GMAT | GRE | CAT | Quantitative | Quant | Math prep

Learn the fundamentals of percentage, its relation to profit and loss, simple and compound interest concepts, and how percentages convert to fractions to solve GMAT, GRE, CAT quantitative questions.

Analyze numeric data and percentages, discuss onset of symptoms and vulnerability, and learn how to solve such quantitative problems.

Examine a sustained escalation scenario using a 136% reference and a price of 89 to illustrate potential outcomes. Assess how friction around 25 influences decisions.

Master percent to decimal conversion and decimal point interpretation, using 64% and 0.64 as examples to reinforce quantitative prep concepts for GMAT, GRE, and CAT.

Explore how to work with percentages, fractions, and decimals, convert between forms, and perform quick calculations to solve quantitative problems.

Calculate the total budget when 85% is spent and 15% remains, equal to 150,000 rupees.

Explore basic percent difference and percentage calculations using examples like 58% and 37%, and interpret numbers in simple statistics to strengthen quantitative reasoning.

Explain how to determine employee counts across locations in a 1,850-employee organization using percentages such as 38%, 28%, and 30%.

Solve percentage and ratio problems by analyzing how a part relates to the total, given 30% and 50%, to find what percent one number is of another.

Set the unknown number as x and relate one seventh of x to the given percentages, including 87.5% and 48, then solve the resulting equation to find x.

Explore basic concepts of profit and loss, including cost-based pricing, price setting, and the effects of price wars on profitability.

Compute selling price, cost, and percentage using basic arithmetic in illustration 1. Use selling price minus cost and multiply by 100 to find the percentage.

Learn how to compute loss percent from cost price and selling price, with base price calculations and case-by-case simplifications, including multiple rupee amounts and percent results.

Analyze how to calculate loss and its percentage from cost price and selling price, using the lecture’s discussion of loss, cost price, selling price, and percentage.

Compute cost price and selling price from rupee values to determine whether a transaction yields gain or loss. Determine the final gain percent, shown to be 4% in this illustration.

Explore uniformity and ratio reasoning through step-by-step arithmetic examples, illustrating how percentages and fractions relate in a level 1 illustration for quantitative test prep.

Apply markup and discount to compute selling price and profit percent: cost 100, markup 50%, discount 25% yields selling price 112.50 and 12.5% profit.

Compute the single equivalent discount for sequential discounts of 20%, 10%, and 5% on a 100-rupee price. The net sale price is 68.40 rupees, yielding an equivalent discount of 31.60%.

Practice solving percentage problems by setting 70% of x equal to rupees 1545 to determine x, reinforcing percentage reasoning for GMAT quant prep.

Sharpen percentage and arithmetic reasoning with year-over-year and pricing scenarios drawn from the lecture caption, including percent-based challenges and unit pricing.

Analyze equal play and equitable outcomes in a puzzle involving a ruby sequence, rupees 4.5, and building blocks, with scenarios in New York City, Brooklyn, and Los Angeles.

Compute the cost price from a loss relation and then determine the loss percentage as 25%, confirming the correct option.

Determine the percent loss on cost price when a 10% loss on sales price is given. The method uses sales price 100 to derive 100/11% loss, confirming option B.

Explore the basic concepts of the number system, including natural numbers, integers (positive and negative), primes and composites, and even and odd numbers, with a nod to imaginary numbers.

Explore practical divisibility tests for numbers, including using digit sums to check divisibility by 3 and 9, last digits for 4 and 8, and the alternating sum rule for 11.

Apply the divisibility by nine rule by summing digits; set 24 + x to be divisible by 9 and identify the least x as 3, yielding the number 137.

Apply algebraic formulae to simplify expressions such as (E+B)^2 and (E-B)^2, revealing that the value is always four for this form.

Learn how to find the unique digit in a product by iteratively using unit digits from factors, multiplying step by step to determine the final unit digit.

Master determining the unit digit of a product by taking unit digits of the numbers and simplifying exponents, as shown with seven to the 153 and one to the 72.

explains a four-number puzzle from a GMAT style quant problem, using A+B+C+D=39 with D<C<B<5, to show parity reasoning and identify B as the smallest even number.

