How to solve a hard CAT level Time and Work problem in few confident steps 1
To solve hard math, instead of thinking conventionally and mechanically, use your problem solving skills, inventive thinking and basic math concepts.
This is not specific to any exam. Each article highlights how difficult problems can be solved say in 3 steps instead of conventional 10 steps.
Under this section we will solve typical math problems that a student might find difficult when preparing for competitive tests such as SSC CGL, CAT, GRE etc. We will also cover Secondary school level or even occasionally Olympiad level problems.
The chief criteria that will be common to the problems here will be three:
We don't like to deal with laborious problems. Generally each of these problems can be solved in a number of ways.
As we teach efficient problem solving as a subject, we will always try to find the easiest way to solve a problem explaining the strategy and the process that were required to reach such a quick solution.
It means, each problem and its solution that we explain here won't just be for that specific problem. More importantly, the underlying concepts about how the solution was reached efficiently and in very quick time, form the most valuable treasure to be recognized and owned by the student by understanding the concepts and applying the concepts in future problems.
To solve hard math, instead of thinking conventionally and mechanically, use your problem solving skills, inventive thinking and basic math concepts.
Usually we solve difficult Algebra problems in a few steps using basic and rich Algebra concepts and techniques together with powerful general problem solving techniques. This problem required more of deductive reasoning, enumeration, mathematical reasoning, general problem solving techniques and core algebraic concepts such as symmetry in algebraic expressions and less of algebraic expression manipulation...
In procedural approach to solve Trigonometry or Algebra problems, usually the student has to go through many steps writing the steps using pen and paper without using the useful patterns lying partly hidden in the problem waiting to be used with intelligence so that the solution is reached in a few steps lightning fast, that too without using pen and paper. We are not discussing tricks. We are discussing the anatomy of a rich concept that are based on basic concepts and how a specific rich concept can be used for what we call, efficient problem solving.
To solve many ratio problems including number system problems quickly, use multiple ratio, componendo dividendo and other quick solution techniques.
Algebraic rich concepts and techniques along with general problem solving strategies enable elegant solution to the difficult SSL CGL Algebra problems. In this 12th session we will highlight one of such powerful problem solving technique of continued factor extraction, that can be applied for solving different types of difficult algebraic problems in quick time...
Sometimes in the breakneck hurry while struggling with the questions in a cutting edge leading selection test you might meet a problem that doesn't seem right somehow. You figure out the only way to arrive at the solution but out of sheer curiosity you check back the solution value with the given values to verify the sanctity of the problem definition...
Algebraic rich concepts and techniques along with general problem solving strategies enable elegant solution to the difficult SSL CGL Algebra problem in this eleventh session of algebra problem solving in a few simple steps. This time our emphasis has been analyzing the two feasible solutions of the chosen problem...
Time and distance problems are taught in middle schools and also form an important component of competitive tests. In this second session of time and distance problem solving in a few steps, we have shown the process of reaching solution in a few steps for two chosen problems...
Basic Geometry concepts with general problem solving strategies and techniques produce elegant solutions in difficult Geometry problems just as in Algebra or Profit and loss. In this third session of Geometry problem solving in a few steps we will analyze solution process of three chosen geometry problems...
Applying Basic Geometry concepts together with general problem solving strategies and techniques produce elegant solutions in difficult Geometry problems just as in Algebra or Profit and loss. In this second episode of Geometry problem solving in a few steps we will analyze solution process of four chosen geometry problems...