We shall see the following myths about the CAT being smashed as this blog progresses: (A) the erroneous impression that the QUANT Section at the CAT is a test of mathematics (B) the delusion that the Verbal Reasoning Section at the CAT is a test of command over the English language (C) the wrong notion that Data Interpretation Section at the CAT is a test of one’s ability to quickly carry out complex calculations.
What is the number of distinct terms in the expansion of (a + b + c)20?
(1) 231 (2) 253 (3) 242 (4) 210 (5) 228
If you see the question and the options, the least number of terms as per the options is 210. If you think the CAT is about mathematics, try expanding (a+b+c)^20 in which you will have to write down at least 210 terms. This might take a full day for a perseverant soul. You have less than two minutes per question. Writing down 210 or more terms and then counting them? Goodness gracious! That would be a daunting task. Is this question an isolated instance of long apparently gigantic questions? No way, dear! Only the QUANT Section in the CAT of 2017 had 60% of such questions. Then how do you solve such questions? You can solve such questions in a blooming jiffy with the logic skill known as Pattern Recognition (PR). And what, pray, is Pattern Recognition?
There are patterns in businesses. Here are some instances:
(I) The budgetary allocation for each government department in India expires in March and government departments do the bulk of their shopping towards end March. Someone selling goods to governments would do well to keep this in mind and try to maximize his sales to the government in March each year instead of pushing off for a holiday, which he could postpone to, say, May each year.
(II) The daily billing at a restaurant is at its least on Wednesday and peaks on Saturday. The restaurant owner would be a comprehensive dud if he did not have enough raw materials in place for Saturdays or gave the day off to himself and the staff on Saturdays.
When you are in business or when you are a manager in a business outfit, Pattern Recognition will have to be your forte if you are to shine out. This is why examinations for entrance to premier business schools test this ability in no small measure.
What do you do when you are asked a question about expansion of (a + b + c)20? First expand (a+b+c)1 and you get (a + b + c) that has three terms.
Then expand (a+b+c)2 and you get (a2+2ab+b2+2ac+2bc+c2) that has 6 terms. Going further, (a+b+c)3 = a3 + 3a2b + 3ab2 + b3 + 3a2c + 6abc + 3b2c + 3ac2 + 3bc2+c3 and thus has 10 terms.
What you see is the following pattern:
(A) There are 3 terms in the expansion of (a+b+c)1. You know that 3 is 1+2.
(B) There are 6 terms in the expansion of (a+b+c)2. You know that 6 is 1+2+3.
(C) There are 10 terms in the expansion of (a+b+c)3. You know that 10 is 1+2+3+4.
You have a huge hint now. Get that hint and the answer will stare you in the face.
In the expansion of (a+b+c)1, and in (a+b+c)2 and so on, if we were to take this as a case of (a+b+c)N, the number of terms in the expansion is 1+2+3…(N+1). Therefore in the expansion of (a+b+c)20 the number of terms would be = 1+2+3+4…+19+20+21= (1+21)/2× 21 = 231. Hence three cheers for Option 1.
The past CAT papers are testimony to the fact that a great deal of questions asked on the CAT test a candidate’s ability to try solving a bigger, complex problems using smaller, manageable values, recognizing patterns and then applying these learning to solve the original questions.
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