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🇮🇳 IBPS PO / SBI PO · subject
IBPS PO / SBI PO Quantitative Aptitude Syllabus
The Quantitative Aptitude syllabus for IBPS PO / SBI PO in full: 5 chapters, 23 topics and 51 sub-topics, every one listed below, plus 51 Quantitative Aptitude flashcards with answers.
Quantitative Aptitude syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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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
- Number Properties and Classification
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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
- Percentage
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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
- Time, Speed and Distance
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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
- Tabular Data Interpretation
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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
- Quadratic Equations and Inequalities
IBPS PO / SBI PO Quantitative Aptitude flashcards — 51 questions with answers
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.
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.
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).
How do you find the LCM and HCF of fractions?
LCM of fractions = LCM(numerators) / HCF(denominators). HCF of fractions = HCF(numerators) / LCM(denominators).
In BODMAS/VBODMAS simplification, what is the order of operations?
Vinculum (bar), Brackets, Of, Division, Multiplication, Addition, Subtraction. Brackets order: ( ) then { } then [ ].
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.
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.
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).
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%.
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%.
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).
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%.
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).
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.
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.
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.
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.
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).
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).
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.
Show the other 31 Quantitative Aptitude flashcards
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).
What is the difference between mean (arithmetic), proportion, and continued proportion?
If a:b = b:c, then b is the mean proportional (b = sqrt(ac)) and a, b, c are in continued proportion; c is the third proportional.
What is the formula for average, and how does adding/removing a value affect it?
Average = (sum of observations)/(number of observations). Sum = average x count; changing the set changes the average via the new total over new count.
State the alligation rule for mixing two ingredients of different values.
(Quantity of cheaper)/(Quantity of dearer) = (Dearer price - Mean price)/(Mean price - Cheaper price).
A vessel has milk; x is replaced with water n times. What fraction of milk remains?
Remaining milk = Initial x (1 - replaced/total)^n. So milk fraction = ((V - x)/V)^n of original volume V.
What is the basic time-work relationship and the combined-rate formula for two workers?
Work = Rate x Time. If A does a job in 'a' days and B in 'b' days, together they finish in ab/(a+b) days (rate 1/a + 1/b).
How is wage divided among workers who work together?
Wages are divided in the ratio of work done, which equals the ratio of their efficiencies (or 1/time taken individually).
State the three core formulas relating speed, distance, and time.
Speed = Distance/Time; Distance = Speed x Time; Time = Distance/Speed.
What is the conversion between km/h and m/s?
Multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 to get km/h.
How do relative speeds work for two objects moving in the same vs opposite directions?
Same direction: relative speed = difference of speeds. Opposite directions: relative speed = sum of speeds.
What is the average speed for equal distances covered at speeds x and y?
Average speed = 2xy/(x + y) (the harmonic mean), not the simple average.
In boats and streams, what are downstream and upstream speeds in terms of boat speed b and stream speed s?
Downstream speed = b + s; Upstream speed = b - s. So b = (down + up)/2 and s = (down - up)/2.
What are the area and perimeter formulas for a rectangle, square, and circle?
Rectangle: Area = l x b, Perimeter = 2(l+b). Square: Area = a^2, Perimeter = 4a. Circle: Area = pi r^2, Circumference = 2 pi r.
What are the area formulas for a triangle (base-height and Heron's) and an equilateral triangle?
Triangle = (1/2) x base x height; Heron's = sqrt(s(s-a)(s-b)(s-c)) where s=(a+b+c)/2. Equilateral = (sqrt(3)/4) a^2.
What is the area of a trapezium and the area of a rhombus?
Trapezium = (1/2)(sum of parallel sides) x height. Rhombus = (1/2) x product of diagonals.
What are the volume and total surface area of a cuboid and a cube?
Cuboid: V = l x b x h, TSA = 2(lb+bh+hl). Cube: V = a^3, TSA = 6a^2.
What are the volume and curved surface area of a cylinder and a cone?
