pemdas wrote:clear, i see
strangely, i caught myself on changing question answers marked towards the end and before moving to other questions, like here and in many of my mock tests. Mostly, I was able to resolve and get the right answers but then was marking different choices. Sometimes adding unnecessary restrictions to combs/perms like on one forum you contributed greatly, or arguing about irrelevant properties, I need more efficient approach. Any advice you could give on my occasions? (I'm asking in this forum, because the issue is specific and mostly quant related)
So you're saying on tests you'll solve a problem, mark an answer, and then before hitting submit, you solve it again? And then you usually end up changing it so that it's wrong? Or do you usually fix it so it's right? I was a little unclear on this point.
If you find yourself going back and changing your answers a lot, it may just be a matter of building up your confidence in certain areas. From your posts it sounds like you have a pretty strong math background, particularly in statistics. Is this correct? But maybe in some areas there's still room to improve your fundamentals.
I think permutations and combinations is just hard for almost everybody, and the vast majority of people wouldn't feel that confident in a purely theoretical approach to hard counting problems until they've spent years working with them. Obviously, most people don't have the luxury of doing that before taking the GMAT, so I think the next best thing is to have a backup plan for those types of problem. That is, don't rely on a theoretical approach alone. Take your best guess as to what the correct method is, and then test that method on a similar, more accessible problem. For example, in that 6 men, 4 women around a table problem, I listed out the possibilities for 4 men, 2 women to demonstrate that my method worked. Obviously you can't list out 72 possibilities on a real test, but you could list out all the possibilities for 3 men and 2 women, as there are only 12 possibilities. If the method you were using also returned 12 for that case, that would give you confidence that you're on the right track. Also, examining a complete list of possibilities for a specific instance like this could give you a lot of information about whether assumptions that you are making are reasonable or unreasonable.
In the case of this inequality, it looks like you again got in trouble by relying on an overly theoretical approach. You were correct that the discriminant for the quadratic that resulted for cases where x<1/2 was negative, however, you applied this information incorrectly. The fact that the discriminant is negative just means that the quadratic expression can never equal zero, so it is in fact either always positive or always negative. In any case, it is not difficult to plug in a couple of values less than 1/2 to see if the results support your theoretical approach. If the test fails, you have an opportunity to reexamine your assumptions.
In sum, try to get in the habit of finding ways to test your theoretical approaches to the harder problems by examining more accessible situations or by doing things like plugging in numbers. It may take a little longer, but it should increase your accuracy and confidence in your solution.
