Formula oriented approach Vs theoretical approach

Lively responses on my Facebook post validated the fact that the subject topic is of interest to many. I appreciate the responses received, however, some of them are slightly off the topic. Well, they have focused on ways to prepare for campus screening tests, but my post is primarily focused on clearing the tests (Meaning – the psychology at the time of test). Of course, how to prepare is a point of discussion, but, not right now.

I would be trying to classify various approaches to solve problems and then substantiate each type by giving an example.

Many, rather most, are of the opinion that one should solve problems logically.  But, I really do not know what exactly they mean by logical approach. There seldom exists any logical approach to a problem. Prasanna seconds by view by rightly mentioning the term ‘smart’ in his post, which is more appropriate. Some, if not all, problems can be solved by rejecting the inappropriate answers. Most of the times, this works.

Extending the point further, I would rather mention the term ‘sensible approach’ or ‘obvious approach’, where one is expected to apply his common sense. This again works for some, if not all, of the problems.

Coming to the theoretical approach, many argue that this is a more preferably approach. I do not disagree, but when it comes to clearing the test, time available for the test plays a very important role. From my experience, one cannot think of using theoretical approach for more than 10% of the total problems.

Formula oriented approach, seems to be a good choice, when it comes to attempting the test in the given time. I personally prefer this approach the most but would like to make a claim here. Chances of getting a problem correct by theoretical approach is slightly more than by the formula oriented approach. This is possibly because most formulae have few exceptions, which we tend to ignore while solving a problem. On the contrary, in case of theoretical approach, we go low, step by step, in detail, and we rarely end up missing the exceptions.

Giving some examples to substantiate my approaches:

1.      What is the remainder if 4536453663 is divided by 45?

A)  18                B) 48            C) 63            D) 3

From the right theory given to me by Prasanna , if the sum of digits (successive sum) of the dividend and divisor both are 9, the remainder has to be a multiple of 9. Clearly, the correct option is 18

Approach:

Some may confuse this with theoretical approach, but I wouldn’t call it so. I was not knowing the background or derivation of this property, neither had the time to validate that. What I used was an obvious and rejecting options approach.

2.      x^y + y^x  = 46, What is the value of x and y ?

Answer: 1 and 45

Approach:

No doubt this is nothing else than an obvious answer using obvious approach.  

3.      In how many ways can we distribute 10 pencils to 4 students, so that each student gets at least pencil?

Answer: ⁹C₃

Approach:

One possibility is that the student may actually derive something by mentioning various possibilities and counting them. Though time consuming, this may give a correct answer.

However, for the ones, who already know the background, will give the answer in matter of seconds, which I would call a formula oriented approach.

4.      There are five distinct integers a, b, c, d, e in ascending order such that (68-a)(68-b)(68-c)(68-d)(68-e)=725. What is a + b + c + d? 

Answer:

Here, I would say we use and prefer theoretical approach as we need to find the prime factors of 725 and then arrange them according to the question. Factorization of the given number is the only way of coming down to a solution, at least for me, which is nothing but pure theory.

All in all, in case of an aptitude test, important is clearing the test and in the given time. Though we cannot generalise one particular approach for all the questions, we can claim to use one particular approach for majority of the questions. Considering the upsides and downsides of the approaches mentioned so far, I would prefer to use a formula oriented approach for clearing an aptitude test. However, I do not debate that this approach will be helpful only if the student has used a theoretical approach while preparation.

For my final verdict, I would like to take reference of a theoretical approach J. Below are the theoretical claims:

1.    Voter A wins 41 votes, Voter B wins 40 votes, others in total win 19 votes.

Voter A wins, because he is in the majority.

2.    People claim India to be a Hindu country from the fact that 79.8% of India’s population is Hindu

This theory explains us the ‘rule of majority’!

Similarly, if we are solving more than 50% problems from a particular test by the formula oriented approach, we can safely claim that this approach has the thumbs up than all other approaches.

Note: In case you observed, I have used ‘theoretical’ approach for preparing my verdict J