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# Note for Simplification - S by Placement Factory

• Simplification - S
• Note
• Quantitative Aptitude
• Placement Preparation
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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

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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.

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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 

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 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.