CAT 2017 NEWS
NATIONAL LEVEL ONLINE TEST
The first section as per the new pattern released for CAT Exam will be of Quantitative Aptitude (QA). Earlier this section also included questions on Data Interpretation (DI) but now it will be separate section For QA there will be 34 questions with a time limit of 60 minutes to solve it.
The new Exam Pattern for CAT will cover following three sections:-
|Section||Number of Questions||Duration|
|Data interpretation and logical reasoning||32||60|
|Verbal and Reading comprehension||34||60|
|Total duration||180 minutes|
This has led to decrease in the weightage of Quantitative ability section from 50 to 34 although all the questions will carry equal marks whether it is an objective type or descriptive one. So, the quant section will have following pattern
|Name of the Section||Number of Questions Asked||Type of Questions||Time allotted for this section|
|Quantitative Aptitude (QA)||34||MCQs and Descriptive||60|
One major point to keep in mind is that you cannot start from any section you like, the periodicity of the sections is to be maintained and you will not be allowed to swap between the sections till the assigned time of 60 minutes for the section is over. Once the time of 60 minutes is over, you will be directed to the next section automatically .So you have to begin your exam from QA section which will cover areas like Arithmetic ,Algebra, Geometry, Trigonometry among other topics to be solved in 60 minutes and will fetch a maximum raw score of 102 marks. On the top of it, most of the Quant questions are the single answer questions as against the DI questions which commonly appear in set of 4-5 questions and you could crack at least 1 or 2 correct out of them.There will be Non-MCQ type of questions in Quant section of CAT 2015 with no answer options.
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It is important to score well in QA section because a candidate scoring high percentile of 99+ in Verbal Ability section and scoring 75+ in Quant section, despite scoring a very high overall percentile of 95-96 cannot hope to be shortlisted by IIM A,B,C,L or even by the newer IIMs as the sectional percentile is below the prescribed cut off level.
To score well in QA section you must prepare rigorously , clear your basics thoroughly & take mock tests as much as possible , Below mentioned are some tips that you can follow while attempting the QA section
For preparing for geometry part you must be familier with the basic theorems of involving triangles, circles and parallel lines. You may have encounter a question like find the value of certain angles or length of certain sides many a times while going through a CAT’s previous question paper . Therefore, make sure that you cover topics such as congruency and similarity of triangles.
For preparing for coordinate geometry focus mainly on 2 topics straight lines and circles. Don’t give much emphasis on topics like conic sections and other advanced topics. Some sample questions on coordinate geometry which will provide you a vague idea about coordinate geometry questions
Que:Determine the equation of a line, the intercepts of which are twice those of the line 2x – 3y – 12 = 0.
1. 3x – 2y = 24 2. 2x – 3y = 12
3. 2x – 3y = 24 4. None of these
Answer : 3
Solution: If x = 0, y = – 4
Thus, the y intercept is – 4
Put y = 0, in that case x = 6
Hence the x intercept = 12 and -8
Thus, the intercepts of the required line are 12 and – 8. So the equation of the line is
(x/12) + (y/-8) = 1-8x + 12y = -96
2x – 3y = 24 , So 3rd option is correct
Few short cuts to keep in mind while solving coordinate geometry questions
If ABCD is a parallelogram, then D= A-B+C
For mensuration- For preparing for this part , learn all the basic formulae on areas, surface areas and volumes of triangles, circles, cylinders, cones, cuboids and spheres from NCERT school text book of class 8th,9th & 10th . Mensuration problems are calculation intensive, and require lots of practice so try to attempt them at the last hour of section.
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Important formulae to solve mensuration based problems
Important Formulae for Geometry based questions
|Total Surface Area||6a2|
|Length of face diagonal b||√2a|
|Length of body diagonal c||√3a|
|Total Surface Area||2(lb+bh+hl)|
|Length of four equal body diagonals AF||√l2+b2+h2|
|Length of face diagonal AC||√l2+h2|
|Length of face diagonal BF||√b2+h2|
|Length of face diagonal DF||√l2+b2|
|Radius of sphere circumscribed in cuboid||Diagonal /2 , √l2+b2+h2/2|
|Surface area of the sphere||4πr2|
|Volume of the sphere||4πr3|
|Volume of the shell||4/3πr3|
|Total number of vertices||4|
|Curved Surface Area||3√3a2/4|
|Total Surface Area||√3a2|
Permutations and Combinations important formulae
Formula 1:-If n distinct items are arranged in a row, then the number of ways they can be rearranged such that none of them occupies its original position is,
|n! * ((1/0!) - (1/1!) + (1/2!) - (1/3!) + ... ((-1)n/n!))|
Note: De-arrangement of 1 object is not possible.
Dearr(2) = 1; Dearr(3) = 2; Dearr(4) =12 4 + 1 = 9; Dearr(5) = 60 20 + 5 1 = 44
For eg- A person has eight balls and eight bags corresponding to those balls. In how many ways can he put those balls in the bags such that exactly 5 of them get into the correct bag correctly?
