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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In triangle ABC, point X is the midpoint of side AC and poin ##### This topic has 1 expert reply and 0 member replies ### Top Member ## In triangle ABC, point X is the midpoint of side AC and poin ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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. OA A Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: 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. Triangles RCS and ABC: Side RC = 1/4(AC). Side SC = 1/4(BC). The two triangles share angle BCA. Triangles with a shared angle (BCA) formed by corresponding sides in the same proportion (RC:AC = 1:4, SC:BC = 1:4) are SIMILAR. Thus, triangle RCS is similar to triangle ABC. In similar triangles, corresponding bases and heights are in the same proportion as corresponding sides. Thus, the base of triangle RCS is 1/4 the base of triangle ABC, and the height of triangle RCS is 1/4 the height of triangle ABC. Area of triangle ABC = (1/2)bh. Area of triangle RCS = (1/2)*1/4(b)*1/4(h) = (1/16)(1/2)bh. Thus, the area of triangle RCS is 1/16 the area of triangle ABC. Question rephrased: What is the area of triangle ABC? Statement 1: ABX = 32. In triangle ABX, AX = 1/2(AC). In other words, the base of triangle ABX is 1/2 the base of triangle ABC. Triangles ABX and ABC share height BZ. Since AX = 1/2(AC), and the two triangles have the same height, ABX = 1/2(ABC). Thus, the area of triangle ABC = 64, and the area of triangle RCS = (1/16)(64) = 4. SUFFICIENT. Statement 2: height = 8. No way to determine the area of triangle ABC or of triangle RCS. INSUFFICIENT. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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