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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 in a few steps, Profit and loss problem 1 brief


A man sells two wrist watches one at a profit of 30% and another at a loss of 30%, but each at a same selling price of Rs.400. The net profit or loss is to be found out. This type of problem can be solved following clear steps based on basic and rich concepts of profit and loss within a minute with ease...

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 a difficult SSC CGL level problem in a few conceptual steps, Trigonometry 8

thumb How to solve SSC CGL level difficult problem in quick conceptual steps trigonometry 8

This problem in contrast to the earlier one looked difficult. The challenge was on - would we be able to achieve its elegant solution? Not always we know about the end in the beginning of our journey, but finally concept based strategic approach provided the initial breakthrough and then led us to the elegant solution in a few more steps...

How to solve not so difficult SSC CGL level problem in a few light steps, Trigonometry 7

thumb How to solve SSC CGL level problem in quick steps trigonometry 7

For some problems that don't look particularly difficult, the conventional steps to the solution may not seem to take long, but invariably it will be a mundane and wasteful few extra steps. The elegant lighted up way would have been just a few quick steps away from the goal, waiting to be believed and discovered, always...

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 problem in a few quick steps, Trigonometry 6

thumb_How to solve SSC CGL level problem in a few steps trigonometry 6

Some problems look difficult, but if you have a clear strategy of dealing with this type of problems, and is ready to change track by reevaluating the strategy midway, chances are high that you will reach the efficient solution in a few quick steps...

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 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...


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