CAT Quant 42 Hours Preparation | CAT 99%ile Instructor

Define prime and composite numbers by examining factors and divisors. Show primes have two factors, and composites have more than two, with five and six as examples.

Learn how prime factorization writes a number as a product of prime factors, with examples like 12 and 980, using divisibility to extract primes such as 2, 5, and 7.

Learn how a variable acts as a placeholder for an unknown value, convert words to equations, and solve by substitution with examples of ages and costs.

Check whether a number is prime by testing divisibility up to the next square. Factors occur in pairs; primes are 6k plus or minus one, but form alone isn't enough.

Practice prime factorization by repeatedly taking out factors of 2, then 3, to express numbers like 288 as 2^5·3^2 and 512 as 2^9, using divisibility rules.

Explore the concepts of the highest common factor (HCF) or greatest common divisor (GCD), and learn to find it by listing factors, identifying common factors, and using prime factorization.

Learn to find the lowest common multiple (Elsom) using multiples, with 12 and 18 showing the result 36, and apply common factors or prime factorization.

Practice solving scaf and hcf by factoring out common factors, then compute the elsom (lcm) and contrast with ecf using the examples 28, 42, 70 and 25, 15, 21.

Solve a practice problem that shows filling 120, 180, and 240 liters of oil into equal-capacity bins, revealing 60 liters as the greatest bin capacity.

Find the least common multiple of 12, 15, and 21 to equalize biscuit counts across brands, resulting in 35 packets of A, 28 of B, and 20 of C.

Discover how to find the hcf and lcm of fractions by using the gcd of numerators and the lcm of denominators, with emphasis on fractions' simplification.

Explore proper, improper, mixed, and equivalent fractions, learn converting between mixed and improper forms, and apply numerator–denominator operations to establish equal fractions.

Learn to add and subtract fractions by converting to a common denominator using the least common multiple, illustrated with 2/3 plus 4/5 equals 22/15 and 7/9 minus 1/2 equals 5/18.

Learn to compare fractions by converting them to like fractions with a common denominator, using common factors to simplify, then compare numerators to identify the larger fraction.

Learn how to multiply fractions by multiplying numerators and denominators, and divide by multiplying by the inverse, with examples like 7/13 times 3/5 and 2/5 divided by 3/7 equals 14/15.

Master the expanded form of a decimal by multiplying each digit by its place value, from the integer part to tenths, hundredths, and thousandths, illustrated with 78.325.

Master addition and subtraction of decimals by aligning decimal points, padding zeros, and carrying over, then subtracting with the decimal point aligned and preserving order.

Multiply decimal numbers by treating them as whole numbers, then shift the decimal point left by the total number of decimal digits; illustrated with examples like 3.5×2 and 2.34×3.12.

Learn to divide decimal numbers by converting to whole-number division, moving the decimal via multiplying by a power of ten, and simplifying to the quotient.

Classify numbers into natural, whole, integers, rational, and irrational. Learn how rational numbers use P by Q with Q not zero; irrational numbers differ; both are real numbers.

Decimal expansions reveal whether a number is rational or irrational. Rational numbers produce terminating or non-terminating recurring decimals, while irrational numbers have non-terminating, non-recurring expansions.

Convert terminating decimals to p/q form by multiplying numerator and denominator by a power of ten and simplifying, illustrating that terminating decimals are rational numbers.

Learn to convert non terminating recurring decimals to rational numbers by shifting the repeating block with multiplication and solving for X, with examples like 0.3 bar and 0.345 bar.

Learn a shortcut to convert non terminating recurring decimals to p/q by using a repeating-block denominator of nines and subtracting the nonrepeating part, with examples.

Examine whether operations with irrational numbers yield irrational results, highlighting that pi is irrational and that pi minus pi equals zero, a rational result.

Apply the bodmas rule to determine the order of operations, prioritizing brackets, powers, then division and multiplication, followed by addition and subtraction, evaluating left to right when priorities are equal.

Explore four types of brackets and learn to open inner brackets first to simplify expressions, using color-coding ideas to match opening and closing brackets and solve step-by-step.

Learn the laws of exponents: add exponents with the same base, subtract in division, apply zero and negative exponents, and combine powers with (a^m)^n or (ab)^m when exponents match.

Explore the laws of exponents, including real, rational, and irrational exponents, and why negative exponents become fractions. Practice simplifying expressions like 2^-7 and (3/4)^-2.

