IBPS PO / SBI PO 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 IBPS PO / SBI PO, not a summary of it.

1. 1

   Number System and Simplification

   5 topics

   • Number Properties and Classification
     • Natural, whole, integer, rational and irrational numbers
     • Prime, composite and co-prime numbers
     • Divisibility rules (2, 3, 4, 5, 6, 8, 9, 11)
     • Unit digit determination and cyclicity of powers
   • HCF and LCM
     • HCF by prime factorisation and division method
     • LCM and the HCF x LCM = product of numbers relation
     • Application problems on bells, gears and remainders
   • Simplification and Approximation
     • BODMAS rule and order of operations
     • Approximation of decimals, surds and fractions
     • Square root and cube root estimation
   • Surds, Indices and Powers
     • Laws of indices and rationalisation of surds
     • Solving equations with fractional and negative exponents
   • Fractions, Decimals and Percent Equivalents
     • Comparison and ordering of fractions
     • Recurring decimals to fractions conversion
2. 2

   Arithmetic and Commercial Mathematics

   6 topics

   • Percentage
     • Percentage increase, decrease and successive change
     • Population and depreciation problems
   • Profit, Loss and Discount
     • Cost price, selling price and marked price relations
     • Successive discounts and dishonest dealer problems
   • Simple and Compound Interest
     • SI and CI formulae and the difference between them
     • Half-yearly and quarterly compounding
     • Instalment and EMI based banking problems
   • Ratio, Proportion and Partnership
     • Compound and inverse proportion
     • Profit sharing based on capital and time
   • Average and Mixture-Alligation
     • Average of numbers, ages and speeds
     • Rule of alligation for two and more mixtures
   • Time, Work and Wages
     • Individual and combined efficiency
     • Pipes and cisterns with inlets and outlets
3. 3

   Speed, Distance and Mensuration

   4 topics

   • Time, Speed and Distance
     • Average speed and relative speed
     • Trains crossing poles, platforms and each other
   • Boats and Streams
     • Upstream and downstream speed
     • Round trip and still-water speed problems
   • Mensuration 2D
     • Area and perimeter of triangle, rectangle and circle
     • Sectors, rings and composite figures
   • Mensuration 3D
     • Volume and surface area of cube, cuboid and cylinder
     • Cone, sphere, hemisphere and frustum
4. 4

   Data Interpretation

   4 topics

   • Tabular Data Interpretation
     • Single and multi-column tables
     • Missing value tables with calculation
   • Graphical Data Interpretation
     • Bar graphs and line graphs
     • Pie charts and percentage distribution
   • Caselet and Paragraph DI
     • Word-based data extraction
     • Venn diagram based caselets
   • Advanced and Mixed DI
     • Combined graph sets (bar plus line)
     • Data sufficiency in DI
5. 5

   Algebra, Quadratic Equations and Number Series

   4 topics

   • Quadratic Equations and Inequalities
     • Roots, factorisation and nature of roots
     • Comparison of two equations (x and y relationship)
   • Number Series
     • Missing number series
     • Wrong number series identification
   • Linear Equations and Algebraic Identities
     • Solving two and three variable equations
     • Standard algebraic identities and simplification
   • Permutation, Combination and Probability
     • Arrangements, selections and factorial
     • Probability of cards, dice and balls

Quantitative Aptitude flashcards for IBPS PO / SBI PO

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

1. How do you classify a natural number as prime, composite, or unit?

   A prime has exactly two distinct factors (1 and itself); a composite has more than two factors; 1 is a unit (neither prime nor composite). 2 is the only even prime.

2. What is the divisibility rule for 8, and for 11?

   Divisible by 8 if the last 3 digits form a number divisible by 8. Divisible by 11 if the difference between the sum of digits in odd positions and even positions is 0 or a multiple of 11.

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

   HCF(a,b) x LCM(a,b) = a x b. This holds for exactly two numbers (not for three or more).

4. How do you find the LCM and HCF of fractions?

   LCM of fractions = LCM(numerators) / HCF(denominators). HCF of fractions = HCF(numerators) / LCM(denominators).

5. In BODMAS/VBODMAS simplification, what is the order of operations?

   Vinculum (bar), Brackets, Of, Division, Multiplication, Addition, Subtraction. Brackets order: ( ) then { } then [ ].

6. What value is sqrt(2), sqrt(3), and sqrt(5) approximately equal to (for approximation questions)?

   sqrt(2) is about 1.414, sqrt(3) is about 1.732, sqrt(5) is about 2.236.

7. State the key laws of indices: a^m x a^n, a^m / a^n, (a^m)^n, a^0, and a^(-n).

   a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn); a^0 = 1 (a not 0); a^(-n) = 1/a^n.

8. How do you rationalize the denominator of 1/(a + sqrt(b))?

   Multiply numerator and denominator by the conjugate (a - sqrt(b)), giving (a - sqrt(b)) / (a^2 - b).

9. What are the percent equivalents of 1/8, 1/6, 1/3, and 5/8?

   1/8 = 12.5%; 1/6 = 16.67%; 1/3 = 33.33%; 5/8 = 62.5%.

10. What are the percent equivalents of 1/7, 1/9, 1/11, and 1/12?

    1/7 is about 14.28%; 1/9 is about 11.11%; 1/11 is about 9.09%; 1/12 is about 8.33%.

11. How do you convert a fraction to a percentage and a percentage to a decimal?

    Fraction to percent: multiply by 100. Percent to decimal: divide by 100 (move decimal two places left).

12. If a quantity increases by x% then decreases by x%, what is the net effect?

    There is a net decrease of x^2/100 percent (never zero). Example: +20% then -20% gives a net -4%.

13. What is the successive percentage change formula for two changes a% and b%?

    Net change % = a + b + (ab/100), using signs (+ for increase, - for decrease).

14. What are the formulas for Profit% and Loss% (based on cost price)?

    Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Selling Price = CP x (100 + Profit%)/100.

15. What is the difference between discount and markup, and how do they relate to marked price?

    Markup is the increase over CP to set the Marked Price; Discount is the reduction off the Marked Price. SP = MP x (100 - Discount%)/100.

16. A shopkeeper uses a false weight and sells at cost price. What is the gain%?

    Gain% = [Error / (True value - Error)] x 100, i.e. (true weight - given weight)/given weight x 100.

17. What is the simple interest formula and the amount under simple interest?

    SI = (P x R x T)/100. Amount = P + SI = P(1 + RT/100), where R is rate% per annum, T in years.

18. What is the compound interest amount formula for annual compounding?

    A = P(1 + R/100)^T, and CI = A - P. For n compoundings per year: A = P(1 + R/(100n))^(nT).

19. What is the difference between CI and SI for 2 years at rate R% on principal P?

    CI - SI (2 years) = P(R/100)^2. For 3 years: P(R/100)^2 x (3 + R/100).

20. How do you split a profit in a partnership when capitals and time periods differ?

    Profit is shared in the ratio of (capital x time) for each partner. Equal time means share is just the ratio of capitals.

21. If a:b = m:n and b:c = p:q, how do you find a:b:c?

    Make b common: a:b:c = m x p : n x p : n x q (scale each ratio so the shared term matches).

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