DU LLB Entrance Quantitative and Numerical Aptitude Syllabus

Quantitative and Numerical Aptitude syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative and Numerical Aptitude in DU LLB Entrance, not a summary of it.

1. 1

   Number System and Arithmetic Foundations

   4 topics

   • Number System Basics
     • Factors, multiples, LCM and HCF
     • Divisibility rules
   • Simplification and Approximation
     • BODMAS and surds/indices
   • Percentages
     • Percentage change and applications
   • Ratio, Proportion and Averages
     • Ratio and proportion
     • Averages and mixtures
2. 2

   Commercial Arithmetic

   3 topics

   • Profit, Loss and Discount
     • Cost price, selling price, marked price
   • Simple and Compound Interest
     • Interest formulas and applications
   • Partnership and Mixtures
     • Profit sharing
     • Alligation
3. 3

   Time, Speed, Work and Distance

   3 topics

   • Time and Work
     • Work efficiency and combined work
     • Pipes and cisterns
   • Time, Speed and Distance
     • Relative speed
     • Trains, boats and streams
   • Problems on Trains and Races
     • Train crossing problems
     • Races and circular tracks
4. 4

   Algebra, Geometry and Mensuration

   3 topics

   • Basic Algebra
     • Linear equations and identities
   • Geometry and Mensuration
     • Lines, angles and triangles
     • Area and volume of basic figures
   • Permutation, Combination and Probability
     • Counting principles
     • Basic probability
5. 5

   Data Interpretation

   3 topics

   • Tables and Charts
     • Tabular data analysis
     • Bar and line graphs
   • Pie Charts and Caselets
     • Pie chart interpretation
     • Caselet-based DI
   • Data Comparison and Sufficiency
     • Comparing quantities

Quantitative and Numerical Aptitude flashcards for DU LLB Entrance

24 of 50 cards from the Quantitative and Numerical Aptitude deck — real questions with worked answers.

1. What is a prime number, and what is the only even prime number?

   A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. The only even prime number is 2.

2. State the divisibility rules for 3 and 9.

   A number is divisible by 3 if the sum of its digits is divisible by 3. It is divisible by 9 if the sum of its digits is divisible by 9.

3. How do you test divisibility by 11?

   Find the difference between the sum of digits in odd positions and the sum of digits in even positions. If the difference is 0 or a multiple of 11, the number is divisible by 11.

4. What is the relationship between LCM, HCF, and two numbers a and b?

   Product of the two numbers = LCM x HCF, i.e. a x b = LCM(a,b) x HCF(a,b).

5. What is the order of operations used in simplification (BODMAS)?

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction - performed in that sequence, with division and multiplication left to right, then addition and subtraction left to right.

6. In approximation problems, how is a value like 19.8 typically rounded for quick estimation?

   It is rounded to the nearest convenient whole number, e.g. 19.8 is approximated as 20, to simplify the calculation.

7. How do you convert a fraction into a percentage?

   Multiply the fraction by 100 and add the percent sign. For example, 3/4 = (3/4) x 100 = 75%.

8. If a quantity increases from A to B, what is the formula for percentage increase?

   Percentage increase = [(B - A) / A] x 100.

9. If the price of an item increases by x%, by what percentage must consumption decrease to keep expenditure unchanged?

   Required decrease = [x / (100 + x)] x 100 %.

10. A number is increased by 20% and then decreased by 20%. What is the net percentage change?

    A net decrease of 4%, because successive changes of +20% and -20% give 100 x 1.2 x 0.8 = 96, a 4% loss.

11. What does the ratio a : b mean, and what is meant by a proportion?

    The ratio a : b is the comparison a/b of two quantities. A proportion states that two ratios are equal, e.g. a : b = c : d, equivalent to a/b = c/d.

12. In the proportion a : b = c : d, what is the product relationship between the terms?

    The product of the means equals the product of the extremes: b x c = a x d.

13. What is the formula for the average of n quantities?

    Average = (sum of all quantities) / n, the number of quantities.

14. The average of 10 numbers is 15. If one number 8 is removed, what is the new average?

    New average = (10 x 15 - 8) / 9 = (150 - 8) / 9 = 142/9 ≈ 15.78.

15. Define cost price (CP), selling price (SP), profit, and loss.

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

16. What are the formulas for profit percentage and loss percentage?

    Profit% = (Profit / CP) x 100; Loss% = (Loss / CP) x 100. Both are calculated on the cost price.

17. How is discount calculated, and on which price?

    Discount is a reduction on the marked price (list price): Discount = Marked Price - Selling Price; Discount% = (Discount / Marked Price) x 100.

18. What is the formula for selling price given cost price and profit percentage?

    SP = CP x (100 + Profit%) / 100. For a loss, SP = CP x (100 - Loss%) / 100.

19. State the formula for simple interest.

    Simple Interest (SI) = (P x R x T) / 100, where P is principal, R is annual rate percent, and T is time in years.

20. State the formula for the amount under compound interest (compounded annually).

    Amount A = P x (1 + R/100)^T, and Compound Interest = A - P, where P is principal, R is rate per annum, T is time in years.

21. How does compound interest differ from simple interest for the same P, R, and T (T > 1)?

    Compound interest is always greater than simple interest (for T > 1) because interest is earned on accumulated interest as well as on the principal.

22. For 2 years, what is the difference between compound and simple interest in terms of P and R?

    Difference = P x (R/100)^2, when interest is compounded annually.

23. In a partnership, how are profits shared when partners invest different amounts for different time periods?

    Profits are shared in the ratio of each partner's (investment x time). For partners A and B: profit ratio = (A's capital x months) : (B's capital x months).

24. What is the alligation rule used in mixture problems?

    Alligation gives the ratio in which two ingredients at different prices are mixed: (Quantity cheaper)/(Quantity dearer) = (Price dearer - Mean price)/(Mean price - Price cheaper).

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