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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 a SSC CGL level tricky age ratio problem lightning fast

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Use of the rich ratio technique of multiple of ratio value 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. The chosen problem here is a tricky one and we will solve it using multiple of ratio value technique as well as conventionally to highlight the power of the rich ratio technique...

How to solve SSC CGL level Profit and loss problems by change analysis in a few steps 6

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In profit and loss problems when price or profit changes by certain percentages, without calculating the actual changed values and just by using the change and its effect, solution can be achieved very fast. We would solve two problems on profit and loss to highlight the power of this technique...

How to solve a SSC CGL level Profit and loss problem with equal sale price in a few steps 5

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We have already treated an interesting type of profit and loss problem with equal sale prices and equal profit and loss figures in two transactions. This session we will be solving such a problem with equal sale prices but with unequal profit and loss percentages very fast and in two ways. We will use basic and rich profit and loss concepts, fraction concepts and mathematical reasoning to achieve the speed and elegance...

How to solve a difficult SSC CGL level problem in a few reasoned steps, Trigonometry 10

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The chosen problem in this session is awkward and if you attempt to solve it through conventional deductions, it would be tedious and time consuming. You may even lose your way in confusion. Instead, if you are able to identify useful patterns and apply mathematical reasoning, solution would take just a few tens of seconds...

How to solve a difficult SSC CGL level algebra question by variable ratio equality in a few steps 18

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Problems based on variable ratio equality may seem to be quite tough in competitive test environment unless you know the underlying concept. The chosen problem with its solution highlights use of the concept for quick mental solution of the apparently hard algebra problem...

How to solve a difficult surd algebra question by repeated componendo dividendo in a few steps 17

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The problem we have chosen this time is to highlight, Importance of recognition of simplifying powerful patterns inherent in a difficult problem, the power of Componendo dividendo to speed up solution considerably, and the unfailing effectiveness of principle of interaction of inverses if you can recognize its presence and apply it...

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