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# Is the measure of one of the interior angles of quadrilatera

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Is the measure of one of the interior angles of quadrilatera  [#permalink]

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01 Nov 2009, 13:08
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95% (hard)

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36% (01:41) correct 64% (01:50) wrong based on 653 sessions

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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

(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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01 Nov 2009, 13:19
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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?
(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.

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)
(1) Angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.
(2) <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120 Not sufficient.

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01 Nov 2009, 13:42
Thanks, seems like a very easy prob.
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17 Jun 2010, 02:15
The trick here is to note that x can be either 60 or 45 degrees.
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17 Aug 2010, 10:29
I think this question tests the ability to identify a quadrliateral different than regular quadrilaterals.

Need to make sure that you don't get caught using a regular quadrilateral...
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14 Dec 2010, 07:14
amazing i got trap by chosing C. You all are great, gmat prep has a lot of traps so i will be more careful
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06 Nov 2011, 21:15
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 90 degrees
2) The degree measure of angle ABC is twice the degree measure of angle BCD

1. Insufficient

2. Insufficient

1+2
We don't know whether the sum of BCD & ABC equals 180.
Hence the combination of the two statements can't necessarily give the value of the angle.
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09 Nov 2011, 05:58
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 90 degrees
2) The degree measure of angle ABC is twice the degree measure of angle BCD

The diagram shows you two cases using both the statements. In one case, you have a 60 degree angle, in the other case, you don't. Hence both statements together are insufficient.

Attachment:

Ques4.jpg [ 6.16 KiB | Viewed 8971 times ]

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Re: Is the measure of one of the interior angles of  [#permalink]

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10 Nov 2011, 02:04
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in statement 1 it has been told us that two of the interior angles are of 180 hence substract 360-180=180 now reaching to second statement. One of the angle is twice the another. in that case i would go with formula
x+2x=180 or 3x=180 hence x=60.

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Re: Is the measure of one of the interior angles of  [#permalink]

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10 Nov 2011, 02:20
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ankit123suhane wrote:
in statement 1 it has been told us that two of the interior angles are of 180 hence substract 360-180=180 now reaching to second statement. One of the angle is twice the another. in that case i would go with formula
x+2x=180 or 3x=180 hence x=60.

It is not given that the angle which is twice another angle is not 90. When you say x + 2x is 180, you are assuming that 2x is not one of the 90 degree angles. It is possible that the angles are 90, 90, 45 and 135 (look at the diagram above)
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06 Jan 2012, 18:50
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1. 2 right angles. Others could be any degree measure. Insuff.
2. ABC = 2 BCD. Nothing conclusive here, we can have 60-120. 45-90....

Together, 2 right, so other two could be 60-120 OR we can have 45-90-90-135. Insuff.

E
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Re: Is the measure of one of the interior angles of quadrilatera  [#permalink]

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10 Mar 2012, 00:24
Another problem you can get without putting pen to paper! (I so like these!)
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Re: Is the measure of one of the interior angles of quadrilatera  [#permalink]

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20 Jun 2014, 04:22
Bunuel wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?
(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.

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)
(1) Angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.
(2) <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120 Not sufficient.

And I spent 1 min 33 sec to make diagrams, evaluate the possibilities and solve the problem!
Gosh, your approach seems so simple...
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Re: Is the measure of one of the interior angles of quadrilatera  [#permalink]

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29 Aug 2016, 13:54
kt00381n wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

(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.

This question is similar to in-the-figure-above-what-is-the-perimeter-of-rectangle-abpq-2821.html in that both are from GMAT Prep and both use the same trap. Check it out! And if you fell for this Q please don't fall for the question in the link. I fell for both
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Re: Is the measure of one of the interior angles of quadrilatera  [#permalink]

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30 Oct 2018, 04:50
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Re: Is the measure of one of the interior angles of quadrilatera   [#permalink] 30 Oct 2018, 04:50
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