Geometry DS 3- GMAT PREP

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GMATDUD: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Tue Jan 16, 2007 9:40 am; Location: Arlington,VA

by GMATDUD » Fri Feb 08, 2008 9:50 am

Hi All,

Another one where I kind of need help with the basics. For a quadrilateral , is it always true that t he sum of interior angles = 180?

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Source: Beat The GMAT — Data Sufficiency | Fri Feb 08, 2008 9:50 am

its_me07: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Oct 22, 2007 4:44 am; Thanked: 1 times

by its_me07 » Fri Feb 08, 2008 11:00 am

Is the ans B?
The sum of the interior angles of a quad is 360.

Statement 1 is INSUFf bcoz it gives info abt only two angles(i.e right angles) and the other two could be 90 and 90 or 60 and 120 so INSUFF.

Statement 2 is SUFF bcoz we know any two angles in a quad are equal to 180 so it says 2x + x =180 => x=60 ,hence SUFF.

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GMATDUD: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Tue Jan 16, 2007 9:40 am; Location: Arlington,VA

by GMATDUD » Fri Feb 08, 2008 4:35 pm

OA is E

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its_me07: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Oct 22, 2007 4:44 am; Thanked: 1 times

by its_me07 » Fri Feb 08, 2008 10:05 pm

Staurt can u help?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Feb 09, 2008 10:29 am

We know that the interior angles of a quadrilateral (4 sided figure) always sum to 360 degrees.

Q: is one of the angles 60 degrees?

(1) ABCD contains 2 right angles.

That accounts for 180 of the 360, but we have no clue how the remaining 180 degrees are split up between the last two angles: insufficient.

(2) ABC = 2*BCD

We have the relationship between two of our angles, but we don't know anything about specific measurements.

We could have ABC = 120 and BCD = 60 (yes answer); or
ABC = 130 and BCD = 65 (not sure answer): insufficient.

Combined, we know that we have two 90 degree angles and that one angle is double the other. However, we still don't know WHICH angles follow each piece of information.

The following 4 angles fit all the rules we have:

(a) 90 90 120 60 : 2 90 degree angles and 120 = 2*60
(yes, we have a 60 degree angle)

(b) 90 90 45 135 : 2 90 degree angles and 90 = 2*45
(no, we don't have a 60 degree angle)

We can get both a "yes" and a "no" even after combining: choose (e).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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GMATDUD: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Tue Jan 16, 2007 9:40 am; Location: Arlington,VA

by GMATDUD » Sat Feb 09, 2008 12:32 pm

Stuart ,

Thanks for the explanation . My mind was stuck at 2 adjoining angles being 90 degrees and then the properties of parallel lines would dictate the other 2 angles to be 60 and 120 . I was thinking symetric figures.

This helps.

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