CAT Quantitative Aptitude: What are the IIMs looking for?

This article deals with the overt and covert dimensions of the CAT Quantitative Section. Overt is the dimension which is apparent, obvious and seeming; while covert is the deeper and latent dimension. This kind of a dichotomous treatment will enable you to appreciate that the CAT Quantitative Section is not merely a test of discrete mathematic skills, but a true measure of your managerial potential!
Questions in the CAT Quantitative Section can be aligned into the following four distinct modules:
  • Arithmetic: Number System, Ratio & Proportion, Percentage, Profit & Loss, Mixtures, Averages
  • Algebra: Linear Equations, Simultaneous Equations, Quadratic Equations, Time-Speed-Distance, Time-Work
  • Geometry: Lines-Angles, Triangles, Quadrilaterals & Higher Polygons, Circles, 3-D Figures, Trignometry, Coordinate Geometry
  • Modern Math: Probability, Permutations & Combinations, Logarithms, Functions, Set Theory

Let us take a question from each of these four modules and validate the fact that understanding the covert vibe in the question is imperative for you to establish a stronger connection with the question and ensure a smoother handling thereof.
Q.1. 1025 - 7 should be divided by which of the following numbers so as to give remainder zero?
1. 2
2. 3
3. 9
4. Both (2) and (3)
Explanation: Firstly, find the number of factors of the given number and express the number as a product of powers of prime numbers.
1025 - 7 = (1025 - 1) - 6
1025 - 1 = 99.....9 (25 digits); is divisible by 3.
Therefore, (1025 - 1) - 6 = (24 nines and unit digit is 3) 99.......93.
This number is divisible by 3 (from the given choices).
Overtly, it is a test of Arithmetic as gauged through your ability to process numbers; but covertly it is a test of your ability to understand symmetry, patterns and formations, which facilitates a better understanding of business processes, human behavior and markets as they all evolve around this golden principle of nature –symmetry!
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Q. 2. Deepa entered a florist shop and bought 'x' flowers for 'y' rupees (x and y are integers). If she had bought 10 more flowers, she would have got all for Rs. 2 and saved 80 paise a dozen. Find x and y.
1. x=3, y=2
2. X=4, y=1
3. X=5, y=1
4. None of these
This question is apparently based on the topic of Equations (Algebra), stating a correlation between rupees spent and flowers bought. The starting point of this question is to understand that if 'x' flowers are bought for 'y' rupees and x+10 bought for 2 rupees, then 'y' will have a value less than 2; the only integer satisfying this condition is 1. Hence the value of y is 1, which will help you to eliminate option 1 as the answer. Further, keep in mind the saving as 80 paise a dozen will yield the following equation:
(1/x)- (2/(x+10)) = 0.8/12 = 1/5
From the options, it can be quickly inferred that the value of x is 5. Hence answer is option 3. Overtly, it is a test of your ability to solve equations, but covertly it is a reflection of your ability to correlate variables into relationships, a skill which helps managers to understand business challenges more insightfully.
Q.3. A solid spherical ball is cut into eight identical pieces by three mutually perpendicular planes. The proportion of the area of any of these pieces to the area of the uncut solid spherical ball is …………
This question is visibly sourced from the Geometry Module. The starting point is to imagine the way the sphere is cut into eight identical pieces by the three orthogonal planes. This will yield 8 quadrants, 4 in each hemisphere. The skill here is to form a visual imagery and appreciate the fact that each such quadrant will have 3 cut surfaces and 1 uncut surface. Further, each of the three cut surfaces is ¼ of a circle and will therefore have an area equal to one fourth of that of a circle; while the uncut surface will have an area of one eighth of that of the sphere (as there are 8 such quadrants). Now just add the two areas and divide the result by the total surface area of the sphere to get the required ratio as 5/16. Thus this question is not just a test of Geometry but of your ability to understand space which is analogous to decoding the market space in a competitive business scenario, and hence becomes covertly connected with managerial aptitude.
Q.4. A die bearing the numbers 0,1,2,3,4,5 on its faces is repeatedly thrown until the total of the throws exceeds 12. What is the most likely total that will be thus obtained?
This question is seemingly extracted from the topic of Probability which is largely perceived to be a problem area and may thus keep certain candidates away from attempting it.
A careful scrutiny however reveals that the question is only a trap woven around words and can be easily solved by considering the penultimate throw (the throw before the last throw). The total at the end of the penultimate throw needs to be one of the following : 8, 9, 10, 11, 12. Each of these would solicit different outcomes in the last throw for the total to exceed 12, as shown:-
8 ---- the possible value of the final throw can be only 5, making the total 13 (hence more than 12)
9----- the possible values of the final throw can be 5 and 4 making the total 14 and 13 respectively
10----the possible values of the final throw can be 5,4 and 3 making the total 15, 14 and 13 respectively
11----the possible values of the final throw can be 5,4,3 and 2 making the total 16, 15, 14 and 13 respectively
12----the possible values of the final throw can be 5,4,3, 2 and 1 making the total 17, 16, 15, 14 and 13 respectively
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Thus the most likely total to be obtained in this process is 13 (common to all outcomes); hence the answer is 13.
In conclusion, it is important to understand that the various modules in the CAT Quantitative Section apparently pose mathematical challenges, but at a more evolved and covert level, they can be seen as opportunities for solving management problems camouflaged in the quant Math envelope!
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