🔢 Quantitative Aptitude — Formulas, Charts & Concepts

IBPS PO • IBPS Clerk • SBI PO • SBI Clerk • RBI Grade B • All Banking Exams

📌 Quant Exam Pattern (IBPS PO Pre): 35 questions — 20 min | (IBPS Clerk Pre): 35 questions — 20 min
Sections: Simplification (5–10), Number Series (5), Arithmetic (15–20), Data Interpretation (5–10)

A. SIMPLIFICATION & APPROXIMATION

BODMAS Rule — Order of Operations

B
Brackets
( ) then { } then [ ]

O
Of
(Powers/Exponents)

D
Division
÷

M
Multiplication
×

A
Addition
+

S
Subtraction
−

Example: 18 ÷ 3 × (4 + 2) − 5² + 1
= 18 ÷ 3 × 6 − 25 + 1 [Brackets first]
= 6 × 6 − 25 + 1 [Division]
= 36 − 25 + 1 [Multiplication]
= 12 [Left to right: 36−25=11, 11+1=12]

Squares, Cubes & Fraction Table — Must Memorise

n	n²	n³	√n (approx)	n	n²	n³	√n (approx)
1	1	1	1.000	11	121	1331	3.317
2	4	8	1.414	12	144	1728	3.464
3	9	27	1.732	13	169	2197	3.606
4	16	64	2.000	14	196	2744	3.742
5	25	125	2.236	15	225	3375	3.873
6	36	216	2.449	16	256	4096	4.000
7	49	343	2.646	17	289	4913	4.123
8	64	512	2.828	18	324	5832	4.243
9	81	729	3.000	19	361	6859	4.359
10	100	1000	3.162	20	400	8000	4.472

Fraction ↔ Decimal ↔ Percentage Conversion Chart

Fraction	Decimal	%	Fraction	Decimal	%
1/2	0.5	50%	1/8	0.125	12.5%
1/3	0.333	33.33%	3/8	0.375	37.5%
2/3	0.667	66.67%	5/8	0.625	62.5%
1/4	0.25	25%	7/8	0.875	87.5%
3/4	0.75	75%	1/6	0.1667	16.67%
1/5	0.2	20%	5/6	0.8333	83.33%
2/5	0.4	40%	1/9	0.111	11.11%
3/5	0.6	60%	1/11	0.0909	9.09%

B. NUMBER SERIES

Types of Number Series & How to Identify Them

Series Type	Pattern	Example	Identify by
Arithmetic (AP)	Add/subtract constant	3, 7, 11, 15, 19 (+4)	Constant difference
Geometric (GP)	Multiply/divide constant	2, 6, 18, 54, 162 (×3)	Constant ratio
Squares / Cubes	n² or n³ pattern	1, 4, 9, 16, 25 (n²)	Check if numbers are perfect squares/cubes
Two-step difference	Differences are in AP/GP	1, 2, 4, 8, 16 (diff ×2)	1st difference not constant; find 2nd level
Mixed (n² ± n)	n² + k or n² − k	2, 6, 12, 20, 30 (n(n+1))	Subtract to get square or triangle numbers
Fibonacci-type	Sum of two preceding terms	1, 1, 2, 3, 5, 8, 13	a₃ = a₁ + a₂
Prime numbers	Sequence of primes	2, 3, 5, 7, 11, 13	Check divisibility
Alternating series	Two interleaved series	2, 10, 4, 8, 6, 6	Separate odd/even-positioned terms

⚡ Speed Tip for Wrong Number Series: Calculate differences → if one difference breaks the pattern, the number causing that break is the wrong number. Check the number just before the pattern breaks.

C. QUADRATIC EQUATIONS

Solving & Comparing Roots

Standard form: ax² + bx + c = 0

Factorization method: Find two numbers whose product = a×c and sum = b

Example: x² − 7x + 12 = 0
Find two numbers: product = 12, sum = 7 → 3 and 4
→ (x − 3)(x − 4) = 0 → x = 3 or x = 4

Quadratic Formula: x = [−b ± √(b² − 4ac)] / 2a

Discriminant (D = b²−4ac)	Nature of Roots
D > 0	Two distinct real roots
D = 0	Two equal real roots
D < 0	No real roots (complex)

Comparison of roots (banking exam format):
Equation I: x² − 5x + 6 = 0 → x = 2, 3
Equation II: y² − 7y + 10 = 0 → y = 2, 5
Comparison: x = {2,3} vs y = {2,5}
Min of y (2) = Min of x (2), Max of y (5) > Max of x (3) → x ≤ y

D. DATA INTERPRETATION (DI)

Types of DI & How to Approach Each

DI Type	What to look for	Key Formulas Used
Table DI	Read row & column headers carefully; check units	%, Average, Ratio
Bar Graph	Compare bar heights; find totals for marked bars	%, Difference, Ratio
Line Graph	Rising/falling trend; compare two lines at same point	% change, Average over period
Pie Chart	Sectors = degrees or %; total = 360° or 100%	Degree = (value/total)×360; % = (value/total)×100
Caselet DI	Read paragraph; extract numbers; draw table first	All arithmetic formulas
Missing DI	Use given totals/averages to find missing cell values	Algebra + %, Average
Mixed DI	Combine data from two different chart types	All types combined
Data Sufficiency	Check if statement I alone / II alone / both needed	Logic + check conditions

DI — Quick Calculation Formulas

Calculation	Formula	Example
% of a number	(x/100) × Total	15% of 480 = 72
% change	[(New − Old) / Old] × 100	(60−50)/50 × 100 = 20%
Ratio from pie chart	Sector A° / Sector B°	90° : 60° = 3 : 2
Average	Sum of values / Number of values	(10+20+30)/3 = 20
Value from % in pie chart	(Sector% / 100) × Total	25% of 1200 = 300

⚡ DI Speed Strategy for Banking Exams

Read the heading first — understand what data is given (units, years, categories)
Scan all 5 questions before solving — find which questions can be solved together
Approximate for 5-option MCQs — round to nearest 10 or 100 when options are far apart
For Pie Charts — memorise degrees: 1% = 3.6°; convert % to value using total
For Caselet — write down all given data in table form before calculating
For Missing DI — use row/column totals as equations to find missing value
Time allocation — spend max 8–10 min on one DI set; skip hard sub-questions

Approximation Techniques

Technique	How to Apply	Example
Round to nearest integer	Round each number, then calculate	48.7 × 19.3 ≈ 49 × 19 = 931
Use fraction equivalents	Convert % to fraction	33.33% of 180 = 1/3 × 180 = 60
Break & combine	Split into easy parts	17 × 23 = 17 × (20+3) = 340+51 = 391
Square root approximation	Use nearest perfect square	√146 ≈ √144 = 12 (since 146 ≈ 144)

⚡ Quick Revision — Key Points

BODMAS: always solve Brackets first, then Of, Division, Multiplication, Addition, Subtraction
√2 = 1.414, √3 = 1.732, √5 = 2.236 — memorise these
1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/11 = 9.09%
For number series: always calculate differences at 2 levels before giving up
Quadratic: sum of roots = −b/a, product of roots = c/a
Pie chart degrees: multiply % by 3.6 to convert
DI: approximate aggressively — exact calculation wastes time

Quantitative Aptitude — Formulas, Charts & Concepts for Banking Exams