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Can someone please address this question

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Can someone please address this question

by bpolley00 » Wed Jul 24, 2013 6:00 am
If AD is 6 square root 3, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Can someone explain why this isn't A? If you know that ABD is 60 degrees then you know that BD=6 and AB= 12. Therefore you know the entire left triangle. Now, Since AD= y square root 3 you know that ACD is 60 degrees as well as in any 30- 60- 90 triangle the angle that is directly across from square root 3 is always 60 degrees. Thus you would know DC is 6 and AC = 6 square root 2.
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by bpolley00 » Wed Jul 24, 2013 6:03 am
Too illustrate what I am saying take a look at this triangle. C has to have a degree of 60 degrees. The answer to this questions is definitively A, as simply knowing one side will tell you all the angles in the triangle. There is another question similar to this one somewhere where all they do is give you the adjacent number. Any number adjacent to 60 degrees is always X whereas the line directly across from an angle with 60 degrees is always x squareroot 3. You can google search 30 60 90 triangles to see this illustrated as well.
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by bpolley00 » Wed Jul 24, 2013 6:06 am
Actually, You don't need either 1 or 2 to answer this. You can simply answer it from the question stem ......
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by [email protected] » Wed Jul 24, 2013 11:28 am
Hi bp,

Right up front, you need to remember that a DS question will present you with an incomplete situation (you won't have enough info to answer the question with what you start off with; you'll need more info, which is why the Facts are presented underneath).

In DS questions, you should be suspicious of any drawings that you're given, since they're not necessarily to scale. In this case, the picture you've included certainly LOOKS LIKE an isosceles triangle, but we don't know if it actually is one.

The question asks for the area of the big triangle, so we'll need the base and the height. The question tells us the height is 6(root3).

Fact 1 tells us about the 60 degree angle, so we can figure out the area of the "left" triangle. However, we don't know about the "right" triangle. The angle in the corner is unknown. Just because the height is 6(root3) does NOT mean that the missing angle is 60 degrees. If we had the other side lengths, then we could make that deduction, but we don't have that info. Try drawing a picture in which the "right" triangle is "fatter" or "thinner" than the "left" triangle and you'll see that you don't know enough about it to answer the question. Fact 1 is INSUFFICIENT.

Fact 2 gives us the hypoteneuse of the "right" triangle, so we could use the Pythagorean Thm to figure out its area, but this doesn't tell us anything about the "left" triangle. We have the same problem as in Fact 1 (above). Fact 2 is INSUFFICIENT.

Combining facts, we'd have the area of the "left" triangle and the area of the "right" triangle, so we'd have the area of the entire big triangle.

Final Answer: C

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by bpolley00 » Wed Jul 24, 2013 11:39 am
Rich, I understand that is how DS questions typically go. It isn't an isosceles it is a 30 60 90 which is clearly indicated by the line AD being 6 square root 3

Fact 1- Yes it does. Look at every single 30 60 90 triangle. In fact, Google them all. Every single one of them the 60 degree angle is directly opposite of the X squareroot 3 in a 30 60 90. Just like the line adjacent (this is actually a GMAT question somewhere where they assume this) to 60 degrees is always X.
Fact 2- the same is true here. It has to be 60 degrees if it is a right triangle; which, based on the drawing you know that one side is 90 degrees so the other must be as well.

This question is just incorrect.
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by bpolley00 » Wed Jul 24, 2013 5:16 pm
Rich,

That last comment came off as pretty direct, my apologies,I was dead tired earlier. Does anyone else have any thoughts on what I am saying with this question? I think it has important implications for all triangle ds questions if I am correct. If anyone else wants to take a look at this that would be much appreciated! The source is a Manhattan test and it is a 700-800 level question.

-BP
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by [email protected] » Wed Jul 24, 2013 6:12 pm
Hi bp,

I think that you're letting your assumptions about one type of triangle influence how you're looking at this DS question. Here's an easy way to communicate the idea that I was attempting to explain:

1) Draw a right triangle
2) Label the "height" as 6(root3)
3) You have no other information, so leave everything else blank.

Now, looking at this picture, does that mean that the other 2 sides have to be 6 and 12? Really think about it. Does knowing just 1 side of a right triangle, and no other info, tell you what the other two sides are? Unfortunately, knowing just one side (without having the corresponding angle) doesn't tell us what the other sides (or the other angles) are.

It COULD BE a 30/60/90 right triangle, and then the other 2 sides would be 6 and 12.
However, it COULD BE a 45/45/90 right triangle and the other two sides would be 6(root3) and 6(root6).
It COULD ALSO BE any other possible right triangle, so the other two sides could be anything.

DS questions oftentimes test the thoroughness of your thinking. If you can't see the "other possibilities", then you're going to miss out on some points.

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by bpolley00 » Thu Jul 25, 2013 2:28 am
I get what you are saying. Thanks for the help

-BP
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by [email protected] » Thu Jul 25, 2013 7:47 pm
Hi BP,

I think that demonizing the GMAT doesn't serve any real purpose. The test is standardized and it's based on rules that you already know; these are both things that work in your favor. So, here's a factual point that might help you out, specifically on DS questions:

DS questions always have AT LEAST one answer. The real question is whether there's more than one or not. So, think about (and do some work to seek out) other answers. If you can find more than one answer, then you have to bubble a different answer choice.

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