CLAT Quantitative Techniques Syllabus

Quantitative Techniques syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Techniques in CLAT, not a summary of it.

1. 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. 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. 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. 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

Quantitative Techniques flashcards for CLAT

24 of 50 cards from the Quantitative Techniques deck — real questions with worked 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).

21. 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.

22. What is the formula for Simple Interest?

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

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

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

24. 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).

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