teal wrote:
Hello Mike,
How will SU help is determining the required measurement? Can you please explain?
Yes. This is a tricky thing about geometry DS problems. The basic idea is:
to get a length, you need to be given a length. That Big Idea #1 in this problem. When you understand the implications of that statement, it's pure gold. If all you are given is angular relationships, as this prompt gives us, then the figures could be any size. This is the basic geometry idea of
similarity. If you make scaled-up or scaled-down versions of any shape (square, pentagon, equilateral triangle, etc.), then all the absolute lengths are different, but both the angles and the ratio of the lengths are the same.
What this prompt gives us allows us to see that the figure consists of a 30-60-90 triangle and a 45-45-90 triangle, with hypotenuses of the same length. That means all the angles are determined, and all the ratios are determined, but we still don't know in absolute terms how big or small anything is. From the prompt alone, any length --- say SR --- could be 1 inch long or 1 mile long. It could be arbitrarily small or big.
When we are given the length of SU, that fixes one length, which has the consequence of fixing all the lengths. Now that we know one length, the figure cannot be arbitrarily big or small. It has to have exactly one size --- only one size of the shape will result in SU being exactly [2/sqrt(2) - 4] meters. So, knowing SU, we
could calculate all the other lengths.
Here's the other big idea ----
in DS, don't do unnecessary calculations. You are not actually be asked to find the numerical answer for the prompt question. All you are being asked to to figure out whether the statements provide information sufficient to answer the prompt question. That's Big Idea #2. Here's a blog about DS on the GMAT.
http://magoosh.com/gmat/2012/introducti ... fficiency/In geometry questions in particular, it's often the case that just one piece of information --- here, the length of SU --- is enough to determine everything. Actually doing that calculation, going through all the steps to figure out the difference (TV - RV) given that SU = [2/sqrt(2) - 4] ---- that would be a royal pain in the tuckus, and it is absolutely unnecessarily for answering this particular question.
If this were a PS problem --- given the prompt, and given SU = [2/sqrt(2) - 4], which of the following equals (TV - RV) --- that would be a 800+ level question, very difficult, because you would actually have to work through that solution. That is a highly unlikely question to see on the GMAT, unless you are getting absolutely everything else in the Quant section correct. By contrast, this question, the DS question in which you just have to judge whether it is sufficient or not, that's probably a 600 level question, not particular hard by GMAT standards. You really need to see how to use these geometric shortcuts to your advantage on the DS section.
Here's a blog that talks about another set of these geometric shortcuts.
http://magoosh.com/gmat/2012/gmat-data- ... nce-rules/Does all this make sense?
Mike
Thanks for the breakdown. For arguments sake(i'm trying to bridge the gap) -- i can see the ratios of the angles and the sides. I originally thought that we would need to know a FULL length of the sides in question to determine the value, meaning, we would need to know SV instead of just SU. Are you saying we don't need to know that because at some point (if we were to solve it), we could find a single value that will make this SU true?