Ans:- five balls that gets into the correct bags can be done in 8c5 ways
So the rest three balls must be put into wrong bags which can be done in Dearr(3)= 2
Hence the total ways =2* 8C5=2*56=112 ways
Formula 2:- Partitioning
To arrange n identical items in r distinctive groups and there is no restrictions= n+r-1Cr-1
Formula 3:- Number of ways of arranging n items, out of which p are alike, q are alike and r are alike given that p + q + r = n
Number of ways of dividing n distinct items, in groups of size p, q and r given that p + q + r = n is
|n! / (p! * q! * r!)|
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For preparing this topic first of all you should be well aware of how to frame numbers into algebraic form ,( for e.g. a three digit number having digits xyz can be represented as 100x + 10y + z). You should also learn about divisibility tests and the ‘modulo’ notation and its applications (for programmers, 10%5==0 is also referred to as 10 modulo 5 is 0, that is, the remainder when 10 is divided by 5, is zero).
Different divisibility tests and modulo notations that will help you to solve questions based on number
Basic formulae to solve algebraic equations
Important Divisibility Tests
Important divisibility rule forCo-primes- If a number is divisible by pas well as q , where p and q are co-primes, then the given number is divisible by pq. If p and q are not co-primes, then the given number need not be divisible by pq, even when it is divisible by both p and q.
36 is divisible by both 4 and 6, but it is not divisible by (4∗6 )=24, since 4 and 6 are not co - primes.
Important Results for solving AP based questions
An A.P. with first term a and common difference d is given by a, (a+d),(a+2d),(a+3d),.....
The nth term of this A.P. is given by
The sum of n terms of this A.P.
|Sn= (n2)[2a+(n−1)d]=(n2)∗(first term + last term).|
Some Important Results:
Geometric Progressions Results to kept in mind
A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression
A G.P. with first term a and common ratio r is :a,ar,ar2,.....
In this G.P. nth term, Tn =arn−1
sum of n terms,
|Sn=a(1−rn)(1−r) when r<1|
Remainder and Quotient problem’s solving tricks
Let us try it using an example , when we divide 7 by 3 we get a remainder 1 which means 7=3∗2+1
Presenting it notationally let the two numbers be p and q , when we divide p by q we get p=kq+r where k is quotient and r is remainder
Dividing both sides of p=kq+r by k we get a result
Let us solve a question based in above result:-
The remainder is 57 when a number is divided by 10,00. What is the remainder when the same number is divided by 1,00?
(A) 5 (B) 7 (C) 43 (D) 57 (E) 570
Since it is given that the remainder is 57 when the number is divided by 10,00, the number can be expressed as 10,00n+57, where n is an integer.
Rewriting 10,000 as 1,00∗10 we get
Now, since n is an integer, 10n is also an integer. Let 10n=q , we get
Hence, the remainder is still 57 (by the p=kq+r form) when the number is divided by 1,000.
So,the answer is (D).
Method II (Alternative form):
Since the remainder is 57 when the number is divided by 10,00, the number can be expressed as 10,00n+57. Dividing this number by 1,000 yields
10,00n+57100 =10,00n100+57100 =10n+57100
Hence, the remainder is 57 (by the alternative form pk=q+rk ), and the answer is (D).
Some more sample questions
This question was in CAT 2005 question paper for 2 marks
Que :-What is the righmost non-zero digit of the number 302720?
Correct Answer: Choice (1).
The given number is a multiple of 10, so the last 2720 digits will be 0s.
The right most non-zero digit of the number will be the unit digit of the number 32720.
The unit digit of the powers of "3" follow a cyclicity of "4"
i.e., The units digit of 31 is 3
The units digit of 32 is 9
The units digit of 33 is 7
The units digit of 34 is 1. Then the cyclicity sets in.
The units digits of 35 is 3.
The units digits of 36 is 9 and so on.
In 32720 as 2720 is a multiple of "4", the number will have the same units digit as 34 which is "1".
Miscellaneous problems are those problems which do not fall under any head. They are rarely asked, and even when they do appear in a CAT paper they do not number more than one or two. They are basically used to check the mathematical aptitude of the students, and you cannot learn how to solve them. One way to solve questions based on this topic is to try back-substitution of answer choices, or to avoid these problems altogether.
Although for preparing for QA section you have to clear your basic fundamentals and practice thoroughly , here are some techniques you can use to solve the questions :-
|Name of topic||Weightage in %|
|Number Systems, LCM HCF||15|
|Mixtures and Alligations||6|
|Time, distance and speed||4|
|Pipes and Cisterns||4|
|Ratio and Proportion||4|
|Races and Games||4|
|Boats and Streams||4|
|Time and Work||4|
|Boats and Streams||4|
|Problems on Trains||4|
|Calendar and Clocks||2|
|Profit, Loss and Discounts||2|
|Progressions (AP, GP & HP)||2|
|Problems on Age||2|
|Average, Percentage, Inequalities||1|
|Simple and Compound Interest||1|
|Linear and Quadratic Equations||2|
Last year difficulty level of QA section was average , questions were basically formed to test the basic fundamentals of the students ,However you need to prepare really well for this section if you want to get enrolled in A,B,C, level IIM’s because QA is one of the section in which students had outshown in last 2 CATs
|Book Name||Author/Publisher Name||ISBN||Price||Book Reviews|
|How to Prepare for Quantitative Aptitude for the CAT Common Admission Test 5th Edition (Paperback)||Arun Sharma||1259027015||650/-|
|The Pearson Guide To Quantitative Aptitude And Data Interpretation||Nishit Sinha||9332528829||650/-|
|Quantitative Aptitude For Competitive Examinations Tips, Techniques, And Short-cut Methods||Guha Abhijit||0070706352||450/-|
|Quantum CAT||Sarvesh K Verma||9350944146||550/-|