Typically Untypical Questions

There many various exams that we have to undertake during our study years. Those include easy tests, serious exams and graduation examinations. In addition to all those, when we one is seeking to continue his education beyond high school (and towards higher degrees later), he or she has to attend some kind of multiple choice time limited test – such as GMAT, SAT, GRE etc.

Those tests are present in almost any country and as over the years they have proven themselves quite worthy in assessing person ability to successfully complete higher education studies. Of course, neither GMAT nor GRE are perfect, but no better tool has yet been found to estimate one’s ability to learn effectively.

The ultimate target of such tests is to estimate one’s ability to cope with large amount of new data and information in a limited period of time. Does he or she understand what is important and what is unnecessary? How fast can he or she achieve a correct conclusion based on the newly received data? Those are the questions that multiple choice time limited tests try to answer.

That is also the reason it is so hard to effectively prepare for those test. The whole idea is to make the examinee handle NEW type of questions, something he had never encountered yet. And with our formal education being, well, quite formal – it is not really that hard.

During our school years we learn and practice to apply certain techniques in order to solve typical problems of different complexity – from simple linear equations in elementary school to complex trigonometric identities in high school. But the techniques used are usually regarded by students only as means for achieving the result. The whole idea behind them is either not mentioned at all or quickly forgotten.

Here is an example:
When solving this simple equation
5x + 8 = x

Any mid-school student will quickly transfer 5x to the right part, not forgetting, hopefully to reverse the sing:

8 = x – 5x
8 = -4x

And then divide by the left part by -4, getting

8/(-4) = x
x = -2

But ask him or her – why does he/she do it? I bet this student, who had just solved the equation does not remember the reason for his operation – which is, actually, pretty straightforward: you can apply the same operation to both parts of the equation. So the first step was actually:

5x + 8 = x -> 5x + 8 – 5x = x – 5x -> 8 = x-5x. The same, of course, is true for the division by -4.

What about the difference between the next three:

  1. 0x = 0
  2. 5x = 5
  3. 0x = 5

How many of the students can immediately answer state that the difference is not in the SOLUTION, but in the NUMBER of the solutions? The first one, of course, has infinite number of solutions, as any x will fulfill the equation. The second one is the “normal” equation, which has one exact solution – x=1. The third one, as you might have noticed has NO solution, as there is no such x that can preserve the equilibrium. I am not saying this is COMPLEX. I am saying – you have never THOUGHT of it. And this is exactly what GMAT/GRE creators are looking for. They try to pose questions that are new to you – and every other examinee as well.

That’s why the diagrams presented in the test are mostly not the usual graphs we accustomed to see and create using Excel or similar software. And even when they DO look familiar, there is many times a “hidden trick”.

For example – imagine two “pie-type” diagrams, one depicting unemployed women according to profession (teachers, engineers etc.) and the second – unemployed men. The question is asked – according to those diagrams, which number is greater: the number of unemployed female teachers or the number of unemployed male engineers? Looking into the circles you can easily see that teachers comprise 40% of the women circle, and engineers being 24% of the men pie. Does this say that there are more unemployed female teachers than unemployed male engineers? Of course not – as we know NOTHING about the total number of unemployed men and women! It can definitely be true that 40% of unemployed women is actually smaller number than 24% of unemployed men – for example, if there are 10000 unemployed women and 50000 unemployed men…

In summary, when preparing for the GMAT/GRE/SAT and other similar exams, you should always be prepared to face the unknown. Be ready to look at the knowledge you possess from a different perspective and do not afraid to analyze the techniques you apply frequently in your everyday life.

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