OG Quant Supp #117

Question

Can someone help explain this problem?

GMATT73 · Answer

Never knew the rule either, but the degree measure of the exterior angle of a triangle is equal to the sum of the remote interior angles. Therefore AD and BC have the same length, 6.

(A)

Expect a problem of this level to be the first or second question you see on the actual exam.

kidderek · Answer

I'm sorry, can you go step by step, please. I understand that angle DAB + angle ABD = 2x. Then what is the next step? The OA explanation names angle ABD as y and angle DAB as x, hence x+y=2x. But isn't that just an assumption that angle DAB=x? Accordingly, isn't it just an assumption that triangle ABD=isosceles. Couldn't angle DAB=.5x and angle ABD=1.5x?

ps_dahiya · Answer

You are absolutely correct. I think there is a typo in the book or we are missing a key concept. :roll:

sangarelli · Answer

I think the answer is (C).cant be (A) for sure

Mikhail Bondarenko · Answer

I guess it's C clearly neither is suficient on its own. However combining the two statement we get: 1. DC = BD, angle DBC = 180-72-72 = 36 ADB = 180-72 (thru exterior angle/complementary angles) = 108 DAB+DBA = 72 (exterior angle) 2. Now, let BC=BD= x. on to the law of cosines https://en.wikipedia.org/wiki/Cosine_law 1. CD^2 = x^2 + x^2 - 2*x*x*cos36 2. 6 = x^2 + AB^2 -2*x*AB*cosABD 3. AB = x^2 + (6+CD)^2 - 2x(6+CD)*cos72 plus according to law of sines: https://en.wikipedia.org/wiki/Law_of_sines sin (ABD)/AD = Sin (DAB)/BD, or sin (ABD) / 6 = sin (180-108-ABD)/x 4. sin(ABD)*x = 6 sin(72-ABD) we have 4 equations in 4 unknowns: CD (will then substitute it in 3), x - expressed as sin ABD in 4; sin(72-ABD) can be reprsented as sum of the two; AB; and cos ABD that can be expressed thru sinABD (sqrt (1-sin^ABD) so finally by substituting 1 and 4 in 2 and 3, we will have 2 equations in two unknowns AB and sinABD That system is potentially solvable (don't ask me to!). Once it's solved, x can be determined. I know it sounds complicated (and takes a lot more that 1:45..) but anyway.

iced_tea · Answer

there is a typo in this problem - missing info actually in OG

the correct version is there in MGMAT geometry (in DS rephrasing section)
and the missing info is: 
angle BAD is marked x degrees.

ak_idc · Answer

yeah..only with this "BAD is x degrees" information we can solve the problem. Otherwise, I think the answer is E.

mbafall2011 · Answer

Knowing x=36 degrees, the answer should be D but the GMAT prep showed the answer as A.

hence i assume they dont expect us to use/know the law of cosines?

Bunuel · Answer

Discussed here: in-triangle-abc-106669.html Some OG books (just like the image in the initial post) have a typo missing the info that trig2uc8.png In triangle ABC above, what is the length of side BC? As AD=BD=BC . Question: BC=? (1) Line segment AD has length 6 --> AD=BD=BC=6. Sufficient. (2) x = 36 --> we know only angles which is insufficient to get the length of any line segment. Answer: A.

mbafall2011 · Answer

Bunuel if x - 36 degrees, 2x will be 72 degrees, and we would know 2 angles of the triangle and hence we can derive the third angle. Knowing three angles we could use Law of cosines to get the three sides. Here is a question from the challenge which is similar to the point im trying to make. ds-angle-formed-by-diagonal-in-rectangle-57397.html#p884841

fluke · Answer

True. The idea of finding BC just by statement 2 was too fantastic for me. Thanks for clarification. I don't suppose any law of mathematics can find a definitive value for BC just by knowing the angles 70,70,40 because we can make infinite number of triangles with same angle dimensions and varying BC.

Bunuel · Answer

You are wrong. Knowing the angles of a triangle is not enough to get the sides as you can have infinitely many similar triangles withe same angles and different sides.

mbafall2011 · Answer

Sorry! thanks for correcting me. I had sides and angles switched. Effect of being up from 4:30am. By the way, could you comment on the other thread if the gmat expects you to know Law of cosines.

Bunuel · Answer

Again:  every GMAT geometry question can be answered without trigonometry .

OG Quant Supp #117

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