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measure of interior angle of quad

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by crak.gmat » Sun Aug 24, 2008 11:36 am
is the measure of one of the intereior angle of quad 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
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Source: — Data Sufficiency |
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by parallel_chase » Sun Aug 24, 2008 1:30 pm
I think the answer is E.

Statement I

Two angles are of 90 degrees, no info about the other two angles.

Hence Insufficient.

Statement II

one angle is twice its opposite angle, that angle could be 60 and 120, we dont know. Insufficient.

Combining I & II

two angles 90, one angle is twice the other.
that angle could also be 45. 2*45 = 90

Therefore Insufficient.

Hence E is the answer.

Whats the OA?
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by LSB » Sun Aug 24, 2008 3:28 pm
I would say it's C

Statement 1 not suff. as per previous post

Statement 2 not suff. One angle is double the other. The angles could be

150
75
25
110

or
120
60
90
90
.. and many other combinations


Both statments combined:
two angles are at 90 degrees. A quadrilateral has a total angle measure of 360. This leaves 180 for the other two angles where one of these two must be twice the other.

Set up equation:
X+Y = 180
2X = Y
Substitute
X+2X = 180
X=60
Y=120

Both statments combined are suff. Answer C
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by LSB » Sun Aug 24, 2008 4:18 pm
what's the OA?
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by crak.gmat » Sun Aug 24, 2008 6:05 pm
OA is E
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by crak.gmat » Sun Aug 24, 2008 6:07 pm
Btw, I don't get it how it can be E. IMHO its C
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by Ian Stewart » Sun Aug 24, 2008 6:57 pm
LSB wrote:
Both statments combined:
two angles are at 90 degrees. A quadrilateral has a total angle measure of 360. This leaves 180 for the other two angles where one of these two must be twice the other.

Set up equation:
X+Y = 180
2X = Y
Substitute
X+2X = 180
X=60
Y=120
You are assuming that the angles mentioned in Statement 2 are not the right angles mentioned in Statement 1. parallel_chase already pointed this out, but ABC could be one of the right angles, making BCD 45 degrees, and the other two angles 90 and 135 degrees. Or, as you point out above, we could have a 60-120-90-90 quadrilateral. Since we don't know which case we have, the information is insufficient- E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by LSB » Mon Aug 25, 2008 2:11 am
Good point. Thanks Ian
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