CAT 2022 notification has been released on July 31. IIM Bangalore will be conducting the exam this year. CAT entrance exam is the key to one's selection for the management courses offered by the prestigious IIMs. Time management is something that has always prevailed as an essential element in the exam. More specifically, time management for CAT QA section makes all the difference while attempting the paper.

For maximum students, the QA section of CAT exam is the toughest to crack. In order to secure a 99+ percentile in CAT Quant section, somewhere between 15-16 questions, out of the total tally of 22 questions, need to be accurately answered within the allotted time of 40 minutes.

Read the complete article to know some of the highly beneficial time-saving tricks that are crucial for solving questions in CAT Quantitative Aptitude section with optimum accuracy. These tricks for CAT QA section will help you in improving your time management skills and at the same time, make your calculations much easier, thereby increasing the number of questions you attempt in CAT 2022 exam. 

How to Approach CAT QA section?

The approach can be divided into 3 main rounds of problem-solving.

• The first round should be targeted towards the questions that are from the topics of your interest. They should not be lengthy and must give you a clear picture in the first reading. This round can go up to 25 minutes of your duration from the total allotted 40 minutes and you should try to cover as many questions as possible.
• The second round can be targeted at questions that you were confident of solving, even at the first reading, but were a bit lengthy and critical. Even if you utilize 15 minutes of the remaining time, both these rounds should fetch you 15+ correct answers.
• If you are still left with time, you can move on to further questions.

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Number System Tricks for CAT 2022

• HCF * LCM = Product of numbers(a*b)
• There are 2 methods for finding the LCM - Factor method and the Division method.
• The HCF is the factor of the difference of the given numbers.
  • For e.g. HCF of 30 and 42 Difference = 12(42-30)
  • Factors of 12 in descending order - 12, 6, 4, 3, 2, 1
  • Divide both 30 and 42 by the factors in the above order to check which number divides both completely, that number is your HCF.
• Dividend = (Divisor * Quotient) + Remainder
• If A and B are two numbers and are completely divisible by divisor D, then the given rules hold true:
  • A+B and A-B are also divisible by D
  • Product of A or B with any other integer is also divisible by D
• Sum of first n natural numbers = [n(n+1)] / 2
• Sum of squares of first n natural numbers = [n(n+1)(2n+1)] / 6
• Sum of cubes of first n natural numbers = [n(n+1)]^2 / 4
• Sum of squares of first n even natural numbers = [2n(n+1)(2n+1)] / 3
• Sum of squares of first n odd natural numbers = [2n(2n+1)(2n-1)] / 3
• Sum of first n even natural numbers = n(n+1)
• Sum of first n odd natural numbers = n^2

Time and Work Tricks for CAT 2022

Time and Work are interrelated in terms of their equation. The steps to minimize time along with simple calculations are:

• Take the LCM of the given set of numbers
• Add or subtract as per the question and requirement
• The obtained LCM will be the total work done
• Divide the total work with the result of step 2 to get your desired answer

Ques. X, Y, and Z can complete a piece of work in 5, 9, and 45 days respectively, working together, they will complete the same work in?

Sol. Take the LCM of 5, 9, and 45: 45

So individually, the work of X, Y, and Z is: 45/5, 45/9, and 45/45= 9, 5, 1

So, total work = 9+5+1=15

Thus, together, they can complete the work in 45/15=3 days

Time, Speed & Distance Tricks for CAT 2022

Some essential formulae that make these types of questions just as the breeze:

• Multiply by 5/18 when converting km/hr to m/s
• Multiply by 18/5 when converting m/s to km/hr
• Distance = [a/(x-y)]*y, where a is a certain distance amount and x & y are two different speed quantities
• Distance = [(x*y)/(x+y)]*a, where a is a certain time duration and x & y are two different speed quantities
• Time Taken = 2*[x-(y/2)], where x is a time duration in one mode of walking/transportation and y is another time duration for a different mode/pace of walking/transportation

Ques. If a rider covers a certain distance in 11 hours on a scooter, he covers half of the distance at a speed of 35 km/h and another half distance at a speed of 20 km/h. What will be the distance covered by him?

Sol.

• Time duration (a) = 11 hrs, Speed I (x) = 35 km/hr, Speed II (y) = 20 km/hr
  • As per the formula, Distance = [(x*y)/(x+y)]*a
  • Thus, Distance = [(35*20)/(35+20)]*11 = 140.03 km

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CAT 2022 Tricks for Boats and Stream 

Few of the critical formulae related to boats and streams:

• Net Downstream Speed = b+s, where b is the speed of the boat in still water and s is the speed of the stream. (Downstream is referred to when the boat is moving in the direction of the stream).
• Net Upstream Speed = b-s, where b is the speed of the boat in still water and s is the speed of the stream. (Upstream is referred to when the boat is moving against the direction of the stream).
• Speed of boat in still water = ½ * (Downstream speed + Upstream Speed)
• Speed of stream = ½ * (Downstream speed - Upstream Speed)

Ques. If a man rows 12 km downstream in 6 hours and 4 km upstream in 4 hours, then, how long will he take to cover 9 km in still water?

