Formula & Tip for CAT

Formulae & Tips for CAT Brought to you by

The Competition Master 126, Industrial Area-1, Chandigarh - 160002 India

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The Competition Master

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FORMULAE AND TIPS FOR CAT There are several things that you have to keep in mind: a) Differentiate between speed and hurry: Many students think that speed means making guesses and blundering on. This is wrong. Do the q u e s t i o n s w i t h concentration. Don’t worry about questions you could not attempt, because you possibly cannot do 180 questions in two hours. Speed means avoiding u n n e c e s s a r y calculations. ☛ Hot tip: Allow yourself 30 seconds to glance over the section before starting. This will help you locate the easy questions. b) Keep your cool. There will be some difficult

questions and some easy ones. When you hit the difficult ones, you must stay calm. Skip a few questions. Don’t panic, because if you do, you have almost certainly lost the battle. ☛ Hot tip: If you become tense, just close your eyes and take a few deep breaths. Return to the paper once you are composed again. c) Manage your time: Keep a watch before you. Write down the time when you should move over to the new section. Don’t be tempted to stick to the previous section when the time is over. Just keep moving on. ☛ Hot tip: Each section should be

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attempted in 28 minutes. Allow yourself 2 minutes to go back on questions you could not solve, or for making some intelligent guesses.

COMPREHENSION

☛ Tips for speed reading Next time you are reading a paper, try this. First stage: Sweep your hand from left to right across the page so your finger underlines each line. Follow your finger with your eyes. The difficulty of the material determines the speed, but move your hand a little faster than your eye can follow comfortably. Make your eyes work to keep up. Soon you will find yourself reading whole phrases and ideas. As it gets easier, keep increasing the speed. As you improve, instead of sweeping whole lines with your finger, just sweep the middle part. Your eyes

will scan the beginning and the end of the line automatically. When you’ve mastered this, your reading speed will be between 500 and 1,000 words per minute. This is the practical limit. Second Stage: The next speed increase comes from area reading. Instead of sweeping lines, use broader hand motions to make a series of zigzags of S’s down the page and read several lines at once. You can even read backward as your hand moves to the left. You’ll comprehend very little at first, but if you keep your eyes following your finger, you’ll find yourself absorbing whole chunks of the page at once. Six hot tips for comprehension: 1. Read the questions before you read the passage. This will help you locate the ideas faster.

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2. Force your eyes to sweep entire phrases and ideas. Don’t read word for word. Avoid pronouncing words as you read. 3. Don’t reread sentences. Don’t skip lines. 4. Let the context define unfamiliar words. Don’t stop to look for them. 5. Adjust reading speed to the type of material. 6. Look for key ideas and phrases in each paragraph. What you should read: Read the editorial page of one good English newspaper everyday by the above method. This should not take more than 15 minutes everyday. Make it a point to read the economic articles and business news. Look up difficult words that you encounter in a dictionary. Also read a magazine on current affairs. Your best bet is THE COMPETITION MASTER, which has a regular management section. Read the debates

regularly as well as the editorials, features and current affairs and Business GK. This will help you form your opinions and increase your awareness. A number of people who have cleared CAT have told us that the magazine was priceless for their preparation. Additional reading and exercises: Norman Lewis: How to Read Better and Faster.

VERBAL ABILITY It is important to have a good vocabulary, know good grammar and again, have the reading habit. Vocabulary: A good vocabulary is built up over time. Reading helps. Check up important words in a dictionary. Or take a good word-list, such as the one published in Master Guide for MBA Entrance, and learn the usage of the words. Knowing about

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roots of words helps. ☛ Hot tip: The best way to learn a word list is through vocabulary cards. Making them is an investment, because they will be helpful over a period of time. Analogies, Odd man out: This means finding relations among words. What is the relation between SALT : SALTY? We can say that salty things contain salt. The best choice would be COW : BOVINE, because that best suits the relationship. A good vocabulary helps in such questions. ☛ Hot tip: Do as many analogies as you can, to know the kind of relations that can be asked. The Test of Reasoning in THE COMPETITION MASTER contains analogies regularly. If you do it every month, you will have a good understanding of

analogies. Arranging sentences, blanks: These are tricky, especially if they contain large sentences. The selections are usually from current newspapers, so extra reading increases speed in such questions. ☛ Hot tip: Usually, the answer can be obtained by getting at the central idea and thinking what it should start or end with, or by working from the choices. Do not waste time arranging the entire paragraph.