Explore the difference between place value and face value for digits using number 956921, and see how a digit's face value is 6 while its place value depends on position.

Explore the difference between the place values of digits in numbers, illustrated with examples like 897547 and 975247, and see how digit positions affect a number's value.

Explore the units of numbers and how multiplying by four, seven, and three yields unit outcomes, while considering a unit of objectivity in choosing methods.

Identify unity and patterns in powers of seven, such as 7, 49, 343, and 7^4, to solve related questions.

Explore solving a challenging exponent and sequence problem by converting values to powers, analyzing base relations from three to seven, and using subtraction and digit reasoning to select the correct option.

Solve a basic arithmetic puzzle to determine the value of x using simple subtraction patterns, highlighting a straightforward method for common exam questions in GMAT, GRE, and CAT quantitative prep.

Explore simplified handling of 3375 by repeated division by 5 and 9, revealing irreducible components like 3 and 4. Use these steps to decide which option matches the symbolic value.

Learn to apply known algebraic formulas to solve GMAT level questions. Recognize square forms and transform expressions involving E and B to simplify calculations using observation.

Apply the difference of squares formula to simplify expressions and verify results using generic properties and form, illustrated with numbers like 64 and 36.

Practice simplifying algebraic expressions using a generic formula, including operations with squares and minus signs, and apply it to expressions in a and b with numerical examples.

Explore counting numbers from 300 to 400 where the digit 7 appears once, using examples like 307771 and 317. Read the condition carefully to avoid extra sevens in exam questions.

Explore divisibility by nine through digit-sum reasoning, determining digits so the total sum forms a multiple of nine for GMAT, GRE, and CAT quantitative prep.

Explore the divisibility of 6n^2 + 6n by 6 and 12 for natural numbers, and identify option B (18 only) as the correct choice.

Apply the divisibility by 11 rule to a four-digit sum formed from two three-digit numbers, deducing E and B and determining E plus B.

Analyze how parity and the product of six natural numbers a, b, c, d, e, f determine which statements are true, using even-odd reasoning and two-at-a-time combinations.

Explore the properties of numbers, from natural numbers to negative numbers and zero, and see how addition and basic rules reveal structure across number sets.

Explore algebraic problem solving by evaluating expressions, recognizing squares and exponent patterns, and identifying correct formulas among multiple options in a GMAT style setting.

Develops mastery of basic number properties, including zero, one, and reciprocals, and practicing multiplication of negatives with examples like five and minus eight for option-based problem solving.

Explore finite numbers and boolean numbers inside a box, evaluate options like one and one, and one and two, to identify feasible combinations.

Explore a quantitative problem presented as a three-by-four multiple-choice question, examining numbers, the initial number, and equalities to practice decision-making in GMAT prep.

Explore basic concepts and key formulae for arithmetic and geometric progressions, learn how to compute sums with sigma notation, and apply these methods to solve problems.

Master arithmetic progression problems by deriving and applying sum formulas and identifying the common difference to determine the number of terms and sequence sums.

Apply a numeric formula to natural numbers, explore plus or minus one adjustments, and determine equalities to solve a level 1 question.

Explore evaluating series using sigma notation, splitting sums into parts, and applying the plus-number formula to compute term sums for competitive math problems.

Explore square roots, powers, and index rules through examples like 15625 = 5^6, 1331 = 11^3, and a^2−b^2 = (a−b)(a+b), plus the sum of odd numbers equals a square.

Apply the division method to find the square root of three to three decimal places, and conclude with the value 1.73.

Illustration 1 level 1 demonstrates solving a quantitative problem by dividing by two, using powers and roots, and applying index properties to obtain a product of 48.

Illustration 2 level 1 demonstrates finding the square root using the method of division, working through numbers step by step.

Master quick calculation strategies using the rule of 40, the rule of 40 plus, and the rule of 56. Remember the squares of the first 20 numbers for fast calculations.

Practice divisibility checks on a given number by two and seven, verify nondivisibility by three, and determine the resulting group size, which is 28.

Illustrates solving a square root problem by long division. It shows that 13,376 trees can be arranged with 124 rows of 124 trees each.

A basic square-root question solving 53824 using division (with base from left) and factorization; it confirms the root is exact, selects option B, and assigns factorization homework.

