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SSC Quantitative Aptitude preparation tips: Simplification

Sep 7, 2018 11:37 IST
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SSC Quantitative Aptitude tips
SSC Quantitative Aptitude tips

Simplification is among the most important section in SSC exams as there are minimum of 1-2 questions generally asked out of this topic. The question complexity ranges from simple to difficult. To solve such questions, you have to remember several arithmetic formulas and certain conditions at the time of solving them.

In Simplification questions, an expression is given comprising of literals, numbers, and both sometimes. You have to find out its definite value. It can be only done with the help of some basic formulas and theorems.

In this article, we will discuss the concepts, tips, and tricks to solve these questions. Let us find out-

SSC Quantitative Aptitude tips: Simplification

In SSC exams, Questions are formed on the topic based on algebraic formulae and VBODMAS rule. To understand this topic, you should have the understanding of-

-          Proper use of VBODMAS rule in simplification

-          The in-depth knowledge of Algebraic formulas and their further implications

-          Surds, indices, and rationalization of complex numbers

-          Fractions and their simplification

SSC Quantitative Aptitude Tips and Tricks: Partnership

What is VBODMAS rule?

This rule states that the expression needs to be solved in a proper sequence and it is decided by the precedence of mathematical operators to simplify the equation. VBODMAS is the sequence for evaluating the expressions. Now, let us see what these letters mean -

V- Vinculum or bar (‘Bar bracket’) ‘---‘

B (Brackets)- Brackets are to be solved in the following sequence-

  • Small brackets (‘Circular bracket’) ‘()’
  • Middle brackets (‘Curly bracket’) ‘{}’
  • Square bracket (‘Big bracket’) ‘[]’

O (of) - Operation of ‘of’ is simplified.

D (Division) - Operation of division is done.

M (Multiplication) - Operation of multiplication is done.

A (Addition) -  Addition operation is done.

S (Subtraction) - Subtraction operation is done.

SSC Quantitative Aptitude tips & tricks: Boats & Streams

Order of the above operations is same as the order given and applied from left to right-

Simplification rules for real number, indices, surds, and some series

  • If m is a real number, then its absolute value can defined as
    • |m|=m, if m>0; otherwise, -m, if m<0;
  • amxan= am+n;
  • am÷an= am-n;
  • (am)n= amn;
  • (ab)n= anbn;
  • a=1;
  • (a/b)n= an/bn ;
  • a-n= 1/an;

SSC Quantitative Aptitude tricks: Algebraic formulae & their applications

Common formulas to remember

  • a2 – b2 = (a – b)(a + b)
  • (a + b)2 = a2 + 2ab + b2
  • a2 + b2 = (a – b)2 + 2ab
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
  • (a + b + c)3 = a3 + b3 + c3 + 3(a + b)(b + c)(c + a)
  • a3 + b3 + c3- 3abc = (a + b+ c) (a2 + b2 + c2 - ab - ac - bc)
  • (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  • a4 – b4 = (a – b)(a + b)(a2 + b2)
  • a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  • If n is a natural number, an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
  • If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  • If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
  • (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….

Examples

SSC Quantitative Aptitude tricks: Simple & Compound Interest

We at www.jagranjosh.com are dedicated to provide you all important tips, and overview of every topic. Keep on visiting us for more such information.

All the Best!

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