Explore how fractional exponents equal roots, such as square roots and fifth roots, and simplify expressions like 4^(5/2) and 32^(2/5) using exponent rules.

Practice problems on rational powers show combining like bases and exponents, using rules for addition and subtraction of exponents, reciprocal identities, and manipulating different bases via common denominators and roots.

Explore even and odd numbers, their end digits and divisibility by two, and note that zero is even; decimals are neither even nor odd.

Learn how to solve linear equations by balancing left-hand and right-hand sides around the equality sign, using add, subtract, multiply, divide, and transposing to isolate x for a definite value.

Let the number be x and set x/2 = x/3 + 5, then transpose and use a common denominator of six to find x = 30.

Explore distributivity by applying the distributive property to sums, products, and equations, with worked examples of expanding brackets, cross-multiplication, and solving linear equations.

Explore solving linear equations with multiple variables, starting with two-variable problems and extending to three variables through elimination and substitution, with practical word problems on flats and fruit costs.

Practise Problem 1, 2, 3 cover solving three algebraic word problems: cows and chickens by heads and legs, daughter’s age from mother’s age, and fixed plus variable travel costs.

Identify no solution, unique solution, or infinite solutions for a two-variable system using the coefficients and the ratios a1/a2, b1/b2, c1/c2, with concrete examples.

Explore key algebraic identities, including expansions of (a+b)^2 and (a+b)^3, sums and differences of cubes, and a geometric view of a^2 - b^2.

Explore the basics of percentages, unitary method, and converting fractions to percentages, with examples like 20/40 equals 50% and computing what percentage of X is Y.

Learn how to compute absolute and percentage changes using Mr. Han's money example, defining percentage change as the change divided by the initial amount and showing a 200% result.

Compute the percentage point change from 40% to 50% and the corresponding percentage change, 10 percentage points and 25 percent, to illustrate how pass percentage thresholds are compared.

Master how to increase or decrease a value by a given percentage using multiplication by factors like 1.25 or 0.75, illustrated with 20 by 25% and 20 by 25% decrease.

Practice problem on percentage change and score comparisons: derive Amy's score from Bob's 80 and Andy's 85, then compute how much more or less Amy scored than Andy in percentage.

Learn constant product problems by keeping expenditure constant while price changes, using shotgun shortcuts to adjust consumption, with a 20% price rise yielding about 16.67% drop.

Convert fractions to percentages using key reciprocals. Memorize common values like 1/2 equals 50% and 1/3 equals 33.33% to speed up calculations.

Compute how a 12.5% price rise and 180 km monthly travel at 15 km per liter lead to a 20 km reduction in riding to keep expenditure constant.

Practice problem shows maintaining a rectangle's area while increasing length by 20 percent; reduce breadth by one by six (sixteen point six seven percent) to keep the area constant.

Learn a fast method for income comparison problems. See how a percent increase in one income leads to a corresponding percent decrease in the other, with 20 percent examples.

Practice problem 1 shows that a salary 30 percent higher than an ombudsperson equates to a 23 percent decrease when compared to the target; demonstrate shortcut and logical methods.

Solve a consecutive salary hikes problem with a 32% net increase; the second hike is half the first, yielding 20% then 10% as the correct sequence.

Compute the arithmetic mean by summing values and dividing by count, as with 21, 18, 15, 16 yielding 17.5, illustrating the center point.

Learn two essential average-based CAT quant problems: updating the average after the sixth game and finding sixth-game minutes, using a fast logical method over the conventional approach.

Visualize the 30 games at 50 minutes and the 35 games at 55 minutes to determine the minutes in the last five games. This approach yields 25 minutes.

Resolve a CAT practice problem on averages and primes by finding the total games so the new average after a 91-point game is a prime under 65.

Practice problem on averages: twenty-nine students have a sixty-five average, a new student with eight joins, and the average becomes sixty-five point five after distributing fifteen marks across thirty students.

Apply average change methods to a class problem: compute the old sum, set the new average with the teacher's age, and use conventional and shortcut approaches to find 35.

Solve a word problem on averages by tracking the change from 26 to 25 after one employee quits, using both conventional and shortcut methods to find the quitter's age, 45.

Learn how to maximize the number of players scoring at least eight goals among 16 players with an average of six, given a minimum of two and maximum of ten.

Solve a CAT quant average problem: eight members, 60 kg average; two move away, two join by marriage, new average 58 kg; movers 66 kg, new members 58 kg.

