Angle of measure in a Quadrilateral

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Wed May 06, 2009 9:49 am

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

OA – E

Last edited by crackgmat007 on Wed May 06, 2009 4:11 pm, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Wed May 06, 2009 9:49 am

Uri: Master | Next Rank: 500 Posts; Posts: 229; Joined: Tue Jan 13, 2009 6:56 am; Thanked: 8 times; GMAT Score:700

by Uri » Wed May 06, 2009 12:26 pm

(1) is insufficient.
(2) is also insufficient.
(1) & (2):
the two right angles can be adjacent to each other or opposite to each other. angle BCD can not be a right angle; otherwise angle ABC will become 180.
i can think of two quadrilaterals. in one the right angles are adjacent to each other. suppose they are A and D. So, angle B and C are not right-angles. in this scenario, if B=2C, then one angle is obviously 60 deg.
in the other quadrilateral, B and D are right-angles. So they are opposite to each other. in this scenario, if B=2C, then C=45 deg and A=135 deg.
So combining also, we don't get any unique result.
i am also getting (E).

can anyone help please?

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Wed May 06, 2009 2:39 pm

That problem is from GMATPrep, and the OA is not C; it's E. I'm not sure why you think the OA is C? In any case, as pointed out above, even with both statements the angles could be 90,90,45,135 or 90,90,60,120.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Wed May 06, 2009 4:07 pm

Actually I found this question on the web, looks like answer stated is wrong.

If the answer is E, then perfect. Thanks for clarifying.

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