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...
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...
A problem that looks difficult but not awkward, with some symmetry in the expressions, you should be able to detect the key patterns and discover the methods to use the patterns as well as general strategies to solve it quickly in a few steps...
In a problem involving both the given and target three variable expressions as symmetric and balanced between the three variables, pattern based general strategies should give you the desired result in quick time...
Occasionally the distinctive expression appears in one of the expressions, but its inseparable pair, the fraction of the two variables, is not readily available in the problem statement. We say in these cases that componendo dividendo appears in partial form, and the problem is of hidden componendo dividendo type. We need to change the given expression to match the target expression in such cases...
Learn how to use proportion based componendo and dividendo formula for quick solution of a wide range of componendo dividendo questions on algebra.
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...
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...
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...
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...
