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OG DS-Triangle Question

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by aaggar7 » Thu Mar 14, 2013 11:42 pm
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
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Source: — Data Sufficiency |
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by neha24 » Thu Mar 14, 2013 11:52 pm
my take A . the area of the required triangle wud come out to be 4 units
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by aaggar7 » Fri Mar 15, 2013 1:35 am
Hi Neha,

Thanks !The correct answer is A.Please explain how you tackled this question.
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by Anju@Gurome » Fri Mar 15, 2013 1:59 am
Refer to the diagram below,
Image

As, X is the midpoint of AC and Y is the midpoint of BC, XY = AB/2
Also, the height of the triangle ABC with respect to base AB will be twice the height of the triangle XYC with respect to base XY. [Try to prove this yourself using the concepts of similarity of triangles]

Hence, area of triangle ABC = 4*(area of triangle XYC)

Similarly, area of triangle XYC = 4*(area of triangle RSC)

Hence, area of triangle RSC = (area of triangle ABC)/16

So, if we can know the area of ABC, we can determine the area of RSC.

Statement 1: Clearly sufficient.

Statement 2: As we don't the length of the base of triangle ABC, the area of ABC can have different values.

Not sufficient

The correct answer is A.
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by GMATGuruNY » Fri Mar 15, 2013 5:14 am
Check my post here, which explains a useful a concept regarding statement 1:

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