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DS quesiton . please help

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by silvia928 » Mon May 26, 2008 10:54 pm
In triangle ABC, point X is the midpoint of 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

Ans. (A)

Thanks !!
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Source: — Data Sufficiency |
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by amitansu » Tue May 27, 2008 12:34 am
This is based on geometry principle that says median divides a triangle in to two halves.

When you try dividing the ABC triangle , eventually would get the area of triangle RCS.If you solve the ans would be 4.

So ans is A.

Stem 2 doesn't give any info to find out this.Insufficient.
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by shiraj » Wed May 28, 2008 1:35 am
From geometry we know that a median divides a triangle in to two halves.

(1) Area of Triangle ABX = 32 means that area of triangle BCX is also 32
Now XY is a median, so area of Triangle CXY = 16

Again RY is a median, so area of triangle RYC = 8

Again RS is a median, so area of triangle RCS = 4

So this condition is sufficient. So correct answer option can be A, D

(2) It does not provide you the area of Triangle ABC in numerical values.

Hence, answer A
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