Discover how average age problems work: a group's current average X, future averages after years added, birth timing, and total ages with practice questions.

Explore a four-sibling age problem by computing the current average age, the five-years-ago average, and the six-years-later average to compare age progression.

Work through an eight-member age problem: track deaths at 70, births, and year-by-year totals to compute the current average age and identify the nearest option.

Average speed equals total distance divided by total time, not the mean of speeds; for A to B back at 40 and 50 km/h, it's 400/9 km/h.

Compute average speed for a journey in which one-fifth of the distance is traveled at 2 km/h and the rest at 3 km/h, as shown in CAT quant preparation problem.

Learn how to compute the average of the first n natural numbers using the sum formula, deriving (n+1)/2, with examples for 100 and 999 numbers.

Learn how to compute a combined average using weights, summing weighted values by group sizes. See two perspectives: class averages and paper-based weights to derive the overall score.

Compute the overall average age from two divisions by summing ages (20 into 13) and (10 into 14) and dividing by total students (30), yielding 13.3 years.

Explore mixtures and alligation to find ratios from group averages, using the combined average and differences to relate counts, as with boys 40 and girls 60 averaging 52.

Master profit and loss, mixture problems, and percentage challenges using ratio and allegations method, plus simple interest calculations through practical shopkeeper scenarios.

Solve a staff age puzzle: 120 employees, initial average age 25, males to females 2:1; after changing counts to keep 120 and new average 22, the male average is 31.

Learn to compute the weighted average of B and C's ages by deriving the employee ratio from given averages, then verify with a second method; the result is 29.5 years.

Solve a 90-litre milk mixture problem where 15% water makes it 85% milk, replace part with pure milk to reach 95% milk using a 1:2 milk-to-water ratio.

Explains a shortcut for a special type of problem using an eight-liter vessel, removing B liters and adding B liters of liquid B, repeated n times, with a derived ratio.

Apply successive replacements to solve ratio and percentage problems, illustrated by milk to water after three operations and coconut juice after four operations, yielding 8:19 and about 66%.

Learn how to find the median by sorting data and averaging the two middle values for even sets, and identify the mode as the most frequent number.

Solve quiz-style cat quant questions on percentages, averages, age problems, votes, mixtures, speeds, ratios, and simple interest with step-by-step video solutions.

The lecture explains the basics of interest, defining creditor, debtor, and principal, and contrasts simple and compound interest with yearly examples.

Compare simple interest and compound interest by calculating on a fixed principal over three years at five percent, highlighting how interest accrues on the principal versus accumulated amounts.

Apply the simple interest formula P × T × R / 100 to compute interest and total repayment, illustrated with 1000 at 10% for 3 years (300 interest, 2300 total).

Apply the simple interest formula to find the rate: given principal 8000, time 5 years, and interest 1200, compute rate as 3 percent.

Compute the interest Sara pays on an $800 loan at 10 percent per year for nine months using simple interest and converting time to the same unit.

solve a cat quant problem using simple interest on two loans, 800 and 1600, with the second at double the rate for nine months, yielding 10 percent per annum.

Explore compound interest as successive percentage changes, learn the formula for amount equals principal times (1 + r/100)^n, and apply with half-yearly and quarterly compounding examples.

Solve a compound interest problem with principal 1800 at 5% per annum for two years, compute the amount and interest, and identify the interest as 184.5 dollars.

Solve a practice CAT problem on compound interest with half-yearly compounding, converting 10% per year to 5% per half year and applying it for three six-month periods using (1.05)^3.

Solve a compound interest problem by testing options to find the annual percentage rate that turns 2000 into 5488 in three years, using 50% and 40% as checks.

Explore how the difference between compound interest and simple interest over two years is calculated, using a sample problem and three solution approaches, including a logical, detailed, and option-based method.

Compare simple and compound interest after two years on a principal, show how compound interest yields higher amounts, and derive the first-year interest as fifteen percent of the principal.

Test the difference between simple and compound interest by evaluating options and matching first-year interest to the principal, concluding that ten thousand by three (option C) is correct.

Compare simple interest of 20 percent for three years on $1,000 with compound interest at 15 percent, and determine the difference in interest earned.

Depreciation explains how asset value declines over time, unlike compound interest, with the formula final value equals initial value times (1 − rate/100)^time and wear and tear examples.