QUANTITATIVE ABILITY

The importance of knowing your tables, decimals, fractions and formulae cannot be overemphasised. Many questions can be solved by looking at the choices. Develop this ability and your speed will surely increase. We give below

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some things which can be remembered easily. 1. Numbers: Remember the power of 10 in the following: millions (6), lakhs (5), billions (9) and crores (7). Some questions may confuse on the units. 2. Rational irrational

and numbers:

Numbers which can be expressed in the form p , where p and q are q integers and q ≠ 0 .

Examples of numbers are

rational

1 3 −8 , , , 0, 3, 150 etc, 2 5 5

Irrational numbers are those which when expressed in decimal would be in nonterminating and nonrepeating form. Examples of irrational numbers are: 2, 3, 5, 7, and so on. 3. Division: Dividend = (Divisor ×

Quotient) + Remainder. 4. Tests of divisibility: A number can be checked for divisibility by the following methods: By 2: If the last digit of the given number is even or zero. By 3: If the sum of the digits of the number are divisible by 3. By 4: If the sum of the last two digits of the number is divisible by 4. By 5: If the last digit of the number is either zero or 5. By 6: If the number is divisible by 2 as well as 3. By 8: If the sum of the last three digits of the number is divisible by 8. By 9: If the sum of the digits is divisible by 9. By 10: If the last digit is zero. By 11: If the difference between the sum of the odd digits and the even digits in a number is either zero or divisible by 11.

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5. Short cuts for multiplying: Large multiplication should be avoided. Instead, look for shortcuts to do the sums: (a) To multiply by 99, 999, 9999 ... : Place as many zeroes after the number and subtract the number. (b) To multiply by 5n: Put n zeroes to the right of the number and divide it by 2n. 6. HCF and LCM: The HCF of two or more numbers is the greatest number that divides each one of them exactly. The LCM of two or more numbers is the product of the highest powers of all the prime factors that occur in the numbers. Product of two numbers = HCF × LCM. HCF of Fractions =

LCM of numerators . HCF of denominators

LCM of Fractions =

HCF of numerators LCM of denominators

7. Simplification: To simplify an expression, always use the order specified in BODMAS: Brackets, Of, Division, Multiplication, Addition and Subtraction. 8. Square roots: Learn the square roots upto 16 and squares upto 32. Make memory cards to help remember these figures. ☛ Hot tips: 1. Square roots can be approximated by using r a2 + , where a is the 2a nearest root of the number and r is the remainder. 4 Hence 85 = 92 + 18 , which gives the square root of 85 as 9.22 approximately. One can approximate square roots easily by this method. 2. To square a number, try putting it in the form (a + b)2.

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Thus 115 = (100 + 15) = 1002 + 152 + 2(100 x 15), which can be easily computed. 2

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8. Percentages: Learn the fraction equivalents. 1 = 25%, 1 = 33%, 1 4 3 5 1 = 20%, = 16% etc. 6

Many questions can be solved faster if we know these figures. To find growth percentage or percentage change, always use: New Quantity – Old quantity ×100 Old Quantity

9. Averages: Averages are found by adding up the values and dividing by the number of values. 10. Ratio and proportion: Can be written as a : b a

or b . If a : b = c : d, then bc = ad. 11. Partnership: The share of profits divided between two partners is:

(Amount of money invested by A × No. of months invested by A) : (Amount of money invested by B × No. of months invested by B). 12. Shares: It is important to know the following terms: Face value: The price at which shares are issued. Always a round figure. Market value: The price at which shares are traded. Will fluctuate and will seldom be a round figure. If market value = face value, the shares are traded at par. If market value > face value, the share commands a premium. If market value < face value, the share is at a discount. Return: The interest earned by the shares after one year. Always calculated on face value. Yield: Return calculated on what is actually invested. Calculated by dividing return by market

