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In triangle ABC, point X is the midpoint of side AC and https://gmatclub.com/forum/intriangleabcpointxisthemidpointofsideacand89433.html 
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Author:  burnttwinky [ 19 Jan 2010, 21:04 ] 
Post subject:  In triangle ABC, point X is the midpoint of side AC and 
In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ? (1) The area of triangular region ABX is 32. (2) The length of one of the altitudes of triangle ABC is 8. OPEN DISCUSSION OF THIS QUESTION IS HERE: intriangleabcpointxisthemidpointofsideacand82671.html 
Author:  gurpreetsingh [ 19 Jan 2010, 21:27 ]  
Post subject:  Re: OG #12 Problem 109  
IMO ans should be A. Area of triangle ABX = area of BXC as median divides the triangle into 2 equal areas. similarly area of XYC = 1/2 BXC = ( 1/2 ABX) = 1/2 * 32 = 16 Now XYC and RSC are similar triangles Since we have area of XYC , we can find the area of triangle RSC. Thus statement 1 is sufficient. Statement 2 seems not sufficient, not enough parameters given. ANS  A.. OA please.

Author:  burnttwinky [ 19 Jan 2010, 21:57 ] 
Post subject:  Re: OG #12 Problem 109 
You are correct. The official answer is A. 
Author:  burnttwinky [ 19 Jan 2010, 22:05 ] 
Post subject:  Re: OG #12 Problem 109 
Okay, I didn't see that. So, if you draw a line from the vertex of a triangle to the midpoint of an opposite line, does that automatically split the triangle into two smaller equal triangles? If so, the problem makes a lot more sense. Thanks for the explanation. 
Author:  gurpreetsingh [ 19 Jan 2010, 22:13 ] 
Post subject:  Re: OG #12 Problem 109 
Yes the line joining mid point and opp vertex divides it into 2 triangles having equal area. Area of triangle = 1/2 base * height since height remains the same and base is divided into 2 equal parts...thus areas are also divided into 2 equal parts.. Letme know if u got the concept else I will elaborate it. 
Author:  siddhans [ 02 Jul 2011, 21:41 ] 
Post subject:  Re: OG #12 Problem 109 
I had one question though . Since Area of Traingle ABX = Area of Trianglr BXC Will Area of triangle XYC = 1/2 Area of triangle ABC? i.e Area of triangle XYC = 1/2 *64 = 32? and will Area of triangle RCS = 1/4 (Area of triangle ABC)???? therefore, Area of triangle RCS = 1/4 *64 = 16??? Is this correct? Can someone please verify if what I have done is correct? 
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