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 difficult SSC CGL level Profit and loss problem in a few steps 4

thumb_How to solve difficult SSC CGL profit loss problems in a few steps 4

Basic profit and loss concepts though are simple, which of the price values to be used as reference for applying profit or discount percentages sometimes create doubts. Further, the free offer concept and easily visible option for calculation of actual price values not only complicates the situation, but introduces harmful calculation delay...

How to solve a School Math problem in a few direct steps, Trigonometry 5

thumb_How to solve a school math problem in a few direct steps rigonometry5

After crossing the first barrier in the process of proving a Trigonometric identity, if you go straight ahead without looking at the goal state on the RHS, you might reach a situation where you would have to start again from the goal state expression and backtrack to the simple result you had reached on the first go, not only an awkward solution but also technically an invalid one....

How to solve a difficult SSC CGL level problem on percentage in seconds by conceptual reasoning

thumb_How to solve SSC CGL level percentage problem in seconds

In this session of efficient math problem solving we will show how a difficult SSC CGL level percentage problem can be solved in seconds by using very basic number domain concepts along with basic percentage concepts...

How to solve a hard CAT level Time and Work problem in a few confident steps 3

thumb_How to solve a hard CAT level time work problem in a few confident steps3

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. In this third session on hard problem solving we have shown again how to do it...

How to solve a hard CAT level Time and Work problem in a few confident steps 2

thumb_How to solve a hard CAT level time work problem in a few confident steps2

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. In this second session on hard problem solving we have shown how to do it...

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 SSC CGL level number and age ratio problems lightning fast

thumb_How to solve SSC CGL level number and age ratio problems lightning fast

Use of a rich ratio concept based on a most basic ratio concept helps to solve a broad spectrum of ratio problems and specifically many standard number or age ratio problems elegantly in a few steps much faster than conventional procedural methods...

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...

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