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**Quantitative Aptitude**Offline Downloads:
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SIMPLIFICATION TECHNIQUES AND TRICKS
The topic Simplification is asked in each and every exam. In bank
exams, Simplification covers almost 30-40% of the Quant section.
Simplification also covers the percentage chapter. There might be 2-3
questions that have asked to simplify but they are related to
percentages. Simplification topic is asked to check the ability of
students to find their ability to deal with the numbers. So, it’s
important to have knowledge about simplification. Let’s try to
understand about simplificationSimplification means to play with the questions by doing complex
calculations.
Some of the tricks and tactics you must know to score good by saving your
valuable time
Learn BODMAS.
Use the concept of digital sum.
Memorize tables up to 30.
Memorize cubes and squares of numbers up to 35.
Learn tricks to find squares and cubes of numbers greater than
35.
Learn tricks to find cube roots and square roots
of large number.
Learn the concept of percentages (conversion of fractions to
percentage & percentage to fractions)
Memorize the reciprocals.
RULES OF SIMPLIFICATION
V → Vinculum
B → Remove Brackets - in the order ( ) , { }, [ ]
O → Of
D → Division

M → Multiplication
A → Addition
S → Subtraction
B Brackets first
O Orders (i.e. Powers and Square Roots, etc.)
DM Division and Multiplication (left-to-right)
AS Addition and Subtraction (left-to-right)
Let’s discuss an example based on BODMAS Example: 152 × 23 + (228 ÷ 19)2 =?
Sol:
⇒ 15✕(12)2 [brackets are solved first and table of 19 and 15 must be on tips]
⇒ 120+144 [must know the squares]
⇒ 264
IMPORTANT PARTS OF SIMPLIFICATION
Digital Sum
Number System
Reciprocals
HCF & LCM
Percentages
Square & Cube
Approximation
Fractions & Decimals
Surds & Indices
DIGITAL SUM
Digital sum is the sum obtained after adding all the digits of any given number
successively.
Example: 568 = 5+6+8 = 19, 1 + 9 = 10.
Note: if any number multiplied by 9, then the digital sum is always 9.

Example: 6 ✕ 9 = 54, 5+4 = 9
Trick: In order to save time if we find digit 9 or multiples of 9, then 9 or its
multiple can be neglected.
Example: 293 = 2 + 9 + 3 = 2 + 3 = 5 [ ‘9’ is omitted ]
‘9’ is omitted to reduce the calculation.
If we don’t omit ‘9’, then also the digital sum remains same.
Example: 293 = 2 + 9 + 3 = 14, 1 + 4 = 5 [answer remains same]
Let’s discuss one more exampleEXAMPLE: 326 ✕ 890 =?
a. 291140
b. 290100
c. 290140
d. 293990
Sol: We can find out the answer by option method without doing multiplication.
This is only possible with the help of Digital sum.
Now, Digital sum, 326 ✕ 890 = (3 + 2 +6) ✕ ( 8 +9 + 0 )
⇒ 11 ✕ 17
⇒ (1+1) ✕ (1+7)
⇒ 2 ✕ 8 = 16
⇒ digital sum (16) = 7
Now find out the digital sum of the given options1.
2.
3.
4.
DS (291140) = 8
DS (290100) = 3
DS (290140) = 7
DS (293990) = 5
Option C has the same digital sum as ‘7’ as we have already found out. Thus the
correct option is C.
NUMBER SYSTEM
Classification
Divisibility Test
Division& Remainder Rules

Sum Rules
Classification
Types
Description
Natural
Numbers:
all counting numbers ( 1,2,3,4,5....∞)
Whole
Numbers:
natural number + zero( 0,1,2,3,4,5...∞)
Integers:
All whole numbers including Negative number + Positive
number(∞......-4,-3,-2,-1,0,1,2,3,4,5....∞)
Even &
Odd
Numbers :
All whole number divisible by 2 is Even (0,2,4,6,8,10,12.....∞) and
which does not divide by 2 are Odd (1,3,5,7,9,11,13,15,17,19....∞)
Prime
Numbers:
It can be positive or negative except 1, if the number is not
divisible by any number except the number
itself.(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61....∞)
Composite
Numbers:
Natural numbers which are not prime
Co-Prime:
Two natural number a and b are said to be co-prime if their HCF
is 1.
Divisibility
Numbers
IF A Number
Examples
Divisible
by 2
End with
0,2,4,6,8 are
divisible by 2
254,326,3546,4718 all are divisible by 2
Divisible
by 3
Sum of its
digits is
divisible by 3
375,4251,78123 all are divisible by
3. [549=5+4+9][5+4+9=18]18 is divisible by
3 hence 549 is divisible by 3.

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