triangle question

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Dec 20, 2010 2:35 am

In triangle ABC, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?

A. 2/3
B. 2/9
C. 4/5
D. 4/9
E. 5/9

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Source: Beat The GMAT — Problem Solving | Mon Dec 20, 2010 2:35 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Dec 20, 2010 2:53 am

Refer to the figure above,
Area of ABC = (1/2)*BC*AE
Area of AMN = (1/2)*MN*AD

As, AM/AB = 2/3 and MN parallel to BC,

1. MN/BC = 2/3
2. AD/AE = 2/3

Required ratio = (MN*AD)/(BC*AE) = (MN/BC)*(AD/AE) = (2/3)*(2/3) = 4/9

The correct answer is D.

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minar: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Tue Oct 19, 2010 1:08 am; Thanked: 1 times

by minar » Mon Dec 20, 2010 7:45 am

Rahul@gurome,
Your replies are always easy to understand. Thanks for that...

I have a quick question on the PS.

What about if I consider ABC and AMN both to be equilateral triangle?
If I do so, I get the same answer (D).
Is my approach wrong?

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GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Dec 20, 2010 7:59 am

minar wrote:Rahul@gurome,
Your replies are always easy to understand. Thanks for that...

I'm glad to know that.

minar wrote:What about if I consider ABC and AMN both to be equilateral triangle?
If I do so, I get the same answer (D).
Is my approach wrong?

For this particular problem the logic is fine and it'll not cause any problem. But always try not to choose any special case. That can mislead you.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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