Tricky DS geometry question

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kiton: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed May 18, 2011 10:43 am; Location: Saint-Petersburg, Russia; GMAT Score:560

by kiton » Wed Jul 20, 2011 4:03 am

Hello, everybody! Here is an interesting question.

If CD = 6, what is the length of BC?

(1) BD = 6*r3

(2) x = 60

Source: Magoosh GMAT

Will post the OA later.

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Source: Beat The GMAT — Data Sufficiency | Wed Jul 20, 2011 4:03 am

bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Wed Jul 20, 2011 7:18 am

Draw a perpendicular from point b onto the extended line segment DC. statement one tells us that this triangle formed is a 30-60-90. We r given the length of the hypotenuse 6 root 3.
Thus the base is 9. Also we get the new small right triangle with one perpendicular as 3 root 3(applying 30-60-90 formula to the larger triangle) and the base as 3. Thus this is another 30-60-90 and the length of its hypotenuse bc is 6.

Correct answer is A.

statement 2 is pretty bland without any relevant legnths given. We cant locate the location of point C correctly.

30-60-90 shortcut :

smaller side = 1/2 * hypotenuse
larger side = 1/2 * hypotenuse * root3

Cheers !!

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kiton: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed May 18, 2011 10:43 am; Location: Saint-Petersburg, Russia; GMAT Score:560

by kiton » Wed Jul 20, 2011 7:38 am

(2) works here easy. It is sufficient. I was having problems with (1).

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Wed Jul 20, 2011 7:58 am

kiton wrote:(2) works here easy. It is sufficient. I was having problems with (1).

did i solve ur problem; or I added something to it ?

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kiton: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed May 18, 2011 10:43 am; Location: Saint-Petersburg, Russia; GMAT Score:560

by kiton » Wed Jul 20, 2011 9:14 am

First of all, thank you for your comment ( i was a bit busy and did not have a chance to write a proper reply).

Yes, you definitely have clarified the problem (statement 1) to me.

Secondly, please, notice, that the second statement is also sufficient. The OA is D.

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Thu Jul 21, 2011 12:46 am

wow this was tough, I think the second statement actually follows from reversing the calculation that I have shown.

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