DS prep

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bww: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sun Apr 29, 2007 6:25 am; Location: MA; Thanked: 1 times

by bww » Sun May 13, 2007 3:42 pm

sorry for the fuzzy display. please help...OA is A.

from 1) i see that all the segments correspond with each other. BQ=CR=DS=AP, thus QC=RD=AS=BP because all sides of the square are equal. but knowing that, how do we know that these line segments QS and PR are equal?

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Source: Beat The GMAT — Data Sufficiency | Sun May 13, 2007 3:42 pm

gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

Re: DS prep

by gabriel » Mon May 14, 2007 11:06 am

bww wrote:sorry for the fuzzy display. please help...OA is A.

from 1) i see that all the segments correspond with each other. BQ=CR=DS=AP, thus QC=RD=AS=BP because all sides of the square are equal. but knowing that, how do we know that these line segments QS and PR are equal?

.. bcoz if they werent equal they wuldnt have made equal intercepts on the oppsite sides .. that is they wuldnt have divided the sides in equal ratios ... and this true only bcoz the figure is a square ..

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Wed May 16, 2007 11:51 pm

Since BQ=CR=SD=AP; it’s clear that QC=RD=SA=BP
This also proves that QR=RS=PS=QP (they all represent the hypotenuse of 4 triangles)
All the four triangles would be congruent Triangle CQR, RSD, PAS and PBQ…Hence all angles and sides of PQRS will be equal…thus it becomes a square….hence PR = QS

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