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# Is the measure of one of the interior angles of

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VP
Joined: 18 May 2008
Posts: 1176
Is the measure of one of the interior angles of  [#permalink]

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18 Nov 2008, 23:27
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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 twicde the degree measure of angle BCD.

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Manager
Joined: 14 Nov 2008
Posts: 182
Schools: Stanford...Wait, I will come!!!

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18 Nov 2008, 23:47
ritula wrote:
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 twicde the degree measure of angle BCD.

from 1) the sum of the angle of the other two will be 180..but it can be anthing. (100,80.) )60,120)..Not Sufficient
2) we cannot say anything about the other two angle, so not sufficient.
combining 1 and 2, the sum of the other two angle, is 180.
x + 2x= 180,
It implies.. one angle is 60.
Director
Joined: 14 Aug 2007
Posts: 692

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18 Nov 2008, 23:48
ritula wrote:
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 twicde the degree measure of angle BCD.

E.

1) we know about only 2 angles.
2) again we know about only 2 angles out of 4.

together,
90,90,45,135 case is possible to prove that angle may not be 60 degrees.
VP
Joined: 18 May 2008
Posts: 1176

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19 Nov 2008, 00:18
I had also marked E for the same reasons but the OA is C
alpha_plus_gamma wrote:
ritula wrote:
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 twicde the degree measure of angle BCD.

E.

1) we know about only 2 angles.
2) again we know about only 2 angles out of 4.

together,
90,90,45,135 case is possible to prove that angle may not be 60 degrees.
Director
Joined: 14 Aug 2007
Posts: 692

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19 Nov 2008, 00:24
ritula wrote:
I had also marked E for the same reasons but the OA is C

What is the source of this Q?
VP
Joined: 18 May 2008
Posts: 1176

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19 Nov 2008, 03:07
Source is one of GMATPREP test papers
VP
Joined: 17 Jun 2008
Posts: 1474

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19 Nov 2008, 03:32

The trick here is the visualization. Two right angles can be adjacant or diagonally opposite. But, if diagonally opposite angles are right angles, the other two angles will automatically become right angles.

Hence, in order for stmt2 to be correct. two adjacant angles need to be right angles and in that case including stmt2, one of the angles will be 60 degree.....hence, C should be the answer.
Manager
Joined: 01 Apr 2006
Posts: 172

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27 Dec 2008, 22:10
I ran into this very question during my practice and I got the OA to be E (not C).
Attachments

gmatPrep_DS_abcdAngles.jpg [ 65.8 KiB | Viewed 947 times ]

VP
Joined: 05 Jul 2008
Posts: 1329

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28 Dec 2008, 16:43
alpha_plus_gamma wrote:
ritula wrote:
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 twicde the degree measure of angle BCD.

E.

1) we know about only 2 angles.
2) again we know about only 2 angles out of 4.

together,
90,90,45,135 case is possible to prove that angle may not be 60 degrees.

Good point

We have to note that 45 X 2 =90
Manager
Joined: 21 Dec 2008
Posts: 70

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30 Dec 2008, 10:21
scthakur wrote:

The trick here is the visualization. Two right angles can be adjacant or diagonally opposite. But, if diagonally opposite angles are right angles, the other two angles will automatically become right angles.

Hence, in order for stmt2 to be correct. two adjacant angles need to be right angles and in that case including stmt2, one of the angles will be 60 degree.....hence, C should be the answer.

so wouldn't be E

as, for the same case its coming 60 one time when adj. angles are 90 while other time when opp. diagonal angles are 90 then it won't be 60 degree.

little confuse!!!

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This is not a quality discussion. It has been retired.

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Re: DS: angle &nbs [#permalink] 30 Dec 2008, 10:21
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