CAT 2003 (retest): A milder version of the leaked CAT paper. It was apparent that that paper had been set in a hurry. A lot of concepts from earlier CATs were repeated. While Algebra was given a lot less importance, there were a lot of questions on Geometry — possibly a deliberate attempt to veer students off the track.
The concepts that were checked in this CAT were:
Logarithms: There were 3 questions, all of which required the application of some fundamental logarithmic properties. The first question was based on the solution for x in an equation with logs. The second was a geometric series embedded into logs, while the third was a simple logarithmic equation with two variables, in which one was asked to express one equation in terms of the other.
Quadratic Equations: A general form of a quadratic equation was given as ax^2 + bx + 1= 0. It was required to find how many sets of (a,b) can be selected from (1,2,3,4) so that the quadratic has real roots. A fairly simple and straightforward question.
Equations: The question posed was on the number of integral solutions for 5x+19y = 64, for some conditions of x and y. This concept reappeared, almost verbatim after a period of almost five years.
Series: Arithmetic and geometric series did an encore. So also did a question based on the AM > or = GM concept, albeit in a different format: y-x = z-y and xyz = 4; one had to find the minimum value for y. Another question where the above concept was applied was to find the maximum volume of a cuboid that is formed after snipping squares from the edges of a rectangular sheet. This concept was repeated in CAT after almost a decade.
Common roots: There were 2 cubic equations, the coefficients of the term with degree 3 was same. One was asked to find the number of common roots. This question was similar to one of the questions in the leaked CAT paper.
Range of x: Two questions were asked on the expression for x and one was asked to find the range of values x can take. One of the questions was confusing as the expression looked complicated, while the other was a simple inequality 1 – 1/n < x <= 3 + 1/n. To crack these questions, one needed to have clarity in concepts on number systems.
There was one inequality involving modulus: |b| >or = 1 and x = -|a|b. Based on this, one had to choose the correct option.
And to complete the paper, there were three questions based on some functional operators…The representation was given in a table format (that was the only new part). All three were absolute sitters. The definitions for composite operators were also given, for example, x*y was given in a table; x^2 = x*x…. and so on
Overall, it was a simpler paper as compared to its leaked counterpart.
CAT 2004
Series: The question on this topic went like this: “Sum of 11 terms = sum of the 19 terms of an AP. What is the sum of 30 terms? One could have easily solved it, based on the simple concept of writing the terms in terms of ‘a’ and ‘d’. A smarter way was to apply the concept that the average of middle terms of an AP equals the average of all the terms.
A sequence was given in the form a1 = 81.33, a2 =-19 and a(i) = a(i-1) –a(i-2). One was asked to figure out the sum to 6002 terms. It was obvious from the question that the answer would be a small number. An easy way to reach the solution was to write down the first few terms, so that the pattern becomes obvious.
Quadratic/Cubic Expression: One of the questions was f(x) = x^3 -4x+p; f(0) and f(1) are opposite in signs and the p lies in a range. One were to simply understand that the product of two numbers of opposite signs is negative! Also the check was on the student’s ability to solve quadratic inequalities. The other one was a quadratic expression: f(x) = ax^2 – b|x|, at x=0. One was asked to find out under what conditions of ‘a’ and ‘’b’ is f(x) is maximized or minimized.
Simplification: ‘y was defined as a fraction that had a recurring expression. One had to find the value of y. To solve this, all one needed to do was convert it into a quadratic!
Logs reappeared in this year’s paper as well in the form of Quadratics. It was a fairly simple question.
There were 2 questions on functions: f1(x) was defined for different values of x; f2(x) , f3(x) and f4(x) in terms of the other functions. On was asked to solve two expressions based on these definitions. Even though the question looked complicated, it was actually very easy.
As you can see, the focus on algebra was gradually reducing in this CAT.
CAT 2005
Identities: A simple question was asked based on identities: (30^65 – 29^65) / (30^64+29^64). One had to find the value of this expression, whether greater than or less than 1.
Sequences and series: There were two questions—one wanted us to find out what 1! + 2×2! + 3×3! simplifies to. Once you figure out that 3×3! can also be written as 4!-3!, it becomes a simple question thereafter. In the other question, A1 was given, with An in terms of n and the previous term and one had to find A100. This type of question has appeared in umpteen CATs. A simple way to solve it was to write the first 3 to 4 terms and try to fit the choice into it.
In the question on quadratic, the value of x was asked from the equation: x= (4 + root (4 – root (4 +root (4-……)))). A question similar to this one conceptually was asked in one of the previous CATs. Hence, it was nothing but a standard question!
Graphs: There was a graph |x-y| + |x+y| = 4; one needed to find the area enclosed. This was very similar to one of the questions that came in CAT six years ago.
Functions: This was a tricky one. One was given g(x+1) +g(x-1) = g(x) and was asked to find out for what value of p, g(x+p) = g(x). If one took a look at the choices, one could have easily concluded that you needed to write the expression, at max till g(x+6). That was the way to make it simple.
CAT 2006:
The only question in the CAT 2006 paper worth mentioning in Algebra was the graph in which the 2 axes were x+y and x-y. One was asked to identify the same graph when drawn on the x and y plane. This question needed the application of a concept that involves rotation of the axes. Though no in depth knowledge was needed, it might have surprised a few because such type of question made its appearance for the first time…Could they take this forward? Time only will tell.
On the whole when I sum up the CAT papers over the past 10 years, I can safely conclude that contrary to popular opinion, Algebra is not necessarily gaining in importance. Yes, it is a fact that no longer do we see the basic formulae driven problems. You need to move that one step ahead in order to solve these questions, but those who use the “Dummy” way of solving using choices are going to find a fair bit of Algebra questions to be simple, irrespective of the level of difficulty of CAT.
I do hope students would take a look a the past CAT papers and not believe the ‘rumours” of CAT being so difficult…But why were the mocks tough then…I believe mocks do help in Capturing all the fundas that one needs for CAT…and to crack it !!
Filed under: Know the CATs, Quant Fundas
