · Answer

1. This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

2. The question does not have an image attached to it.

3. This is a geometry question and geometry is no longer tested on the GMAT. So, you can ignore it and move on.

Hope this helps.

In quadrilateral ABCD, is angle BCD a right angle?

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GMAT Data Sufficiency (DS) Questions

In quadrilateral ABCD, is angle BCD a right angle?

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