Explore rationalization of a root five expression and conjugate-based simplification to an a^2+b^2+ab over a^2+b^2−ab form, yielding 4/3.

Explore hcf and lcm by examining the lowest common multiple and common factors, using division-based methods with example numbers.

Apply the long division method to divide numbers, identify remainders, and understand how divisors influence the division process.

Explore divisibility and common factors to determine the greatest common factor among given numbers through examples.

Solve a number puzzle by examining 16, 24, 36, and 54, exploring which numbers are divisible by two and how these relate to balancing the set.

Identify patterns in numerators and denominators and uncover common properties across numbers. Apply theory and axioms to understand simple operations and predictions within the number sets.

Explore number reasoning and variable assignment in a quantitative problem, interpreting figures on the axis and solving for x equals 13.

Solve an algebraic puzzle in a GMAT quantitative prep context using numbers such as 693, 77, and 11 to determine an unknown x across seven days.

Explore determining the greatest common divisor of 95, 90, and 60 by factoring and divisibility to identify the largest common unit.

Identify the greatest common divisor of two numbers using divisibility and subtraction techniques, illustrated with examples like 45 and 1037 to determine their shared factors.

Compute the greatest common factor using the method of factors and prime-power arguments to identify the common divisor across multiple numbers.

Discover how to find the NCM of three numbers by using the maximum powers of primes that divide them, ensuring each given number divides the result.

Find the number that cannot be the other number when the greatest common factor is eight, by checking divisibility of candidates like 24, 48, 56, and 60 by eight.

Determine two numbers with hcf 23 and lcm containing 13 and 14. Using the hcf-lcm product, set them as 23×13 and 23×14, with the larger being 322.

Compute the mean and arithmetic mean as the sum of elements divided by their count, shown with 3, 5, 7 yielding 5, and note the harmonic mean for speed problems.

Illustrates how to compute the average of a set of scores by summing the numbers and dividing by their count, using a seven-element example.

Practice solving algebraic problems with five numbers A through E, using their sum and division by five to determine x, as shown in the illustrated example.

Explore a GMAT style quantitative illustration using 47x and 47y with a denominator to compute an average, arriving at 58.

Analyze the average age of a man and his son by examining the visual of their ages, using equations to reveal the range and equal ages.

this lecture solves a 24-student average age problem including the teacher, using equations to derive how the average changes and the new average becomes 35.4.

Demonstrates a percentage-based expenditure problem: eight people spend rupees 30 each, the ninth spends rupees 20 more than the nine-person average, and the total expenditure is determined.

Using a zero average condition, the sum of twenty numbers is zero, so at most nineteen committee members can be greater than you.

Calculate the mean of a data set by summing all observations and dividing by the number of elements, illustrated with a 12-item example to show how the average is determined.

Illustration 4 level 2 demonstrates identifying five numbers between six and thirty-four and computing their average, which equals twenty.

Explore an exercise on the average of five numbers A, B, C, D, E and the sequence relations used to solve for the values.

Derive the speeds of E, B, and C by using pairwise average speed equations, formulating sums such as E+B+C, and solving for individual values.

Illustration 7 level 2 shows how to find the average of the first 50 natural numbers by the sum formula, yielding 1275 and an average of 25.5.

Compute the mean of prime numbers between 30 and 50 using 31, 37, 41, 43, and 47, totaling 199 for an average of 39.8.

Compute the average of the first n natural numbers using the sum formula n(n+1)/2, yielding (n+1)/2, and confirm option A as correct.

solve a five-number average by setting (7+8+x+11+14)/5 = x and simplifying to 5x = 40 + x, which gives x = 10.

Apply the mean formula to six numbers 6, 7, x, 8, y, 14 to equal 9; sum known numbers is 35. Thus x+y equals 19, making option a correct.

Solve two-number average problems by forming equations from the mean, switching the average to identify both numbers, including the second number from given options.

Apply the sigma-based formula for the sum of the first natural numbers to determine the average of two numbers drawn from the first 22 natural numbers.

Explore why, for twenty numbers with average zero, at most nineteen can be greater than zero, since nineteen positives summing to a require 20th number to be -a to balance.

