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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] New post 01 Nov 2009, 12:08
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40% (02:07) correct 60% (01:16) wrong based on 156 sessions
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.
[Reveal] Spoiler: OA

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Re: GMAT Prep 2 Quadrilateral [#permalink] New post 01 Nov 2009, 12:19
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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.

Answer: E.

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Re: GMAT Prep 2 Quadrilateral [#permalink] New post 01 Nov 2009, 12:42
Thanks, seems like a very easy prob. :oops:

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Re: GMAT Prep 2 Quadrilateral [#permalink] New post 17 Jun 2010, 01:15
The trick here is to note that x can be either 60 or 45 degrees.

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Re: GMAT Prep 2 Quadrilateral [#permalink] New post 17 Aug 2010, 09:29
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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Re: Geometry problem [#permalink] New post 14 Dec 2010, 06:14
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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Re: DS Question [#permalink] New post 06 Nov 2011, 20:15
SwapnilRanadive 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 90 degrees
2) The degree measure of angle ABC is twice the degree measure of angle BCD

Pls discuss answers.


What's your doubt?

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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Re: DS Question [#permalink] New post 09 Nov 2011, 04:58
Expert's post
SwapnilRanadive 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 90 degrees
2) The degree measure of angle ABC is twice the degree measure of angle BCD

Pls discuss answers.


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
Ques4.jpg [ 6.16 KiB | Viewed 3203 times ]

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Re: Is the measure of one of the interior angles of [#permalink] New post 10 Nov 2011, 01:04
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.

please clariy
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Re: Is the measure of one of the interior angles of [#permalink] New post 10 Nov 2011, 01:20
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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.

please clariy


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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Re: Is the measure of one of the interior angles of [#permalink] New post 16 Dec 2011, 23:16
Yep. Tricky one. Got tricked and fell for C. :(

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rr [#permalink] New post 06 Jan 2012, 17:50
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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 [#permalink] New post 29 Jan 2012, 23:55
Thanks for the material
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Re: Is the measure of one of the interior angles of quadrilatera [#permalink] New post 09 Mar 2012, 23:24
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] New post 20 Jun 2014, 03:20
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Re: Is the measure of one of the interior angles of quadrilatera [#permalink] New post 20 Jun 2014, 03:22
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.

Answer: E.


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] 20 Jun 2014, 03:22
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