Simplification Techniques and Tricks
Simplification is one of the most important part of Quantitative Aptitude section of any competitive exam. Today we are sharing all the techniques to solve Simplification questions quickly.
Rules of Simplification
V → Vinculum
B → Remove Brackets – in the order ( ) , { }, [ ]
O → Of
D → Division
M → Multiplication
A → Addition
S → Subtraction
Important Parts of Simplification
- Number System
- HCF & LCM
- Square & Cube
- Fractions & Decimals
- Surds & Indices
Number System
- Classification
- Divisibility Test
- Division& Remainder Rules
- Sum Rules
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Types
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Description
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Natural Numbers:
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all counting numbers ( 1,2,3,4,5….∞) |
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Whole Numbers:
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natural number + zero( 0,1,2,3,4,5…∞) |
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Integers:
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All whole numbers including Negative number + Positive number(∞……-4,-3,-2,-1,0,1,2,3,4,5….∞) |
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Even & Odd Numbers :
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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….∞) |
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Prime Numbers:
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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….∞) |
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Composite Numbers:
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Natural numbers which are not prime |
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Co-Prime:
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Two natural number a and b are said to be co-prime if their HCF is 1 |
Divisibility Rules :
| 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. |
| Divisible by 4 | Last two digit divisible by 4 | 5648 here last 2 digits are 48 which is divisible by 4 hence 5648 is also divisible by 4. |
| Divisible by 5 | Ends with 0 or 5 | 225 or 330 here last digit digit is 0 or 5 that mean both the numbers are divisible by 5. |
| Divisible by 6 | Divides by Both 2 & 3 | 4536 here last digit is 6 so it divisible by 2 & sum of its digit (like 4+5+3+6=18) is 18 which is divisible by 3.Hence 4536 is divisible by 6. |
| Divisible by 8 | Last 3 digit divide by 8 | 746848 here last 3 digit 848 is divisible by 8 hence 746848 is also divisible by 8. |
| Divisible by 10 | End with 0 | 220,450,1450,8450 all numbers has a last digit zero it means all are divisible by 10. |
| Divisible by 11 | [Sum of its digit in odd places-Sum of its digits in even places]= 0 or multiple of 11 |
Consider the number 39798847
(Sum of its digits at odd places)-(Sum of its digits at even places)(7+8+9+9)-(4+8+7+3)
(23-12)
23-12=11, which is divisible by 11. So 39798847 is divisible by 11. |
