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Number System & Simplification for IBPS PO

Master basic concepts of number system, types of numbers, divisibility rules, BODMAS, approximation tricks, and calculation shortcuts. This is the foundation for all Quantitative Aptitude topics.

What is Number System & Why It Matters

Number System and Simplification form the foundation of Quantitative Aptitude for IBPS PO. Typically, 10 to 15 questions are asked directly or indirectly from this topic across Prelims and Mains.

Number System deals with different types of numbers (natural, whole, integers, rational, irrational, prime, composite, etc.) and their properties. Simplification involves solving mathematical expressions using BODMAS rule and approximation techniques.

Why this topic matters: Mastering Number System and Simplification is essential because these concepts are used in every other quant topic like Percentage, Profit-Loss, Average, Time & Work, Data Interpretation, etc. Strong fundamentals here lead to faster calculation speed.

Types of Numbers

Number TypeDescriptionExamples
Natural Numbers (N)Counting numbers starting from 11, 2, 3, 4, 5...
Whole Numbers (W)Natural numbers + Zero0, 1, 2, 3, 4...
Integers (Z)Positive, negative, and zero... -3, -2, -1, 0, 1, 2, 3...
Even NumbersDivisible by 22, 4, 6, 8, 10...
Odd NumbersNot divisible by 21, 3, 5, 7, 9...
Prime NumbersExactly two factors (1 and itself)2, 3, 5, 7, 11, 13, 17, 19, 23...
Composite NumbersMore than two factors4, 6, 8, 9, 10, 12...
Co-prime NumbersHCF = 1(2,3), (4,9), (5,7)...
Rational NumbersCan be expressed as p/q, q≠01/2, 3/4, 5, 0.75...
Irrational NumbersCannot be expressed as p/q√2, √3, π, e...
Quick Tip:

Prime numbers up to 100: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97. Note: 2 is the only even prime number.

Divisibility Rules (Very Important)

DivisorRuleExample
2Last digit is even (0,2,4,6,8)128 → last digit 8, divisible
3Sum of digits divisible by 3123 → 1+2+3=6, divisible
4Last two digits divisible by 41324 → 24 divisible by 4, yes
5Last digit is 0 or 5125 → last digit 5, divisible
6Divisible by both 2 and 3234 → even & sum=9, divisible
7Double last digit, subtract from rest, result divisible by 7343 → 34 - (3×2)=28, divisible
8Last three digits divisible by 85128 → 128÷8=16, divisible
9Sum of digits divisible by 9567 → 5+6+7=18, divisible
10Last digit is 0120 → last digit 0, divisible
11Difference of sum of digits at odd and even positions is 0 or multiple of 11121 → (1+1) - 2 = 0, divisible

BODMAS Rule (Order of Operations)

BODMAS stands for: Brackets, Of (Orders), Division, Multiplication, Addition, Subtraction. This is the order in which mathematical operations must be performed.

B → Brackets ( ), { }, [ ]
O → Orders (powers, square roots, of)
D → Division (÷)
M → Multiplication (×)
A → Addition (+)
S → Subtraction (-)
Example:

Solve: 16 ÷ 4 × 2 - 3 + 5

Step 1: Division first: 16 ÷ 4 = 4
Step 2: Multiplication: 4 × 2 = 8
Step 3: Subtraction and Addition from left: 8 - 3 = 5, then 5 + 5 = 10
Answer: 10

Simplification & Approximation Tricks

Trick 1: Rounding Numbers for Approximation

When numbers are close to round figures, approximate them. Example: 49.8 × 30.2 ≈ 50 × 30 = 1500.

Trick 2: Square Shortcuts

For numbers ending with 5: (n5)² = n×(n+1) followed by 25. Example: 25² = 2×3=6 → 625.

Trick 3: Multiplication by 11

Add adjacent digits. Example: 43 × 11 = 4 (4+3) 3 = 473.

Trick 4: Percentage to Fraction Conversion

33.33% = 1/3, 25% = 1/4, 20% = 1/5, 16.66% = 1/6, 14.28% = 1/7, 12.5% = 1/8, 11.11% = 1/9, 10% = 1/10.

Trick 5: Digital Sum

Digital sum (sum of digits until single digit) can be used to verify calculations. Example: 123 × 456, digital sum 6 × 6 = 36 → 9. Check product's digital sum.

Solved Example 1: Number System

Question:

How many prime numbers are there between 1 and 50?

Solution:

Prime numbers between 1 and 50: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47.
Answer: 15 prime numbers.

Question 2:

Which of the following is divisible by 11? (a) 121 (b) 132 (c) 143 (d) All of these

Solution:

Check 121: (1+1) - 2 = 0 → divisible.
132: (1+2) - 3 = 0 → divisible.
143: (1+3) - 4 = 0 → divisible.
Answer: (d) All of these

Solved Example 2: BODMAS Simplification

Question:

Simplify: 48 ÷ 6 × 3 + (15 - 7) × 2

Solution:

Step 1: Solve brackets: (15 - 7) = 8
Step 2: Division and Multiplication from left: 48 ÷ 6 = 8, then 8 × 3 = 24
Step 3: Now: 24 + 8 × 2 = 24 + 16 = 40
Answer: 40

Solved Example 3: Approximation

Question:

Approximate: 49.8 × 19.9 ÷ 4.1 = ?

Solution:

Step 1: Approximate numbers: 49.8 ≈ 50, 19.9 ≈ 20, 4.1 ≈ 4
Step 2: 50 × 20 = 1000, then 1000 ÷ 4 = 250
Answer: Approximately 250

Practice Questions for Self-Assessment

Practice Question 1:

What is the sum of all prime numbers between 20 and 40?

Practice Question 2:

Simplify: 72 ÷ 8 × 4 + 36 ÷ 6 - 5 × 2

Practice Question 3:

Approximate: 399.8 ÷ 19.9 × 4.1 = ?

Practice Question 4:

Which number is divisible by 7? (a) 245 (b) 378 (c) 511 (d) All

Answers: Q1: 23+29+31+37 = 120 | Q2: 72÷8=9, 9×4=36, 36÷6=6, 5×2=10 → 36+6-10=32 | Q3: 400÷20×4 = 20×4=80 | Q4: (d) All (245÷7=35, 378÷7=54, 511÷7=73)

Frequently Asked Questions about Number System & Simplification

Q1: How many questions come from Number System in IBPS PO?
Directly 3-5 questions, but it is used in every other quant topic. Total indirect questions can be 10-15.
Q2: What is the BODMAS rule?
BODMAS is the order of operations: Brackets, Of (Orders), Division, Multiplication, Addition, Subtraction.
Q3: What is the only even prime number?
2 is the only even prime number.
Q4: How to check divisibility by 11?
Difference between sum of digits at odd and even positions should be 0 or multiple of 11.
Q5: What is the digital sum trick?
Digital sum is the sum of digits until a single digit. It helps verify multiplication and addition quickly.
Q6: What are co-prime numbers?
Two numbers are co-prime if their HCF (highest common factor) is 1. Example: (4,9), (8,15).

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