NABARD Grade A Quantitative Aptitude Syllabus

Quantitative 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 Aptitude in NABARD Grade A, not a summary of it.

1. 1

   Number System and Simplification

   3 topics

   • Number System
     • Types of numbers and divisibility
     • HCF and LCM
   • Simplification and Approximation
     • BODMAS and surds
     • Approximation techniques
   • Number Series
     • Missing number series
     • Wrong number series
2. 2

   Arithmetic

   4 topics

   • Percentage, Ratio and Proportion
     • Percentage applications
     • Ratio, proportion and partnership
   • Profit, Loss and Interest
     • Profit, loss and discount
     • Simple and compound interest
   • Time-based Problems
     • Time and work, pipes and cisterns
     • Time, speed and distance
     • Boats and trains
   • Averages, Ages and Mixtures
     • Averages and ages
     • Mixtures and alligations
3. 3

   Data Interpretation

   3 topics

   • Tabular and Graphical DI
     • Tables and bar graphs
     • Line graphs and pie charts
   • Advanced DI
     • Caselet DI
     • Missing data DI
   • Data Sufficiency
     • Two-statement data sufficiency
     • Quantity comparison
4. 4

   Algebra, Mensuration and Probability

   3 topics

   • Quadratic Equations and Inequalities
     • Roots and quadratic comparison
   • Permutation, Combination and Probability
     • Basic counting principles
     • Probability of events
   • Mensuration
     • Areas of 2D figures
     • Volume and surface area of 3D solids

Quantitative Aptitude flashcards for NABARD Grade A

21 of 51 cards from the Quantitative Aptitude deck — real questions with worked answers.

1. In the number system, what is the difference between a rational and an irrational number?

   A rational number can be expressed as p/q where p and q are integers and q ≠ 0 (e.g., 3/4, 0.25). An irrational number cannot be expressed as a ratio of integers and has a non-terminating, non-repeating decimal (e.g., √2, π).

2. State the divisibility rules for 3, 9, and 11.

   Divisible by 3 if the sum of digits is divisible by 3; by 9 if the sum of digits is divisible by 9; by 11 if the difference between the sum of digits at odd places and even places is 0 or a multiple of 11.

3. How do you find the number of trailing zeros in n! (factorial)?

   Count the number of times 5 is a factor: [n/5] + [n/25] + [n/125] + ... (using floor values), since pairs of 2 and 5 make zeros and 5s are fewer than 2s.

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

   HCF × LCM = a × b (the product of the two numbers equals the product of their HCF and LCM).

5. What is the unit digit of an expression and how do you find the unit digit of large powers?

   The unit (last) digit depends only on the unit digit of the base, which cycles in a pattern (cyclicity). For most digits the cycle length is 4; reduce the exponent modulo 4 (using 4 instead of 0) to find the position in the cycle.

6. In simplification, what does the BODMAS/VBODMAS order of operations stand for?

   Vinculum (bar), Brackets, Of, Division, Multiplication, Addition, Subtraction — the sequence in which operations must be performed.

7. What is the approximation technique for quickly estimating answers in simplification questions?

   Round numbers to the nearest convenient value (e.g., nearest 10, 100, or whole number), compute the estimate, then select the closest option — useful when exact values aren't required.

8. What is the formula for the sum of the first n natural numbers, sum of their squares, and sum of their cubes?

   Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6; Sum of cubes = [n(n+1)/2]².

9. In number series, how do you identify an arithmetic versus a geometric progression pattern?

   Arithmetic progression has a constant common difference between consecutive terms (add/subtract). Geometric progression has a constant common ratio (multiply/divide by the same factor).

10. What are the common patterns to check when solving a number series problem?

    Check for: addition/subtraction of a constant, multiplication/division by a constant, squares/cubes, prime numbers, alternating series, difference-of-differences, and combinations of operations (e.g., ×2 then +1).

11. What is the nth term formula of an arithmetic progression (AP)?

    aₙ = a + (n − 1)d, where a is the first term and d is the common difference.

12. What is the sum of the first n terms of an arithmetic progression?

    Sₙ = n/2 [2a + (n − 1)d] = n/2 (first term + last term).

13. What is the formula for percentage change (increase or decrease)?

    Percentage change = [(Final value − Initial value) / Initial value] × 100. A positive result is an increase; negative is a decrease.

14. If a value is increased by x% and then decreased by x%, what is the net effect?

    There is a net decrease of (x²/100)%. For example, +20% then −20% gives a net 4% decrease.

15. What is the formula for successive percentage change of a% followed by b%?

    Net % change = a + b + (ab/100), where increases are positive and decreases are negative.

16. How do you convert a ratio a : b into percentages of the total?

    Each part's percentage = (part / sum of parts) × 100. For a : b, a's share = a/(a+b) × 100% and b's share = b/(a+b) × 100%.

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

    In direct proportion, as one quantity increases the other increases proportionally (a/b = constant). In inverse proportion, as one increases the other decreases (a × b = constant).

18. What is the formula for profit percentage and loss percentage?

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

19. How do you find Selling Price from Cost Price given a profit or loss percentage?

    SP = CP × (100 + Profit%)/100 for profit; SP = CP × (100 − Loss%)/100 for loss.

20. What is the formula for Simple Interest?

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

21. What is the formula for Compound Interest (amount and interest) compounded annually?

    Amount A = P(1 + R/100)ᵀ; Compound Interest = A − P, where P = principal, R = rate, T = time in years.

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