Explore partnership concepts, including capital investment, active and sleeping partners, and profit and loss allocation in business scenarios.

Explore basic investment concepts and arithmetic through a resource allocation illustration, highlighting how investments and issues relate to competing needs, profits, and numbers.

Explore how to allocate profits among partners by analyzing initial investments and annual profits, and verify shares through ratio calculations.

Illustration 4 demonstrates calculating end-of-year profit distributed among investors based on rupee investments, including equal and different contributions. The scenario highlights basis, enrichment, and potential litigation as it quantifies profit.

This illustration calculates Jacob’s and a partner’s investments and profit shares, starting from an 11,500 rupee investment, applying a 20% reduction, and determining each profit portion.

Explore simple interest and compound interest concepts, defining principal, amount, and rate, and applying formulas for annual, semiannual, and quarterly compounding with varying rates.

Compute simple interest on a 2500 principal for 2.5 years at 6% and determine the total amount: 375 interest and 2875.

Convert 73 days to 1/5 year and apply si = p r t / 100 to 4500 at 8% per year. Obtain 72 rupees interest and 4572 rupees total.

Tackle a finance-oriented GMAT level problem, applying percentages, no compound interest, and rupees calculations to determine outcomes like seats sold and debt values.

Compare simple interest and compound interest over a three-year period at given rates, using standard formulas to compute final amounts.

Compare compound interest and simple interest when interest compounds annually for four years at 6%, solving for the difference and key components.

Explore compound interest calculations using a practical example with an 8% rate over two years, including principal, formula, and resulting rupees value.

Illustration 2 (level 2) demonstrates calculating compound interest with annual compounding at seven and a half percent to determine the future value using the compound interest formula.

Examine a multi-year borrowing scenario using simple interest, financing a community disability support system for 100 students at 14% per annum with a 6% reference, over nine years.

An illustration demonstrates how a sum of money, a loan, and percent rates interact, including the idea of money doubling, and guides students toward a formula to reach goals.

Illustration 6 (level 2) shows how to compute future and present value with annual compound interest, applying the formula and rupees values at 8%.

Illustration seven level two guides solving a two-year, annually compounded interest problem using the formula a = p(1 + r/100)^n, highlighting the denominator and the rate.

Apply the simple interest formula si = p r t / 100 to a 4800 principal at 8.5% for 2 years 3 months, yielding 918 rupees.

Compute the simple interest on ₹16,800 for nine months at 6.25% per annum by converting time to years and applying SI = PRT/100, yielding ₹787.50 (option B).

Solve a level 2 compound interest problem with annual compounding to determine the principal and rate, concluding a 25% per annum.

Tackles a second question on compound interest with annual compounding, using the end amount formula (1+x)^n to solve for x in a given scenario.

Solve a simple interest problem by equating two scenarios: a principal of 15000 at 5% for 1 year 4 months, and a 6.25% rate for two years, yielding 8000.

Compare two simple interest scenarios: 2.5 years at 12% and 3.5 years at 10%, with a 400 rupee difference, to solve for the principal.

Explore decimal fractions and fraction comparison by examining numerators, denominators, and repeating decimals, while learning to convert and compare decimals and simple fractions.

Explore converting decimals to fractions and identifying decimal places. Learn to determine divisibility by four to simplify fractions with examples.

Illustration 2 (level 1) guides you through sorting several fractions in ascending order, identifying the lowest and highest values, and interpreting decimals.

Master arranging numbers in descending order by identifying the largest to smallest values, and practice converting fractions to decimals within quantitative problem solving.

Learn decimal addition by aligning numbers at the decimal point, ensuring four digits after each decimal, and processing carries from the extreme right.

Learn how to read decimals, convert decimals to fractions, and determine digits and zeros after the decimal using place-value rules. Explore significant digits and decimal positioning through practical illustrations.

Match 47.2506 to 40 plus 7 point B plus 2C plus 5D plus 6E to solve for B, C, D, and E, then substitute these values to evaluate the expression.

Convert fractions such as 27/100, 27/1000, and 27/100000 to decimals, analyze zero placement, and determine that option C is correct.

Convert 0.36 to its simplest fractional form as 9/25, then sum the numerator and denominator to get 34, the correct option for q.no.1 (level 2).