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# In triangle ABC, point X is the midpoint of side AC and

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Senior Manager
Joined: 25 Jun 2009
Posts: 286

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In triangle ABC, point X is the midpoint of side AC and [#permalink]

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19 Jan 2010, 22:04
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45% (medium)

Question Stats:

68% (01:12) correct 32% (03:05) wrong based on 75 sessions

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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: in-triangle-abc-point-x-is-the-midpoint-of-side-ac-and-82671.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Jul 2013, 02:29, edited 1 time in total.
Edited the question and added the OA

Kudos [?]: 232 [0], given: 4

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2754

Kudos [?]: 1923 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: OG #12 Problem 109 [#permalink]

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19 Jan 2010, 22:27
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.

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Kudos [?]: 1923 [0], given: 235

Senior Manager
Joined: 25 Jun 2009
Posts: 286

Kudos [?]: 232 [0], given: 4

Re: OG #12 Problem 109 [#permalink]

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19 Jan 2010, 22:57
You are correct. The official answer is A.

Kudos [?]: 232 [0], given: 4

Senior Manager
Joined: 25 Jun 2009
Posts: 286

Kudos [?]: 232 [0], given: 4

Re: OG #12 Problem 109 [#permalink]

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19 Jan 2010, 23:05
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.

Kudos [?]: 232 [0], given: 4

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2754

Kudos [?]: 1923 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: OG #12 Problem 109 [#permalink]

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19 Jan 2010, 23:13
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.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

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Kudos [?]: 1923 [0], given: 235

Senior Manager
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Kudos [?]: 248 [0], given: 87

Re: OG #12 Problem 109 [#permalink]

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02 Jul 2011, 22:41
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?

Kudos [?]: 248 [0], given: 87

Re: OG #12 Problem 109   [#permalink] 02 Jul 2011, 22:41
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