One of the reasons why the CAT seems tough to test-takers is that the questions are deceptively framed. Test-takers tend to expect questions to be neatly classified — areas, topics, concepts — so that the moment they see the problem they know what to do. But the objective of the test is to not to make things so obvious, not to make a question a matter of plugging numbers into to formulas. There are many questions that on the face of it seem to belong to one area but on closer inspection reveal their origins to be in a different area.
The SimCAT question below is a perfect illustration of such a question.
Two real numbers x & y are chosen between – 3 and 3 (both inclusive). What is the probability that x2 +y2 < 9 ?
(1) PI/6 (2) PI/4 (3) PI/3 – 1/2 (4) None of these
So which area does this problem belong to? Algebra & Probability or Modern Math or Numbers & Probability? Most test-takers would see this question and decide that it is better left alone, especially after see they the answer options in terms of PI.
But it is exactly the nature of these answer options that should give you the clue!
You should look at the answer options and they should set you thinking that PI usually occurs is Geometry, to calculate areas or volumes. So does this problem have anything to do with Geometry?
The only way to answer this is by examining the question again.
What does x2 +y2 < 9 stand for? If you have covered the basic concepts in Geometry the equation should ring a bell. It is the equation of a circle with center as (0,0) or the origin and radius 3.
So they are asking you what is the probability that x & y will either lie on the circle, x2 + y2= 9, or inside it, x2 + y2 < 9 .
So now you should approach the whole problem as a Geometry problem and try to represent the entire information diagrammatically.
The equation is nothing but a circle of radius 3. The values of x and y between 3 and -3 can represented by straight lines passing through these values.
Now the whole problem becomes a cakewalk. What is probability that x and y will lie on or inside the circle?
The probability is nothing but Area of the circle (PI*9) / Area of the square (36) or PI/4!
Once you see the equation as a circle, this problem is essentially offering you 3 marks on a platter!
What is important is that you learn to not expect questions to be always posed in a straightforward manner, you do not discriminate questions based on area, length and type of answer options, and have basic concepts (like equation of circle in this problem) across areas in place.
We will take up more of such problems in forthcoming posts.
As always feel free to ask any doubts in the comments section.