Apply annual depreciation of five percent to a thousand-dollar refrigerator and compute its value after two years, showing a compound-interest-like reduction to 902.5 dollars.

Treat population growth like compound interest to reverse-calculate the initial population from a three-year, 20 percent annual increase, using option checks to verify whether the result matches 1,244,416.

Identify the net six percent increase from birth rate and death rate, apply it to the initial population of 300,000, and project the population after two years to 337,080. Avoid the common error of applying rates separately to the base rather than to the population.

Define the simple annual growth rate (sga) and show how to compute it from year-to-year bookshop sales. Demonstrate that cagr aligns with simple interest in steady or varying growth scenarios.

Compute the compound annual growth rate (CAGR) from a three-period sales example, showing 100 million growing to 133.1 million at 10 percent annually, equal to compound interest.

Calculate CAGR by applying a 20 percent annual growth to 10 million over three years to reach about 17.2 million, using a trial-and-check elimination method.

Master the basics of ratios and proportions, including expressing ratios as fractions and percentages, comparing ratios with common denominators, and data sufficiency insights.

Apply ratio reasoning to two problems: with swimmers to runners 4:5 and 60 runners, swimmers equal 48. With red to yellow 2:3 and total 60 flowers, yellow equals 36.

Explore how ratio as a fraction changes when you adjust the numerator or denominator, keeping one constant or changing both, using examples to compare values.

Analyze how to increase the sports-to-fashion magazine ratio in a library by applying equal additions and swapping actions, with simple numerical examples and reasoning.

Learn to compare three-item ratios by using common terms and lcm to make denominators equal, illustrated with a:b:c = 8:12:15 and a library fiction to nonfiction ratio example.

Solve a two-category age problem with history and geography teachers; determine geography's share of the total as 2/5 using h+g=t and 0.4h+0.7g=0.52t.

Combine the ratios f:n = 3:4 and f:r = 2:5 to get f=6x, n=8x, r=15x; with total 29x as a two-digit limit, the maximum nonfiction is 24.

Solve a ratio problem linking screws, bolts, and nuts by combining 4:3 and 4:5 with the LCM, under 50 nuts, and identify the correct screws count.

Explore modifying ratios by adding or subtracting from numerator or denominator, using a 3:4 rose-to-tulip example totaling 210 to remove 60 roses for a 1:4 ratio.

Apply a 7:3 ratio to allocate 50 million stars into red and blue groups. Add blue stars so red becomes 50% of total, yielding 20 million blue stars to add.

Explore proportions and ratios; learn that ad equals bc when a/b equals c/d, and continued proportions yield a/b = b/c, linking density problems.

Use a proportion to estimate the lake’s total fish: 5,000 tagged and 100 of 1,000 sampled are tagged, giving a total population of 50,000.

Explore direct and inverse variation, learn the notation of direct and inverse proportionality, and express them as a = k b or a = k / b with examples.

Apply direct proportionality between coal consumption and distance at a constant speed of 40 mph to compute coal for 240 miles, yielding 12 tons.

Practice problem on direct variation: the score is proportional to the square of bullseye hits in archery. With four hits yielding 64 points, determine eight-hit score and constant k.

solve a balanced seesaw problem using inverse weight–distance relation from the fulcrum; with Alice at 50 pounds and 5 feet, Bob sits 2.5 feet to balance.

Solve a practice problem on inversely proportional acidity to the square root of citrus fruit counts; compute lime acidity for 100 fruits when lemon acidity is 8 at 400 fruits.

Explore combined variation by uniting direct and inverse relations into A = k B / C, and apply e = k a / f in machine efficiency problem, yielding 500.

Compute the cone volume using v = k h a; determine k from 48 = k 8 18, then v = (1/3) 9 20 = 60 cubic feet.

Learn how speed equals distance by time, expressed in kilometers per hour, and how distance and time relate through direct and inverse proportionality.

Explore a practice problem where distance is constant and speed is inversely proportional to time, yielding a 2:1 speed ratio for a 15- and 30-minute trip.

Explore unit conversions for speed, distance, and time, including kilometers, meters, miles, and time units. Learn key relationships like km/h to m/s and mph, and hour to seconds.

calculate average speed by dividing the total distance by the total time for a journey. avoid averaging segment speeds; use total distance and total time instead.

Compute average speed across multi-leg trips by applying total distance divided by total time, with examples on varying leg speeds and equal-distance segments.

