Efficient Math problem solving

Faster math problem solving in a few 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:

  1. The problem should not require too much math knowledge to solve,
  2. The problem should have an inherent difficulty for most of the students or may be too lengthy and,
  3. The problem must be solvable following an elegant method in a very short time.

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.

How to solve a hard CAT level Time and Work problem in few confident steps 1

thumb_How to solve a hard CAT level time work problem in a few confident steps1

The conventional approach to math problem solving relies heavily on manipulation of terms using low level mathematical constructs without using the problem solving abilities of the student. Following only this approach to solving problems, students may tend to become used to mechanical and procedural thinking suppressing their inherent creative and innovative out-of-the-box thinking abilities. On the other hand, conceptual reasoning without firm mathematical base leads to confusion. In solving hard problems you need to strike a balance...

How to solve difficult SSC CGL algebra problems in a few steps 13

thumb_How to solve difficult SSC CGL algebra problems in a few steps 13

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...

How to solve difficult SSC CGL level School Math problems in a few quick steps, Trigonometry 5

thumb_How to solve SSC CGL level school math problems in a few quick steps trigonometry5

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.

How to solve difficult SSC CGL algebra problems in a few steps 12

thumb_How to solve difficult SSC CGL algebra problems in a few steps 12

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...

How to solve intriguing SSC CGL level Geometry problem in a few steps 4

thumb_how to solve intriguing ssc cgl geometry problem in a few steps 4 top

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...

How to solve difficult SSC CGL algebra problems in a few steps 11

thumb_How to solve difficult SSC CGL algebra problems in a few steps 11

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...

How to solve difficult SSC CGL Geometry problems in a few steps 3

thumb_How to solve difficult SSC CGL geometry problems in a few steps 3

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...

How to solve difficult SSC CGL Geometry problems in a few steps 2

thumb_How to solve difficult SSC CGL geometry problems in a few steps 2

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...

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