• Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Need to understand the logic please

This topic has 2 expert replies and 3 member replies
shibsriz@gmail.com Master | Next Rank: 500 Posts Default Avatar
Joined
19 Sep 2012
Posted:
429 messages
Followed by:
4 members
Thanked:
6 times

Need to understand the logic please

Post Wed Jun 05, 2013 4:03 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In triangle ABC, point Xis the midpoint of sideAC and
    point Yis the midpoint of side BC. If point Ris the
    midpoint of line segment XC and if point S is the
    midpoint of line segment YC, what is the area of
    triangular region RCS1
    (1) The area of triangular region ABX is 32.
    (2) The length of one of the altitudes of triangle ABC
    is 8

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

    GMAT/MBA Expert

    Post Wed Jun 05, 2013 2:52 pm
    I tried to illustrate this (picture attached), but here's the basic logic:

    If a line runs through the midpoints of two sides of a triangle, that line is PARALLEL to the third side of the triangle. So XY is parallel to AB, and RS is parallel to XY.

    Since AB, XY, and RS are parallel to one another, they make the same angles where they meet sides AC and BC, respectively, so we have three similar triangles: ABC, XYC, and RSC. Since RC = 1/4 AC and SC = 1/4 BC, all the dimensions of RSC are 1/4 the respective dimensions of ABC, including the base and height. So if the area of ABC is bh/2, the area of RSC is ((b/4)(h/4))/2, or bh/32, and all we need to solve the problem is the area of ABC.

    S1 tells us ABX has an area of 32. From this we can get the area of ABC - SUFFICIENT.
    S2 gives us an altitude of ABC, but not the length of its corresponding base. We aren't able to get the area of ABC - INSUFFICIENT.





    (Problems requiring an understanding of midsegments are uncommon on the GMAT, so I wouldn't sweat this one too much. For more practice on this, check out this link:
    http://www.regentsprep.org/Regents/math/geometry/GP10/MidLineL.htm)

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
    Post Thu Jun 06, 2013 3:19 am
    Quote:
    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
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    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.
    shibsriz@gmail.com Master | Next Rank: 500 Posts Default Avatar
    Joined
    19 Sep 2012
    Posted:
    429 messages
    Followed by:
    4 members
    Thanked:
    6 times
    Post Fri Jun 07, 2013 7:15 am
    Hey Mitch, what I dont understand is that how u got the altitude BZ, i.e ABZ is a rigth angle triangle!

    Thanks
    Shiba

    GaneshMalkar Senior | Next Rank: 100 Posts Default Avatar
    Joined
    31 Jul 2012
    Posted:
    77 messages
    Followed by:
    1 members
    Thanked:
    8 times
    Target GMAT Score:
    800
    Post Sun Jun 09, 2013 5:32 am
    shibsriz@gmail.com wrote:
    Hey Mitch, what I dont understand is that how u got the altitude BZ, i.e ABZ is a rigth angle triangle!

    Thanks
    Shiba
    BZ is the perpendicular drop from the point B to the extended base AC which is the height or altitude of triangle ABC.

    _________________
    If you cant explain it simply you dont understand it well enough!!!
    - Genius

    Nina1987 Senior | Next Rank: 100 Posts Default Avatar
    Joined
    15 Dec 2015
    Posted:
    79 messages
    Followed by:
    1 members
    GMAT Score:
    750
    Post Sat Feb 13, 2016 6:01 am
    The question is testing properties of similar triangles here. There 3 ways to tell if the triangles are similar:

    1. AAA (angle angle angle)
    All three pairs of corresponding angles are the same.
    (We actually need two angles really:)

    2. SSS in same proportion (side side side)
    All three pairs of corresponding sides are in the same proportion

    3. SAS (side angle side)
    Two pairs of sides in the same proportion and the included angle equal.

    It is this 3rd property that is quite handy here. Two triangles ABC and RSC are similar since RC/AC=SC/BC=1/4 and they include the same angle THETA (as shown in the figure)

    1) Tells us that Area(ABX) =32. Since height of triangle ABC is same that of triangle ABX and the base is twice, area (ABC) = 32*2= 64. Since ABC and RSC are similar and their sides are in the ration of 1:4 their ares will be in the ration of 1:16. Sufficient to solve.
    2) Tells us one of the altitudes is 8. Since it does not tell which one, insufficient!

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 ardz24 40 topics
    5 LUANDATO 32 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    141 posts
    2 image description EconomistGMATTutor

    The Economist GMAT Tutor

    107 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    106 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    104 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts