Quantitative Review Official Guide Question 117 DS

[jaredroc]

I'm unsure how in this geometry problem we can assume that the ratio between angle BDC and BAD is 2:1. I understand that the sum of angles BAD & ABD equal BDC but how can we assume that angle BAD is equal to X and thus ABD is also equal to X?

[StaceyKoprince]

Please post the complete text of the problem, including the answer choices. Thanks!

[Guest]

Oh sorry.

In triangle ABC above, what is the length of side BC?

1) Line segment AD has length 6.
2) X = 36

[JAREDDROC]

[dbernst]

Jared,

This is a difficult problem, but also an excellent example of how the GMAT intentionally tries to "push" you toward an incorrect response.

With Geometry, the first step is to recreate the diagram on your scratch board and then label the figure with the provided information. Next, we must utilize our knowledge of geometric rules to infer any additional information that is mathematically provable, and label this information as well.

In the figure provided, BD = BC because their corresponding angles are congruent. This is the obvious step. Now, let's more closely consider triangle ABD. Angle ADB + 2x = 180, since together these angles form a striaght line. Additionally, angles x + ADB + ABD = 180, since together these angles form a triangle. By setting the two equations equal, we know

ADB + 2x = ADB + x + ABD. Subtract ADB from both sides, and we have

x + x = x + ABD. Subtract x from both sides, and we have x = ABD.

Thus, triangle ABD is also isosceles, with side AD = side BD.

Since AD = BD = BC, our rephrased question becomes What is AD?
Now, let's look at the statements:

Statement 1: AD = 6. As this answers our rephrased question, it is SUFFICIENT to solve BC.

Statement 2: x = 36. As this gives us no side lengths, it is INSUFFICIENT to solve BC.

The correct answer is A.

Oh, by the way, the "trap" answer is C. It is relatively obvious that, with the measure of x AND the length of AD, the length of BC can be determined. Thus, it is unlikely that C would ever be the answer to this question. GMAT logic!

-dan

[jaredroc]

Thanks Dan. However I am still confused how we can assume that angle DAB has a 1:2 relationship w/ BDC (i.e BAD = X). The problem does not provide that relationship. There is a smudge on the picture I uploaded. The official question does not provide anything for angle DAB. I don't see how we can assume that angle BAD is equal to X and then therefore ABD is also equal to X.

Thank You!

[RonPurewal]

The official question does not provide anything for angle DAB.

I just went and looked at it, and, on both the question and the answer key, angle DAB is plainly labeled x degrees. If you have a smudge on the question, then look at the version in the answer key (and vice versa). HTH

[jaredroc]

Okay thanks. One more question. If angle DAB was not labled as X, could this problem still be solved?

[StaceyKoprince]

There's actually a typo in OG 11 on this question for some earlier printings of the book - the original question in some books does not show the angle properly labeled as x (it's just left blank), although the diagram in the explanation does label it x. They fixed it in later printings.

If you didn't know that angle was x then, no, you wouldn't have sufficient info to solve.

[jaredroc]

THANK YOU VERY MUCH!!!!

:lol:

[StaceyKoprince]

no problem!