Explore proportionality in motion through practice problems 1-4, learning how speed changes affect travel time for a constant distance using speed–time relationships.

Learn to solve meeting-based questions by applying distance constancy and speed-time relationships, using the A to B example to compute where and when they meet, starting at 4 p.m.

Analyze a same-start-time travel problem with John and Clara, derive speed ratios from the inverse relation between speed and time, and locate their meeting time using constant distance.

Practice problem on not same starting time uses Andy at 2 p.m. and Donna at 4 p.m. with uniform speeds to determine their meeting time at 5:49 p.m.

Explore train meeting problems using time and distance ratios, speed proportional to inverse time, and multi-train scenarios to determine meeting points and arrival times.

Apply uniform speeds and distance time ratios to determine the meeting time of Abhilasha and Donna, concluding they meet at 5:20 p.m.

Solve a two-traveler speed problem where Andy and Donna meet at six after starting at 2 and 5, using inverse speed-time ratios to determine Andy finishes at 8 p.m.

Andy and Donna travel toward each other on a 60 km route with uniform speeds; Andy's 6-hour trip and Donna's 3-hour trip yield a meeting 33 1/3 km from A.

Walkers start at opposite ends of a 100-meter path; with constant speeds, the first meet is 40 meters from X, and the tenth meet lies 60 meters from X.

Learn to analyze relative speed when two bodies move toward each other or in the same direction by treating one as stationary and measuring the other’s speed. Apply the method to compute meeting time using the relative speed, illustrated by speeds 30 and 20 km/h and a 100 km distance.

Apply the relative speed concept to a chase: Meenu closes a 0.3 km lead from Manu at 3 km/h relative speed, and Manu runs a total of 0.8 km.

Solve a boat problem: determine the current speed given 100 km upstream in five hours and downstream in two hours with the downstream speed reduced by 50 percent.

Explore four relative speed problem types, including moving and non-moving bodies, opposite and same directions. See a train crossing example and apply the relation time is distance over speed.

Calculate the crossing time of a 200-meter train relative to a passenger on a parallel-track train by applying relative speed and converting km/h to m/s, 28.8 seconds.

Explore circular track races with speeds 50 and 30 m/min on a 2500 m track, analyzing same-direction and opposite-direction meet times, meeting locations, and repeats using relative speed.

Solve circular-track relative-motion problems by comparing distances and speeds, using time equivalence to find lead, speed ratios, and meeting points in same and opposite directions.

Solve escalator based problems by analyzing visible steps, directions, and the escalator’s movement as you compare steps taken by individuals when moving up versus down.

solve a time zone problem with two cities 3000 km apart and a 30 km/h wind, determining the time difference and train speed: 1 hour and 130 km/h.

Master the basics of work and rate through practical examples with two workers and two pipes and cisterns, learning to convert fractions to percentages and solve combined work problems.

Explore work-rate problems using fractions and percentages to compute combined daily work, total days, and earnings division based on each person's contribution.

Explore negative work by analyzing net progress from cat, fox, and bee (20%, 5%, −10% per day) and apply it to a tank with pipes (1/10, 1/5, −1/8 per hour).

Solve practice problems on work rates: filling and emptying a tank with pipes and a hole. Learn to use fractions, percentages, and alternating schedules for multiple workers.

Practice problems 7–9 cover snail escape with daily net gains and a three-pipe tank filling scenario. The discussion emphasizes step-by-step calculation and recognizing sequential vs non-simultaneous events.

Explore a shortcut for special work-rate problems, derive C = sqrt(A × B) from the together and individual times, and apply it to solve Bob and John's problem.

Learn how work equals work rate times time and how to express work in man-days; explore adjusting men and time to handle workload increases and percentage changes.

Solve work-rate problems using man-days and the product constancy rule, with examples on hiring rates, project completion times, and arithmetic series for daily worker increases.

Use the volume principle to estimate work: volume is proportional to man hours, solving a contractor problem to determine required men for given wall dimensions and days.

Explain efficiency in work problems, showing efficiency inversely proportional to time, and compare Pande, Hene, and Bandha with twofold and threefold efficiency.

Practice solving work-rate problems by analyzing combined daily progress for Bob, John, and Tanya using percentage and fraction methods to determine days to complete the work.

Explore how to compare work rates across groups of workers (men, women, and boys) using man-days and equating scenarios. Practice problems show converting rates and finding days for combined teams.