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Efficient Math problem solving

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.

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 not so difficult SSC CGL level problem in a few light steps, Trigonometry 9

thumb How to solve SSC CGL level problem in quick steps trigonometry 9

The chosen problem this time is not so difficult, and on most occasions it will be solved conventionally. But driven by the general objective of equalizing the denominators, if the lightly hidden key pattern is discovered, everything becomes easy and straightforward with solution only a few light steps away...

How to solve difficult SSC CGL algebra problems in a few steps 14

thumb_How to solve difficult SSC CGL algebra problems in a few steps 14

Usually we solve difficult Algebra problems in a few steps using basic and rich Algebra concepts together with powerful general problem solving techniques visualizing the solution in the beginning itself. But this problem required more of deductive reasoning, mathematical reasoning, and exploratory application of core algebraic concepts such as symmetry in algebraic expressions, variable number reduction by component expression substitution and secondary term value sharing...

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....

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