Quantitative Aptitude for CAT/XAT/CSAT/SSC CGL/GATE/GRE-2021

Classify numbers into real and imaginary, distinguish rational and irrational numbers, and categorize integers as negative, zero, and positive, then cover decimals and fractions such as proper, improper, and mixed.

Classify integers by parity and type, including even and odd numbers, natural and whole numbers, primes, composites, twin primes, perfect numbers, and numbers that are neither prime nor composite.

Explore the Fibonacci sequence and practice applying bodmas to solve expressions with brackets, division, multiplication, addition, and subtraction, including a step-by-step example.

Master decimals and place value, including how to read numbers before and after the decimal, determine place and face values, and round to the nearest tens, hundreds, and thousands.

Convert decimals to fractions and recurring decimals by multiplying by powers of ten and subtracting to isolate the repeating part, as shown by 3.68 with a bar equaling 365/99.

Learn to add and subtract fractions by finding a common denominator, such as 30 for 3/5, 7/15, and 9/10; simplify with cancellation, then multiply and divide using reciprocals.

Convert proper fractions to mixed fractions and back using division to find quotient and remainder. Add and subtract mixed fractions by separating integers from fractions, review vectors, multiples, and factors.

Cover the concepts of LCM and HCF, showing how to find them by listing multiples and factors and by prime factorization, with examples using 4,6,8 and 32,54,96.

Learn to find the lcm and hcf of numbers, and compute the sum and count of factors using prime factorization and divisor formulas with guided examples.

Compute zeros in factorials by counting factors of five across multiples and using division by five; determine the maximum power of six by balancing twos and threes in the factorial.

Explore divisibility rules for numbers, including tests for 2, 3, 4, 5, 7, 8, 9, 10, 11, and 12, using last-digit, digit-sum, and alternating-sum methods to determine divisibility.

Explore the fundamentals of ratios and proportions, distinguishing ratios from fractions while interpreting relationships between quantities. Learn how to compare, combine, and reason about boys-to-girls ratios using real-world examples.

Learn to divide a total value into shares using a 3:4:5 ratio, calculating A, B, and C shares, and to combine ratios by equalizing values through scaling.

Explore the three types of proportion, including main (mean) proportion with the product of means, and direct and inverse proportions, illustrated with formulas and practical examples.

Define percentage as the value divided by the total, multiplied by 100. Use percentages to compare scores across different totals, illustrated with examples like 400/500 and 600/1000.

Calculate percentage change using (change in value divided by original value) multiplied by 100, illustrated by 350 to 450, and convert percentages to fractions by dividing by 100.

Work through percent arithmetic with practical examples, learning to compute 10%, 20%, 40%, and 50% of numbers and apply left-to-right and right-to-left strategies to solve compound percent questions.

Learn to compute percent off and multi-step percentage changes, starting from right to left, with practical examples like 10% off 4000 and shirt and television pricing.

Learn to compute percentage change using a base of 100x, handling increases and decreases, and solving recovery problems like price and population adjustments.

Analyze a 20 percent discount and 20 percent profit scenario, calculate cost price and selling price from a 600 mark price, and visualize relationships graphically.

Explore profit or loss percentage with cost price and selling price in practical problems, including two mobiles bought at the same price and 30% profit vs 20% loss.

Calculate the initial car price from the final price after successive discounts of 30% and 40%, given a final price of 1,026,000 dollars.

Learn the difference between simple interest and compound interest, with formulas for each and how compounding frequency, whether annual or every six months, shapes the final amount.

Learn how to compute averages for linear data, where the average equals first plus last divided by two, with examples like 1 to 5 and ten consecutive odd numbers.

Understand nonlinear data and compute weighted averages from groups. A class of 250 boys, 120 girls, and 30 teachers with averages 12, 8, and 60 has an average of 14.4.

Apply average and total-sum techniques to solve cricket score problems, including the sixth player's score counted twice, and compute the overall class average with a new student.

Learners explore mixtures and allegations, convert two vessels with water-to-resin ratios to equal total quantities using a common multiple, then combine the two mixtures to obtain the final mixture.

Apply mixture and volume ratio techniques using common multiples to solve dual-vessel scenarios, including condensed milk to water to salt, arriving at a 5:12 final mix.

This example solves a milk-to-water ratio problem: starting with 64 liters of milk and 16 liters of water (4:1), add 240 liters of water to achieve a 1:4 milk-to-water ratio.

Master speed, distance, and time concepts with formulas for speed as distance over time, and learn average and relative speed for objects moving in the same or opposite directions.

Two trains start from stations; the first travels 60 mph, the second 80 mph after four hours, meeting 5.5 hours after 10:00, 440 miles from station B, 1010 miles apart.

Compute the average speed for a three-leg journey with 600 miles at 40 mph, 600 miles at 50 mph, and 600 miles at 60 mph, yielding 1800/37 mph.

Compute the distance between house and office by comparing times at 20 m/s and 30 m/s, with 6 seconds late and 4 seconds early, to find normal speed and time.

Use proportion and cross multiplying to calculate inspections: seven of every 400 bulbs yields 350 inspected when producing 20,000.

Identify the direct variation between earnings and audience size, and solve a proportion by cross-multiplication. Conclude that a 20-attendee performance earns $300.

Calculate the profit from a performance, given 120 dollars earned and 43% spent on costs, with eight attendees yielding about 68.4 dollars.

