A difficult problem

ashwin_gowda · Posted: Thu Jun 07, 2007 7:54 am Post subject: A difficult problem

http://www.manhattangmat.com/gmat-prep-global-home.cfm

thumpin_termis · Posted: Thu Jun 07, 2007 8:27 am Post subject:

First,
Angle ADB = 180 - Angle ADC = 180 - 60 = 120

Angle ADB is an exterior angle of triangle ABD, which means it is the sum of two non-adjacent angles. This means:
Angle ADB = Angle CDA + Angle CAD. so,
120 = 60 + Angle CAD => Angle CAD = 120 - 60 = 60

So finally,
x = 180 - Angle CDA - Angle CAD = 180 - 60 - 60 = 60

Answer choice B:

Anyone see it differently?

tejpreet · Posted: Fri Jun 08, 2007 2:17 am Post subject: My Answer is 90 degree

E

Angle ADB + Angle ADC =180
==> Angle ADB = 180 - Angle ADC
= 180 - 60
= 120

Angle BAD = 180 - 120 - 45
= 180 -165
= 15

Angle DAC = 30
As side opposite Angle BAD which is BD is 1 unit and Side opposite Angle DAC which is DC is 2 units so the respective angle DAC is twice of Angle BAD and hence it is equal to 30 degrees

Angle ACD = Angle x = 180- 60 - 30
= 90

800GMAT · Posted: Fri Jun 08, 2007 3:24 am Post subject:

I agree with x=90

thumpin_termis · Posted: Fri Jun 08, 2007 8:13 am Post subject:

Yup. I take my answer back - I see where I made the mistake (Angle ADB is not CDA + CAD; rather, it shoud've been ACD + CAD, which doesn't help it to get the answer)

jayhawk2001 · Posted: Fri Jun 08, 2007 4:22 pm Post subject: Re: My Answer is 90 degree

800GMAT · Posted: Fri Jun 08, 2007 7:04 pm Post subject:

jayhawk, u can apply the angle bisector property only when a line bisects an angle..

How did u assume that the angles originating from A are equal or in other words, how did u assume that the line originating from A bisects A.........can u pls explain how did u arrive at the above conclusion...thnkx

jayhawk2001 · Posted: Fri Jun 08, 2007 8:36 pm Post subject:

800GMAT · Posted: Sat Jun 09, 2007 5:16 pm Post subject:

jayhawk,,u r right...
we cannot assume that the angles will be in the ratio of 2:1 if the line is divided in the ratio of 2:1.

so answer cannot be 90 based on this approach
I too am unable to find an approach to solve this problem

ashwin_gowda · Posted: Mon Jun 11, 2007 2:43 am Post subject: solution to the Difficult Problem

Hi All the solution to the problem is available @ this link.

http://www.manhattangmat.com/ChallProbLastWk.cfm

jayhawk2001 · Posted: Mon Jun 11, 2007 6:57 am Post subject:

Interesting solution.

800GMAT · Posted: Mon Jun 11, 2007 11:29 am Post subject:

Thanks a lot for posting the solution.....

I agree...pretty interesting...