vingmat001 wrote:
Hi Mike - Thanks for your clarifications!
None of the
Magoosh tutorials cover this problem. I just encountered this in my GMAT Prep Exam - 4.
Can you please point me to some resource on where i can learn more about these concepts?
Vin
Dear Vin,
I'm happy to respond.
This is a very funny thing about probability and counting problems, more than many other branches of math. How to explain this? Think about, say, algebra. In algebra, there are very fixed rules, and for such-and-such a problem, there's not much ambiguity about what steps will lead to the answer --- yes, for folks still learning, there might be confusion, but for anyone familiar with the algebra, there's really no debate about what to do: there's a clear linear path to the answer. Algebra depends heavily on left-brain skills: logic, organization, procedures, and precision. If you know the rules & formulas of algebra, you know well over 90% of what you need to know to solve problems.
Probability and counting are two branches of math that are not like this at all. Yes, there are some rules & formulas, but even when you completely know those rules & formulas, you really know only about 20% of what you need to know. What's more important in these branches is perspective and ability to frame the problem in your mind. Instead of the left-brain focus of "what to do?" we have to start with the right-brain focus of "how to see?" --- when a probability or counting problem is properly framed, properly viewed, then what to do becomes quite straightforward.
You ask for resources. This is VERY tricky. You see, with left-brain skills, rules & procedures, we can just give explicit steps --- "do this, then do this, then do that." Left-brain skills lend themselves well to recipes, methods, and step-by-step instructions. Right-brain skills of intuition and pattern-matching are not like that at all --- there's often no quick way to summarize it. You have to develop it though experience, over time. See this blog for more on left-brain/right-brain skills in math:
https://magoosh.com/gmat/2013/how-to-do- ... th-faster/Magoosh actually provides a HUGE resource here. It's true, we have a few probability video lessons that cover the basic rules, but there's no way those lessons could cover all the right-brain skills needed for seeing problems the way you need to see them. The BIG resources are the video explanations following each and every practice question. That's really where a student has the opportunity to see --- after doing a problem for himself, the student can witness how the instructor frames the problem. Students often miss this --- they are so focused on "what to do" that they don't give sufficient attention to the
perceptual choices with which the instructor begins the analysis of the problem. Developing a deep understanding of probability involves thinking critically about these perceptual choices --- why did the instructor look at it this way rather than that way? Those are great questions to ask if you can't figure it out on your own. The fact that every
Magoosh question has its own VE is tremendously valuable resource that, unfortunately, some less perceptive students completely underestimate.
For probability questions you found outside
Magoosh, say here on GMAT club, also pay attention to these perceptual choices that experts make, the very first step they take in framing the problem. Don't focus simply on "what did they do" --- focus first and foremost on "how did they look at the problem? how did they frame it?" Again, if you are unclear, ask. You are always more than welcome to solicit my input on any problem: just send me a private message with a link.
I know this is probably a less satisfying answer than you were hoping to receive. Does all of this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)