Calculate the earth's average orbital speed in miles per hour by dividing 580,000,000 miles by 8,760 hours, yielding about 66,210 mph.

Subtract 20% of calcium's 40 amu to estimate the unknown element's weight as 32 amu.

Master geometry concepts by examining lines, rays, and angles—parallel and perpendicular lines, supplementary and complementary angles, vertical opposite angles, and how three parallel lines with a transversal yield proportional segments.

Master triangle basics: side opposite the largest angle is longest, sum of any two sides exceeds the third, exterior angles equal the sum of the opposite interior angles.

Learn to compute triangle area from base and height, explore equilateral triangle properties, derive height via Pythagoras, and relate area to inradius and semiperimeter.

Master the Pythagorean theorem, c^2 = a^2 + b^2, and the hypotenuse; identify 3-4-5 triplets and their multiples, and explore similar and congruent triangles through ratios.

Explore triangle types: scalene, obtuse, acute, right, isosceles, and equilateral, and define triangle centers (incenter, circumcenter, X center, centroid, orthocenter), plus the midpoint theorem and area relations.

Explore special triangles, including 30-60-90 and 45-45-90, derived from an equilateral triangle; learn the side ratios 1:√3:2 and the hypotenuse √2 times a leg.

Explores quadrilaterals, including square, rectangle, rhombus, parallelogram, and trapezium, with angle sums and diagonals. Explain area and perimeter, base-height, and diagonal relations using d^2 = a^2 + b^2 for diagonals.

Explore how polygons form by adding sides, derive angle sums as (n-2)180 degrees, learn exterior angle sums of 360 degrees, and apply the diagonal count formula n(n-3)/2, plus regular polygons.

Identify major and minor arcs and segments, and relate arc length to the circle's circumference and central angle. Calculate sector area and circle area using standard formulas.

Learn circle properties: angles in a semicircle are 90 degrees; triangles inside semicircles are right; angles in the same segment are equal; cyclic quadrilaterals have opposite angles summing to 180.

Explore three dimensional geometry with cuboids and cubes, learning lateral and total surface areas, volume, the cuboid's longest space diagonal, and other figures like cylinders, cones, spheres, and hemispheres.

explains co-ordinate geometry fundamentals, including quadrant signs, distance between points, slope, midpoints, perpendicular lines, and line equations with x and y intercepts.

Understand algebra by examining algebraic expressions with operations, variables, and constants, such as 3x + 4y + 3, and distinguish monomials, binomials, and trinomials.

Explore exponent basics and formulas, applying product and quotient rules, power of a power, and identities like x^2, (x+y)^2, x^2 - y^2, and (x+y)^3.

Explore functions and algebraic expressions, including one-variable functions and solving simple equations. Solve linear systems by aligning coefficients and identify parallel lines with zero or infinite solutions.

Explore how inequalities operate with arithmetic, including greater than, less than, and their equal forms, using number lines and noting that multiplying or dividing by a negative flips the inequality.

Master absolute values, the modulus function, and inequality ranges by converting expressions like |x| ≥ 5 and |x-3| ≤ 2 into number-line intervals.

Solve quadratic inequalities by factoring x^2-4x+3 into (x-3)(x-1) and using the zero-product rule to find the number-line solution intervals and endpoints for ≥0 and ≤0.

Use a graphical approach to solve x^2-4x+3 for >0, =0, and <0, identifying roots at x=1 and x=3; obtain (-infinity,1) union (3, infinity) and (1,3).

Explore the difference between permutation and combination, focusing on arrangement versus selection, and identify when order matters using examples like two-at-a-time arrangements and three prizes or football-team selections.

Explore permutations and combinations with a 10-person group: compute 10P3 = 720 and 10C3 = 120, then contrast slot methods with the nPr and nCr formulas.

Identify the target and whether order matters, draw slots, and apply permutation or combination rules; illustrated with 30 students forming handshakes, yielding 435 ways.

Explains conditional slots in selection problems, showing how to form a diagonal by choosing two vertices; with eight options for the first and five for the second, giving twenty.

Explore combinatorial counting through selecting 3 boys from 5 and 2 girls from 6 using slot methods, then count rectangles and squares on a 5x5 chessboard using line selections.

Explore the basics of probability, including events, outcomes, and the ratio of favorable to total outcomes, with examples like coin toss and rain showing probabilities range from 0 to 1.

Learn how independent events multiply probabilities when outcomes do not affect each other. See how dependent events modify subsequent chances with without-replacement draws and card intersections.

Explore types of probability questions with coin toss and dice outcomes, showing how the number of outcomes grows as 2^n and 6^n for 1–4 tosses or dice throws.

Learn arithmetic, geometric, and harmonic progressions, including their defining terms such as the common difference and ratio, and how to obtain sums of terms and properties of harmonic progression.

Learn the difference between lists and sets, and master Venn diagrams with union, intersection, and complements. Explore disjoint sets, subsets, and counting elements using universal sets and grids.

Explore two sets using a Venn diagram and the union formula |A∪B|=|A|+|B|-|A∩B| with a class example: 40 students, 25 cricket, 15 football, 5 neither, yielding 5 who play both.

Master three-set problems with Venn diagrams, learning A, B, C, union and intersection, including none and the three-way intersection formula, illustrated by a total-students example.

Organize data with a four-way group grid (boys/girls and vegetarian/non-vegetarian) to solve the problem and find 320 non-vegetarians.