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OG 12190 DS

by kullayappayenugula » Sat Jun 16, 2012 9:39 pm
OG 12 109. In triangle ABC,pointX 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 ?
the units digit of m ?
(1)The area of triangular region ABX is 32.
(2)The length of one of the altitudes of triangle ABC is 8

I was not sure how to approach this question. it was bit difficult since the Diagram was not given. Can somebody let me know any precautions or how GMAC expects us to dram figure..notions etc..
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Source: — Data Sufficiency |
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by gmat_and_me » Sat Jun 16, 2012 10:30 pm
Statement 1 alone should be sufficient here, if I'm right. ABC
similar to XYC similar to RSC. Since they are similar, area of
RSC should be 1/16-th of area of ABC (how ? For triangle XYC,
XY = 1/2 AB (similar triangles, CX = 1/2 AC, CY = 1/2 BC).
Similarly, height of XYC = 1/2 height of ABC. So area = 1/4 ABC.
Apply the same logic to triangle RSC too..). So, what is area of ABC ?

1) says that area of ABX is 32. Since X is the midpoint of AC,
area of ABX will be 1/2 of ABC (because, area = 1/2 * base *
height => 1/2 (1/2 AC) * height of ABC, since height remains the
same for both ABC and ABX. For this, please assume that base is
AC). So area of ABC is 64 and hence we can find area of RSC.

2) not sufficient. We need length of base also to calculate the
area of ABC.

HTH
kullayappayenugula wrote:OG 12 109. In triangle ABC,pointX 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 ?
the units digit of m ?
(1)The area of triangular region ABX is 32.
(2)The length of one of the altitudes of triangle ABC is 8

I was not sure how to approach this question. it was bit difficult since the Diagram was not given. Can somebody let me know any precautions or how GMAC expects us to dram figure..notions etc..
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by GMATGuruNY » Sun Jun 17, 2012 2:56 am
I posted a solution (along with a drawing) here:

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