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DS - quadrilateral properties

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susha0df: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Mar 19, 2013 3:03 am

by susha0df » Sat Mar 30, 2013 5:31 pm

Could someone explain the quadrilateral properties needed for solving this DS?

If ABCD is a quadrilateral, is AB=BC=CD=DA?
(1) AC is perpendicular to BD

(2) AB+CD=BC+AD

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Source: Beat The GMAT — Data Sufficiency | Sat Mar 30, 2013 5:31 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Sat Mar 30, 2013 9:33 pm

susha0df wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?

(1) AC is perpendicular to BD
(2) AB+CD=BC+AD

Statement 1: AC is perpendicular to BD.
As there is no restrictions on the lengths of the sides, they can be same or different.

Not sufficient

Statement 2: AB + CD = BC + AD
There can be various possible combinations of lengths satisfying this condition.

Not sufficient

1 & 2 Together: Choose AB = AD and CD = BC, then statement 2 satisfies and we can make AC perpendicular to BD (as shown in the figure below) but still lengths of all the sides are not same.

Same case for AB = BC and CD = AD.

Not sufficient.

The correct answer is E.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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