Cylinder: V = pi r^2 h, CSA = 2 pi r h. Cone: V = (1/3) pi r^2 h, CSA = pi r l (l = slant height).
What are the volume and surface area of a sphere and a hemisphere?
Sphere: V = (4/3) pi r^3, SA = 4 pi r^2. Hemisphere: V = (2/3) pi r^3, TSA = 3 pi r^2 (CSA = 2 pi r^2).
In Tabular Data Interpretation, what is the standard approach to comparing percentages across rows/columns?
Identify the base for each percentage, compute required values from raw table figures, and compare; avoid mixing different bases. Read row/column headers carefully before calculating.
In a pie chart (graphical DI), how do you convert a sector's degrees or percentage into an actual value?
Value = (sector% of total) x total, or (sector degrees/360) x total. 1% = 3.6 degrees; the whole circle = 360 degrees = 100%.
What distinguishes a Caselet DI from tabular/graphical DI, and how should it be tackled?
A caselet presents data in paragraph form with no table/chart; extract the numbers into your own table or Venn diagram first, then solve.
In Advanced/Mixed DI, what is the key first step before calculating?
Separate the combined formats (e.g., table + chart), reconcile shared totals between them, and find the linking variable before answering.
For ax^2 + bx + c = 0, what is the quadratic formula and the discriminant's role?
x = [-b +/- sqrt(b^2 - 4ac)]/(2a). Discriminant D = b^2 - 4ac: D>0 real distinct roots, D=0 equal roots, D<0 imaginary roots.
What are the sum and product of roots of ax^2 + bx + c = 0?
Sum of roots = -b/a; Product of roots = c/a.
In quadratic-comparison questions comparing x and y, what are the possible relation conclusions?
x > y, x < y, x >= y, x <= y, or 'relationship cannot be established' (when ranges overlap). Solve both equations and compare all root pairs.
How do you find the next term in an arithmetic and a geometric number series?
Arithmetic: add a constant common difference d (nth term = a + (n-1)d). Geometric: multiply by a constant ratio r (nth term = a r^(n-1)).
What are common patterns to check in a 'wrong number' or missing number series?
Check for: constant difference, constant ratio, squares/cubes, prime numbers, difference of differences, and alternating (two interleaved) series.
What methods solve a pair of linear equations in two variables?
Substitution, elimination, or cross-multiplication. Cross-multiplication for a1x+b1y+c1=0 and a2x+b2y+c2=0: x/(b1c2-b2c1) = y/(c1a2-c2a1) = 1/(a1b2-a2b1).
State the algebraic identities for (a+b)^2, (a-b)^2, a^2-b^2, and a^3+b^3.
(a+b)^2 = a^2+2ab+b^2; (a-b)^2 = a^2-2ab+b^2; a^2-b^2 = (a+b)(a-b); a^3+b^3 = (a+b)(a^2-ab+b^2).
What are the formulas for permutations nPr and combinations nCr?
nPr = n!/(n-r)! (order matters); nCr = n!/[r!(n-r)!] (order does not matter). Note nPr = nCr x r!.
What is the basic probability formula and the rule for independent events A and B?
P(event) = (favorable outcomes)/(total outcomes). For independent events, P(A and B) = P(A) x P(B); for mutually exclusive, P(A or B) = P(A) + P(B).
IBPS PO / SBI PO Quantitative Aptitude FAQ
What is in the IBPS PO / SBI PO Quantitative Aptitude syllabus?
IBPS PO / SBI PO Quantitative Aptitude is split into 5 chapters: Number System and Simplification, Arithmetic and Commercial Mathematics, Speed, Distance and Mensuration, Data Interpretation and Algebra, Quadratic Equations and Number Series. Together they contain 23 topics and 51 sub-topics.
How many chapters are in IBPS PO / SBI PO Quantitative Aptitude?
5 chapters, containing 23 topics and 51 sub-topics. The largest chapter is Arithmetic and Commercial Mathematics, with 6 topics.
Are there flashcards for IBPS PO / SBI PO Quantitative Aptitude?
Yes — a 51-card Quantitative Aptitude 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.