geometry ds

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resilient: Legendary Member; Posts: 789; Joined: Sun May 06, 2007 1:25 amFollowed by: 6 members; Location: Southern California, USA; Thanked: 15 times

by resilient » Wed Mar 05, 2008 3:54 pm

quadrilateral pqrs has pq parallel RS and QR parallel PS. What is area of PQRS?

1. the coordinates of point pq are (2,0) and coordinates of Point R (8,2).

2. Coordinates of point S are (6,0).

qa is c. I am convinced that A is solution..

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Source: Beat The GMAT — Data Sufficiency | Wed Mar 05, 2008 3:54 pm

xilef: Master | Next Rank: 500 Posts; Posts: 111; Joined: Thu Jan 31, 2008 4:05 pmFollowed by: 1 member; Thanked: 18 times

by xilef » Wed Mar 05, 2008 4:59 pm

In A you said point PQ, I'll assume you meant P.

I think you are assuming that quadrilateral has all right angles. Here you have a quadrilateral that is also a parallelogram. It can look something like the diagram below. And even knowing P and R, you still need Q or S.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: geometry ds

by Stuart@KaplanGMAT » Wed Mar 05, 2008 5:24 pm

Enginpasa1 wrote:quadrilateral pqrs has pq parallel RS and QR parallel PS. What is area of PQRS?

1. the coordinates of point pq are (2,0) and coordinates of Point R (8,2).

2. Coordinates of point S are (6,0).

qa is c. I am convinced that A is solution..

Since PQRS has two parallel sides, we know that it's a parallelogram. The area of a parallelogram is base * height, so that's what we need to know.

(1) P is at (2,0) and R is at (8,2)

An infinite number of parallelograms can be drawn with just two points. We could have a rectangle with points Q (2,2) and S (8,0). We could also have a paralellogram with points Q (7,2) and S (3,0). Each of these shapes could have a different area: insufficient.

(2) S is at (6,0).

Well, if two points aren't enough, 1 point certainly isn't.

Together: with 3 of the points known, the 4th point becomes fixed (in this case it would be (4,2)): sufficient.

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hemanth28: Master | Next Rank: 500 Posts; Posts: 157; Joined: Tue Dec 04, 2007 9:05 am; Thanked: 9 times; GMAT Score:680

by hemanth28 » Wed Mar 05, 2008 7:54 pm

Enginpasa1,

you are assuming that the quadrilateral is parallel to the x and y axis.Then only your answer is right.
However its not mentioned anywhere.

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