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CLAT Quantitative Techniques Syllabus

The Quantitative Techniques syllabus for CLAT in full: 4 chapters, 13 topics and 17 sub-topics, every one listed below, plus 50 Quantitative Techniques flashcards with answers.

4Chapters
13Topics
17Sub-topics
50Flashcards

Quantitative Techniques syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  1. Number Fundamentals

     3 topics
    • Ratio and Proportion
      • Simple and compound ratios
      • Direct and inverse proportion
    • Percentages
      • Percentage change and successive change
    • Averages
      • Weighted averages from data sets

  2. Commercial Arithmetic

     4 topics
    • Profit, Loss and Discount
      • Cost price, selling price and margins
      • Successive discounts
    • Simple and Compound Interest
      • Computing interest over periods
    • Time, Speed and Distance
      • Average speed and relative speed
    • Time and Work
      • Combined work and efficiency

  3. Data Interpretation

     3 topics
    • Tabular Data
      • Extracting values from passage-based tables
    • Graphs and Charts
      • Bar graphs and line graphs
      • Pie charts and percentage shares
    • Calculation Under Passages
      • Deriving figures from textual data
      • Multi-step computation from given numbers

  4. Basic Algebra and Mensuration

     3 topics
    • Elementary Algebra
      • Linear equations and simple word problems
    • Mensuration
      • Area and perimeter of basic figures
    • Basic Statistics
      • Mean, median and mode

CLAT Quantitative Techniques flashcards — 50 questions with answers

  1. What is the defining property of a proportion a : b = c : d?

    The cross products are equal: a*d = b*c. The terms a and d are the extremes; b and c are the means.

  2. If a : b = 2 : 3 and b : c = 4 : 5, what is a : b : c?

    Make b common: a:b = 8:12, b:c = 12:15, so a:b:c = 8:12:15.

  3. What is the difference between direct proportion and inverse proportion?

    In direct proportion two quantities increase/decrease together (x/y = constant). In inverse proportion one rises as the other falls (x*y = constant).

  4. How do you find the mean proportional (geometric mean) between two numbers a and b?

    Mean proportional = sqrt(a*b). It is the value x such that a : x = x : b.

  5. If a sum is divided in the ratio 3 : 5 : 7, what fraction does the middle share represent?

    5 / (3+5+7) = 5/15 = 1/3 of the total.

  6. What is the formula to convert a fraction or decimal into a percentage?

    Multiply by 100. Percentage = (value) * 100%. e.g. 0.25 = 25%, 3/4 = 75%.

  7. What is the formula for percentage change?

    Percentage change = [(New value - Old value) / Old value] * 100. Positive = increase, negative = decrease.

  8. If a quantity increases by x% and then decreases by x%, what is the net percentage change?

    A net decrease of (x^2/100)%. e.g. +20% then -20% gives a 4% net decrease.

  9. What single multiplying factor corresponds to two successive percentage changes of a% and b%?

    Net % change = a + b + (ab/100). Equivalently multiply by (1 + a/100)*(1 + b/100).

  10. How do you find the original value when a number is the result of a p% increase?

    Original = Final / (1 + p/100). For a p% decrease, Original = Final / (1 - p/100).

  11. What is the formula for the arithmetic mean (average) of n numbers?

    Average = (Sum of all observations) / (Number of observations).

  12. If the average of n numbers is A, what is their total sum?

    Sum = A * n (average multiplied by the count).

  13. A batsman's average is A over n innings; what is the new average after scoring x in the next innings?

    New average = (A*n + x) / (n + 1).

  14. What is the average of the first n natural numbers?

    (n + 1) / 2. (Sum n(n+1)/2 divided by n.)

  15. How does the average change if every number in a set is increased by k?

    The average also increases by exactly k. (Multiplying every number by k multiplies the average by k.)

  16. Define Cost Price (CP), Selling Price (SP), Profit and Loss.

    CP = price at which an item is bought; SP = price at which it is sold. If SP > CP, Profit = SP - CP; if SP < CP, Loss = CP - SP.

  17. What are the formulas for profit% and loss%?

    Profit% = (Profit / CP) * 100; Loss% = (Loss / CP) * 100. Both are always calculated on the Cost Price.

  18. How do you find SP from CP and a given gain%?

    SP = CP * (1 + gain%/100). For a loss: SP = CP * (1 - loss%/100).

  19. What is the difference between Marked Price and Discount?

    Marked Price (MP) is the listed/tag price. Discount is a reduction on MP: SP = MP - Discount, where Discount% = (Discount / MP) * 100.

  20. A shopkeeper gives two successive discounts of x% and y%. What is the single equivalent discount?

    Equivalent discount% = x + y - (xy/100).

Show the other 30 Quantitative Techniques flashcards

  1. What is the dishonest-dealer / false-weight gain formula when goods are sold at cost price using a false weight?

    Gain% = [Error / (True value - Error)] * 100, where error is the shortfall in weight.

  2. What is the formula for Simple Interest?

    SI = (P * R * T) / 100, where P = principal, R = rate% per annum, T = time in years.

  3. What is the formula for the amount under Compound Interest (annual compounding)?

    A = P * (1 + R/100)^T. Compound Interest = A - P.