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value. Brokerage: When you buy a share, the buyer has to pay the brokerage, which is added to the market price. When shares are sold, the seller gets the price after the broker deducts his brokerage from the market price obtained. 13. Profit and Loss: Profit = SP - CP. Loss = CP - SP. Gain or loss per cent

15. Time and distance: Remember the formula, Distance = Speed × Time

Gain or Loss × 100 CP

where x and y are the speeds. To calculate when two bodies will cross each other, use the formula:

=

Marked price is what is marked in the shop. It is neither CP nor SP. 14. Interest: P ×R × T 100 In compound interest, R n A = P(1+ ) . 100 SI =

It is advisable never to use this formula but work from simple interest, by calculating interest on interest.

To convert km/hr into m/s, multiply by 5 . 18

To convert m/s to km/hr, 18

multiply by 5 To calculate average speed, use the formula: Average speed =

Time =

2 xy (x + y)

Distance . Relative Speed

Speed is added when bodies are going in opposite directions and subtracted when bodies are going in the same direction, to find the relative speed. 16. Boats and streams: A boat rowing in still water

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at the rate of x km/hr will be affected if it goes into a stream which is flowing. If the rate of the stream is y km/hr, the rate of the boat when it goes downstream will increase and will be (x + y) km/hr. However, if the boat goes against the current, its speed will decrease and will be given by (x - y) km/hr. Rate in still water is given by: +

1 {(rate with the current) 2

(rate

against

the

current)} Rate of current is given by:

1 {(rate with the current) 2

–(rate against the current)}. 17. Time and work: a person can do a piece of work in x days, the work done by him in 1 day will be 1 . x

Conversely, if 1 day’s 1

work of a person is x , then

he can finish the work in x days. If A is faster than B and is twice as good in his work, the ratio of the work done by A and B will be 2:1. However, the ratio of time taken by A and B will be in the ratio of 1:2. 18. Areas and volumes: Rectangle A = L × B a) Area = Length x Breadth b) Diagonal2 = Length2 + Breadth2 Square Area = Side2 1 = Diagonal2 2 Four walls of a room Area = 2(Length+Breadth) × Height Triangle with sides a, b, c Area = s(s - a)(s - b)(s - c) where s =

1 (a + b + c ) 2

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where s = 1 (a+b+c) 2

Triangle with base b and height h Area =

1 ×b×h 2

Equilateral

triangle

with side x 3 Area = (x2) 4

Parallelogram Area = Base × Height Rhombus with diagonals d1 and d2 1 Area = (d1 × d2) 2

Trapezium Area =

1 2

(sum

of

parallel sides) × height Quadrilateral with diagonal d 1 (d)(sum of perpendi2

culars on d from opposite

vertices) Circle with radius r Circumference = 2r Area = r2 Area of sector = r2/360 Volumes are given by the following table:

Solids Cube with side x Volume = x3 Surface area = 6x2 Longest diagonal = 3x Cuboid with length l, breadth b and height h units Volume = l x b x h Surface area = 2(lb + bh + lh) Longest diagonal = l2 + b2 + h2 Cylinder with radius r and height h Volume = πr 2h Curved surface area = 2 πrh Total surface area = 2πrh + 2 πr 2 Sphere with radius r 4 Volume = π r 3 3 Surface area = 4 πr 2 Cone with radius r and height h Volume = 1 πr 2h 3 2 Slant height l = r + h 2

Curved surface area = πrl 19. AP, GP : In AP, to find the nth term and sum of the series, use the following:

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nth term = a + (n -1)d, where a is the first term and d is the common difference. n Sum = {2a + (n -1)d}, or 2 n Sum = (a + l) 2 where l is the last term. In GP, nth term = a.r n-1, where r is the common ratio. Sum of n terms (rn .1) =a if r >1, r-1 2(1-rn) and if r