CAT PreparationShortcuts for Quants Section

Overview of Quants Section

Numbers,Averages,Quadratic

8 to 10 questions

Geometry,Mensuration

8 to 10 questions

TSD,Mixtures,Alligations

6 to 8 questions

Permutations & Combinations,Inequaliti

es8 to 10 questions

Quants

• The perception with a lot of students with regards to CAT is that CAT is for Engineers. A non engineer finds it difficult as there is a lot of Math in CAT. Most of the students tend to give up on CAT as they can’t find how to break the Math conundrum. They learn formulae by rote and try to use the formulae in different sums in the Mocks only to realize that their scores are not improving.

Topics to be done:

Example 1:• Example: Lets take a question from CAT08• A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The

second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

• (1) 2 ≤ x ≤ 6  (b) 5 ≤ x ≤ 8  (c) 9 ≤ x ≤ 12  (d) 11 ≤ x ≤ 14 (e) 13 ≤ x ≤ 18• Solution:• Usually students who are used to formulae and equation will tend to use x as the initial amount

of rice and try to form an equation to solve the sum. A better way would be to go reverse way. Say the last person has no rice left after he was given half the rice plus half a kg of rice. So he would have (0+1/2) x 2 = 1Kg before the last customer came in. Similarly before the second customer had come the shopkeeper would have (1 + ½) x 2 = 3. Before the first customer came in the shopkeeper would have (3 + ½) x 2 = 7kgs which is the answer.

Example 2:

• X = √(4 + √(4 - √(4 + √(4 ….)))) to infinity. Then x equals  (CAT05)

(a) 3  (b) (√13 – 1)/2  (c) (√13+ 1)/2  (d) √13Solution:

• We know that √4 – anything will be less than 2. So we get √ 4 + (less than 2). Which should be more than 2 but less than 2.5. The only option that satisfied is c option with √13 is approximately 3.5. So (3.5 + 1)/2 = 2.25. The same sum can be solved by formulae but that will take time.

Example 3:• SUMMARY OF PERMUTATIONS &

COMBINATIONS

Contd.:

How to Increase speed in maths?

• Keep away from difficult formulae. The less formulae you know the better it is. Obviously you need to know basic formulae like 1 + 2 + 3 + … = n(n+1)/2 or (a+b)^2 = a^2 + 2ab + b^2. But don’t get into any new formulae you have not heard of. It will only slow you down.

• Learn all the tables,squares,fractions,percentages which will also help you in data interpretation.

Speed Maths:• Square of any two digit number: Easiest

method • Let me explain this trick by taking examples

67^2 = [6^2][7^2]+20*6*7 = 3649+840 = 4489similarly25^2 = [2^2][5^2]+20*2*5 = 425+200 = 625Take one more example97^2 = [9^2][7^2]+20*9*7 = 8149+1260 = 9409

Speed Maths:• How fast can you multiply the following numbers:

11 * 19 = ? 27 * 23 = ? 39 * 31 = ?According to this trick, the first part of the numbers should be the sameexample,in 11 * 19, 27 * 23, 112 * 118, 124 * 126 the first part of the numbers are same,now the second condition is that the second part of the numbers should have the sum exactly 10 as in11 * 19, 27 * 23, 112 * 118, 124 * 126

Only when both conditions are fulfilled, then the method works.Alright, now according to the method multiply the first part of the number with 1 more than the number, i.e. if first part is 11, then multiply with 12, if its 1 then with 2, and so on.11 * 19 = 2_ , 112 * 118 = 132_Next, multiply second part of both the numbers together to get second part of the answer, if it comes a single digit then put a zero in front else no need for zero, like in 11 * 19 = 209 , 112 * 118 = 13216

What can be done to improve maths?

• Go back to all the mocks you have solved and go through the questions again to search for better ways of solving. If you find it write it down next to the sum so that when you go through the paper again you could remember the methods you used. Also once before the exam go and check the shortcut methods you used to solve the sums. This would ensure that it is fresh in your mind when you solve the paper.

• -  Continue writing the usual Mock Papers and analyze it. Try to get better ways of solving it than that provided by explanatory answers.

• -  Go through the 5 previous CAT papers and see if you could get methods to solve the questions there. Understand this that CAT does not repeat questions, but the methods used to solve CAT sums can be repetitive as shown in the examples.

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