vinayrsm wrote:
hi Abhi, can you please share your strategies for Inequality & Overlapping sets? I face some issues in both these areas and will be thankful for any help. Thanks.
For inequalities, having a "feel" of numbers is the key. As soon as I see an inequality ANYWHERE in a question, my mind automatically draws that equation in the cartesian coordinates, and if it involves 3 variables then in 3D. Most often than not I can solve many problems just by imagining those numbers in the plan or 3D. Knowledge of how to imagine rectangle/cube, circle/sphere, parabola, etc helps, at-least for me. If needed I use notebook for questions involving multiple equations. I have never tried substitution as I don't want solve using random number and rather I want to get a feel of these numbers. GMAT problems are simple enough to represent in 2D, or very rarely 3D, and could be solved without writing many complex equations - sometimes of-course you do. But the point is instead of crunching some random number by substitution, I personally like get a feel of those numbers. If you can give me problem that you found most challenging, I will try my best to illustrate how this works but I hope I was able to convey my "personal" idea at high level.
If you are always getting 700-800 level questions, then you can't imagine GMAT to give to straightforward overlapping sets. It's all about ratio in Overlapping Sets. One crude way to solve is to use one of the standard 3 column-3 row strategy (I am sure GMAT books document it with some other name, I don't know) - for 2 overlapping sets, each with 2 mutually exclusive events. However, it can become tricky if you have > 2 sets and > 2 mutually exclusive events per set - the only way to solve these advanced problems is to use Venn Diagram. I always "try" to draw these Venn Diagrams to the same aspect ratio as give in the question. Venn Diagrams give you the feel. I don't memorize any formula as GMAT problems is tricky enough to make those formula confusing. Again I try to get a "feel" of the data given to me.
Hope this helps
Sorry, if this doesn't work for you, as these are some things my mind likes to do when it sees these numbers so I can't say it will work for all.