# CIRCLE OF REASON

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1021 by R. Shiva Kumar, Co-founder, Career Launcher; Published in HINDUSTAN TIMES

Reasoning, as the word itself suggests, is all about rational and logical thinking. Reasoning has become an integral part of most competitive exams. This is a logical corollary to the objective of these exams, which is to cull out the thinking from â€œmuggoosâ€ or, people who memorise for competitive success. There is no one way to check a candidateâ€™s reasoning skills. Most of these institutions / boards which conduct these exams (be it for MBA, MCA, Bank exams..) are in search of students who qualify the threshold level or competence in a wide array of situations.

Reasoning in competitive exams has evolved over a period of time in both its forms and focus in the different competitive exams.

The different sections in which the students are tested are:

1. Quantitative Reasoning

Mathematical reasoning / Data Sufficiency

1. Logical Reasoning

Logic / Deductive Reasoning

1. Verbal Reasoning

Verbal Puzzles / Analogies

1. Analytical Reasoning

The limitation of knowledge base is no major hurdle in each of these sections (except probably Data Sufficiency). The crux of the matter is: do not assume that mugging alone can take you through the exams.

In this first part of the series, we shall take a glimpse at what constitutes mathematical reasoning and look at some of the situations, which demanded it for you.

1.Â If AAA+CDC=C0A0 what are the values of A, C, D ? (0=Zero, No two alphabets are equal)

The logic is simple. It is based on the fundamental arithmetic rules of addition. If two 3 digits numbers are added the value of the resultant is greater than 1000 andÂ  less than 2000. Hence the first digit of the sum can only be equal to 1, So C=1, then A must be equal to 9, which means D=0.

1. There is a cubical cake. From this cake a smaller cube is cut out (we do not know the position of this smaller cake with reference to the whole). You now have to cut the remainder into two equal pieces by a single cut of the knife. How would you do it?

The line of the cut could be determined by the fundamental principles in geometry. If a line is drawn passing though the centre of any square (Cross section of the cube being a square) it cuts the square into two equal halves. Extending the logic if the lien of the cut passes through the centres of the surface of the original cube and cut square we get two halves that are equal in terms of the mass (Since the area of the cross section of the two pieces is same and the height of the cake is the same).

1. Probability, an oft-feared topic, is a veritable treasure house of puzzles. The reasoning for these problems is often based on simple logic.

There was a guy who had two girl friends, one staying to the east of his residence and the other staying to the west. If he wishes to meet them he has to take a suburban train (running in the same directions). He goes to the station at any random time and always takes the train that comes first. At the end of the year the girl friend staying in the west broke off with him since she had discovered that he had spend 9/10th of his time with the â€˜otherâ€™. Can you think of a situation when this could happen?

1. I hope probability doesnâ€™t work against you!!! (Assume the frequency of the trains in either direction is the same)

Data sufficiency problems test the candidateâ€™s ability to judge whether the data given is sufficient to conclude an answer or not.

For instance the question could be. What is the length of the second diagonal? The clues are

1. One of the diagonals is = 9 cm.
2. The area of the rhombus is a perfect square.

You would be required to determine if you can find the area using only one of the clues or by sing both the clues together or if neither of them is god enough for you to find the answer.

(Ans.)Â  Neither. The product of the diagonals gives the area of a Rhombus. If one diagonal is 9 and the area is a perfect square there can infinite number of combinations with the second diagonal that gives the area as a perfect square.

In this case you are obviously expected to have prior knowledge on the topic of relevance.

I hope you have enjoyed this edition of the series. Do stay with us. We shall be back next week on the same day.

Till then, happy reasoning.