geometry ds

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crazy4gmat: Master | Next Rank: 500 Posts; Posts: 160; Joined: Fri Aug 22, 2008 4:54 am; Thanked: 5 times; GMAT Score:660

by crazy4gmat » Sat Nov 08, 2008 1:57 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.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Source: Beat The GMAT — Data Sufficiency | Sat Nov 08, 2008 1:57 am

molson: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Nov 07, 2008 11:56 pm

by molson » Sat Nov 08, 2008 3:09 am

suppose A,B,C,D as four angles of a quadrilateral. with 1 suppose A,B both 90 degrees and with 2 suppose C=120 and D=60 degrees. Since none of them is sufficient alone so Both are sufficient together.

iamcste: Legendary Member; Posts: 940; Joined: Tue Aug 26, 2008 3:22 amFollowed by: 1 member; Thanked: 55 times

IMO C

by iamcste » Sat Nov 08, 2008 4:12 am

1. if two interior anglês are 90 degrees each, sum of the remaining two would be 180

hence it could be 90,90 or 125,55 or anything hence we cannot conclude that one of the inetrior angles is 60 degrees

hence, Ans could be B or C

2. Here, angle ABC=2 angle BCD

Again here we cannot comment on other 2 angles vir BAD and ADC

so, its not B

Lets check for C using info from 1 and 2

Angle ABC+ Angle BCD+Angle BAD+ Angle ADC=360

3Angle BCD=180 ( since from 2, Angle ABC=2 Angle BCD and other two each are 90)

Angle BCD=60, hence, we can conclude using both statments that one of interior angles is 60

C

4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Nov 09, 2008 10:29 am

I got E

OA?
Angles A, B, C and D respectively

90, 120, 60 and 90
90, 90, 45 and 135

stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Sun Nov 09, 2008 10:37 am

4meonly wrote:I got E

OA?
Angles A, B, C and D respectively

90, 120, 60 and 90
90, 90, 45 and 135

Correct

The OA has to be E.

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