PPT: Simplification & Approximation | Quantitative Aptitude for SSC CGL PDF Download

 Page 1


Simplification & 
Approximation
Page 2


Simplification & 
Approximation
Introduction to Quantitative 
Aptitude
1
Exam Structure
Quantitative Aptitude in 
competitive exams covers 
Simplification, Number 
Series, Permutation & 
Combination, Quadratic 
Equations, and Data 
Interpretation/Analysis.
2
Question Distribution
10-12 questions typically 
focus on Percentage, 
Average, Ratio & 
Proportions, Partnerships, 
Profit & Loss, and Simple & 
Compound Interest.
3
Strategic Importance
Mastering simplification and approximation reduces 
calculation time and improves accuracy in competitive exams.
Page 3


Simplification & 
Approximation
Introduction to Quantitative 
Aptitude
1
Exam Structure
Quantitative Aptitude in 
competitive exams covers 
Simplification, Number 
Series, Permutation & 
Combination, Quadratic 
Equations, and Data 
Interpretation/Analysis.
2
Question Distribution
10-12 questions typically 
focus on Percentage, 
Average, Ratio & 
Proportions, Partnerships, 
Profit & Loss, and Simple & 
Compound Interest.
3
Strategic Importance
Mastering simplification and approximation reduces 
calculation time and improves accuracy in competitive exams.
BODMAS Rule for 
Simplification
1
B - Brackets
First, solve operations within brackets following the order: 
(), {} and []. This ensures the correct hierarchical application 
of mathematical operations.
2
O - Order (Powers, Square Roots)
Next, evaluate exponents such as powers, roots, and other 
order operations to establish the base values for further 
calculations.
3
DM - Division and Multiplication
Perform division and multiplication operations from left to 
right. These operations rank equally in priority.
4
AS - Addition and Subtraction
Finally, perform addition and subtraction operations from 
left to right. These also rank equally in priority.
Page 4


Simplification & 
Approximation
Introduction to Quantitative 
Aptitude
1
Exam Structure
Quantitative Aptitude in 
competitive exams covers 
Simplification, Number 
Series, Permutation & 
Combination, Quadratic 
Equations, and Data 
Interpretation/Analysis.
2
Question Distribution
10-12 questions typically 
focus on Percentage, 
Average, Ratio & 
Proportions, Partnerships, 
Profit & Loss, and Simple & 
Compound Interest.
3
Strategic Importance
Mastering simplification and approximation reduces 
calculation time and improves accuracy in competitive exams.
BODMAS Rule for 
Simplification
1
B - Brackets
First, solve operations within brackets following the order: 
(), {} and []. This ensures the correct hierarchical application 
of mathematical operations.
2
O - Order (Powers, Square Roots)
Next, evaluate exponents such as powers, roots, and other 
order operations to establish the base values for further 
calculations.
3
DM - Division and Multiplication
Perform division and multiplication operations from left to 
right. These operations rank equally in priority.
4
AS - Addition and Subtraction
Finally, perform addition and subtraction operations from 
left to right. These also rank equally in priority.
Modulus and Approximation Techniques
Modulus of a Real 
Number
The modulus |x| is always 
positive or zero. For any real 
number x, |x| = x if x g 0, and |x| 
= 2x if x < 0. Examples: |8| = 8 
and |-8| = 8.
Decimal Approximation
Convert decimals to their 
nearest values for quicker 
calculations. Example: 
4433.764 ³ 4434, 2211.993 
³ 2212. Then solve using these 
approximated values.
Percentage 
Approximation
Round percentages to simplify 
calculations. Example: 20.3% 
³ 20%, 16.8% ³ 17%. This 
makes mental math easier with 
minimal accuracy loss.
Page 5


Simplification & 
Approximation
Introduction to Quantitative 
Aptitude
1
Exam Structure
Quantitative Aptitude in 
competitive exams covers 
Simplification, Number 
Series, Permutation & 
Combination, Quadratic 
Equations, and Data 
Interpretation/Analysis.
2
Question Distribution
10-12 questions typically 
focus on Percentage, 
Average, Ratio & 
Proportions, Partnerships, 
Profit & Loss, and Simple & 
Compound Interest.
3
Strategic Importance
Mastering simplification and approximation reduces 
calculation time and improves accuracy in competitive exams.
BODMAS Rule for 
Simplification
1
B - Brackets
First, solve operations within brackets following the order: 
(), {} and []. This ensures the correct hierarchical application 
of mathematical operations.
2
O - Order (Powers, Square Roots)
Next, evaluate exponents such as powers, roots, and other 
order operations to establish the base values for further 
calculations.
3
DM - Division and Multiplication
Perform division and multiplication operations from left to 
right. These operations rank equally in priority.
4
AS - Addition and Subtraction
Finally, perform addition and subtraction operations from 
left to right. These also rank equally in priority.
Modulus and Approximation Techniques
Modulus of a Real 
Number
The modulus |x| is always 
positive or zero. For any real 
number x, |x| = x if x g 0, and |x| 
= 2x if x < 0. Examples: |8| = 8 
and |-8| = 8.
Decimal Approximation
Convert decimals to their 
nearest values for quicker 
calculations. Example: 
4433.764 ³ 4434, 2211.993 
³ 2212. Then solve using these 
approximated values.
Percentage 
Approximation
Round percentages to simplify 
calculations. Example: 20.3% 
³ 20%, 16.8% ³ 17%. This 
makes mental math easier with 
minimal accuracy loss.
Approximation of Square Roots
Factor the Number
Begin by factoring the 
number inside the square 
root sign to identify 
common factors that can be 
simplified.
Remove Pairs of 
Factors
If a factor appears twice, 
move one instance outside 
the square root. For factors 
appearing multiple times, 
move pairs outside while 
leaving any remaining 
instances inside.
Multiply Results
Multiply the numbers 
outside the sign separately 
from those remaining inside. 
Verify that the outside 
number squared times the 
inside number equals the 
original number.
Handle Fractions
For square roots of 
fractions, simplify the 
numerator and denominator 
separately following the 
same principles.