ManHattan Problem

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kakz: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Sep 13, 2011 1:02 am; Thanked: 2 times

by kakz » Tue Nov 15, 2011 2:51 am

Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?

(1) BC is parallel to AD.
(2) Diagonal AC, which lies inside the quadrilateral, has length 10âˆš3.

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Source: Beat The GMAT — Problem Solving | Tue Nov 15, 2011 2:51 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Nov 15, 2011 3:32 am

Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?

(1) BC is parallel to AD.

The resulting quadrilateral ABCD can be a sqaure or a rhombus or an Isosceles Trapezoid (refer attachment).So, it is not possible to find the area without knowing the angle between the sides or without knowing the shape and type of the quadrilateral.

Insufficient !

(2) Diagonal AC, which lies inside the quadrilateral, has length 10âˆš3.

Again insufficient, because it doesn't give any information about the length of side AD or information regarding the shape of the quadrilateral!

From 1 and 2

If the quadrilateral is a Rhombus then the area = 100
If the quadrilateral is an Isosceles Trapezoid = 100 + x (need not to calculate)
Note: The quadrilateral can not be a square

Two different values! IMO Option E

Correct me if I am wrong!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Nov 15, 2011 1:11 pm

kakz wrote:Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?

(1) BC is parallel to AD.
(2) Diagonal AC, which lies inside the quadrilateral, has length 10âˆš3.

Don't calculate. DRAW.
The following figures -- each with a different area -- satisfy both statements:

The correct answer is E.

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