  4. How does the compound-interest formula change for half-yearly compounding?

    A = P * (1 + R/200)^(2T): rate is halved and the number of periods is doubled (quarterly: R/400 and 4T).

  5. What is the key difference between Simple Interest and Compound Interest?

    SI is computed only on the original principal each period; CI is computed on principal plus accumulated interest, so CI grows faster and always >= SI (equal only in the first period).

  6. For 2 years, what is the difference between CI and SI on principal P at rate R%?

    Difference = P * (R/100)^2.

  7. What is the basic relationship between speed, distance and time?

    Speed = Distance / Time; Distance = Speed * Time; Time = Distance / Speed.

  8. How do you convert a speed from km/h to m/s and back?

    km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5.

  9. What is the formula for average speed over equal distances at speeds u and v?

    Average speed = 2uv / (u + v), the harmonic mean (NOT the simple average of u and v).

  10. In relative speed, how do you combine speeds for objects moving in the same vs opposite directions?

    Opposite directions: relative speed = sum of speeds. Same direction: relative speed = difference of speeds.

  11. How long does a train of length L take to cross a stationary platform of length P at speed S?

    Time = (L + P) / S. To cross a pole/man it is L / S (only the train's own length counts).

  12. What is the boats-and-streams relation for downstream and upstream speeds?

    Downstream speed = (boat speed + stream speed); Upstream speed = (boat speed - stream speed). Boat speed = (down + up)/2; stream speed = (down - up)/2.

  13. In time and work, if a person completes a job in n days, what is their one-day work?

    One day's work = 1/n of the job.

  14. If A does a job in a days and B in b days, how long do they take working together?

    Together time = ab / (a + b) days (sum the one-day rates: 1/a + 1/b).

  15. What does the equation M1*D1*H1/W1 = M2*D2*H2/W2 represent in work problems?

    The work-equivalence (chain) rule relating Men, Days, Hours and Work for two situations doing comparable jobs.

  16. What is the relationship between time-and-work efficiency and the ratio of times taken?

    Efficiency is inversely proportional to time: if A is twice as efficient as B, A takes half the time. Ratio of work done in equal time = ratio of efficiencies.

  17. What is the pipes-and-cisterns rule when an inlet fills in x hours and an outlet empties in y hours?

    Net filling rate per hour = 1/x - 1/y; the tank fills in xy/(y - x) hours (if x < y).

  18. In a data table, what does a 'row total' versus a 'column total' tell you?

    A row total sums all values across one category's variables; a column total sums one variable across all categories. They let you compute shares and verify the grand total.

  19. How do you find what percentage one cell of a table is of its row total?

    Percentage = (cell value / row total) * 100.

  20. What is the main strength of a pie chart and what does each sector represent?

    A pie chart shows parts of a whole as proportions; each sector's central angle = (category value / total) * 360 degrees, and its share = angle/360 of the whole.

  21. What angle at the centre of a pie chart corresponds to 25% of the data?

    90 degrees (25% of 360 = 90). In general, angle = percentage * 3.6 degrees.

  22. What is the difference between a bar graph and a line graph?

    A bar graph compares discrete categories using bar heights; a line graph shows trends/change of a quantity over a continuous variable such as time.

  23. In a passage-based calculation set, what is the recommended first step before computing?

    Read the passage to identify the given quantities, units and the relationship asked, then extract only the numbers relevant to the specific question (avoid using unrelated data).

  24. What is a quick way to compare two fractions a/b and c/d without finding a common denominator?

    Cross-multiply: a/b > c/d if a*d > b*c (for positive denominators).

  25. What is the formula for the value of a single instalment / weighted comparison used in approximation under data passages?

    Use approximation: round numbers to convenient values, compute, then adjust. For ratios, compare via percentages or unit values rather than exact division to save time.

  26. What are the standard identities (a+b)^2 and (a-b)^2 in elementary algebra?

    (a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2.

  27. What is the factorisation of a^2 - b^2, and the quadratic formula for ax^2 + bx + c = 0?

    a^2 - b^2 = (a+b)(a-b). Roots: x = [-b +/- sqrt(b^2 - 4ac)] / (2a).

  28. What are the area and perimeter of a rectangle, and the area and circumference of a circle?

    Rectangle: Area = length * breadth, Perimeter = 2(l + b). Circle: Area = pi*r^2, Circumference = 2*pi*r.

  29. What are the formulas for the area of a triangle and the volume of a cube and cuboid?

    Triangle area = (1/2)*base*height. Cube volume = a^3. Cuboid volume = length*breadth*height.

  30. What is the difference between mean, median and mode in basic statistics?

    Mean = arithmetic average (sum/count); Median = the middle value when data is ordered; Mode = the most frequently occurring value.

CLAT Quantitative Techniques FAQ

What is in the CLAT Quantitative Techniques syllabus?

CLAT Quantitative Techniques is split into 4 chapters: Number Fundamentals, Commercial Arithmetic, Data Interpretation and Basic Algebra and Mensuration. Together they contain 13 topics and 17 sub-topics.

How many chapters are in CLAT Quantitative Techniques?

4 chapters, containing 13 topics and 17 sub-topics. The largest chapter is Commercial Arithmetic, with 4 topics.

Are there flashcards for CLAT Quantitative Techniques?

Yes — a 50-card Quantitative Techniques deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.