Sol. Speed of boat in still water = ½ * (Downstream speed + Upstream Speed)

        Thus, Speed = ½ * [(12/6)+(4/4)] = 1.5km/hr

        So, time taken for 9 km = Distance/Speed = 9/1.5 = 6 hours

CAT 2022 Tricks for Trains Based Problems 

Some of the critical formulae related to trains that make complex problems look easy are:

Ques. A train passes a platform in 35 seconds and a man standing on the platform in 18 seconds. If the speed of the train is 54 km/h, find the length of the platform.

Sol.

• As the time is provided in seconds, we convert the speed of the train in m/s.
  • Thus, Speed = 54 * (5/18) = 15 m/s
  • Now, as per the formula for the platform, time (t) = [(Length of train) + (Length of Platform)] / (Speed of train)
  • Thus, 35 = [L(t) + L(p)]/18
  • => [L(t) + L(p)] = 35*18
  • => [L(t) + L(p)] = 630 ….... eq(i)
  • Now, for the man standing, time (t) = (Length of train) / (Speed of train)
  • Thus, 20 = L(t) / 15
  • => L(t) = 20*15
  • => L(t) = 300
  • Now, putting the value of L(t) in eq(i),
  • 300 + L(p) = 630
  • => L(p) = 630-300 = 330 meters 

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CAT 2022 Tricks for Percentage Based Problems

For percentage problems, a mental calculation is extremely important. Some additional tips that can aid you in the cause are:

• If out of the total quantity 70% are bad, i.e., 100% - 60% = 30% are good.
• While calculating maybe, 50% of 600, the ‘00s in 600 and the ‘00s in 100 get canceled, so simply calculate 50*6 = 300.
• 70% of a quantity can be written as simply, 0.7. So, multiply 0.7 with the given figure and put the decimal in the right spot. Quick, right?
• If the Price of Oranges, maybe, increases by 5%, then the reduction required in the consumption so as to maintain the original expenditure will be = 5/(100+5) x 100 = 4.76%
• The total number of students is given as 1850, what is the difference between the number of students studying computer and commerce and chemistry and arts?
  1. Add up the %figures for computer and commerce = 43% (as given)
  2. Add up the %figures for chemistry and arts = 31% (as given)
  3. Get the difference between the 2 sets = 43-31 = 12%
  4. Now, calculate the difference percentage = 12% * 1850 = 222 students
• If the population of a town is, say 20,000 people as of today, and if the population increases at 6% p.a., then what will be the population after 3 years?
  1. Formula being – Population x (1 +R/100)n, where, n is the number of years
  2. Population after 3 years = 20,000 x (1 + 6/100)3 = 23820 approx.

Ratio and Proportion Tricks for CAT 2022

When it comes to ratio and proportions, the pivotal element(s) that matter are the relations and interrelations, likewise:

• The equality of two ratios is known as proportion i.e. a/b = c/d
• So, If a/b = c/d , then it is also equal to a+c/b+d
  1. Then, a^2:b^2 is a duplicate ratio of a:b
  2. a^3:b^3 is a triplicate ratio of a:b
  3. a^1/2:b^1/2 is a sub-duplicate ratio of a:b
  4. a^1/3:b^1/3 is a sub-triplicate ratio of a:b
• If a/b = b/c = c/d =...... so on, then a,b,c,d... are in G.P.
• If a>b and the same positive number is added to each term, the ratio decreases.
• If a<b and the same positive number is added to each term, the ratio increases.
• If we multiply or divide any number, there will be no effect on the ratio.
• If a:b is a ratio,
  1. If a/b = c/d , then a+b/b = c+d/d
  2. If a/b = c/d , then a-b/b = c-d/d
  3. If a/b = c/d , then a+b/a-b = c+d/c-d

Simple and Compound Interest Tricks for CAT 2022

Even if problems related to these topics may churn out to be difficult just by reading it, simply get these formulae within your fingertips and it can be a different story altogether.

• Simple Interest = (P*R*T)/100, where P=Principal, R=Rate of Interest, T=Time
• Amount = P*(1+R/100)^T
• Compound Interest = P*(1+R/100)^T - P
• Amount = Principal + Compound Interest

Ques. The MRP of a bicycle is Rs.3000. The shopkeeper first gave a discount of 15% and then a discount of 20%. Find the price at which one would purchase that bicycle.

Sol. Effective discount at which the bicycle was sold: a + b - ab/100

       Where a = first discount, b = 2nd discount.

       Thus, 15 + 20 + 300/100 = 38%

       Thus, the final selling price is: 3000 * [(100-38)/100] = 1860