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Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT

Document Description: Inequalities - Important Formulae of Number system - Free for CAT 2022 is part of 2.6 Inequalities for Quantitative Aptitude (Quant) preparation. The notes and questions for Inequalities - Important Formulae of Number system - Free have been prepared according to the CAT exam syllabus. Information about Inequalities - Important Formulae of Number system - Free covers topics like and Inequalities - Important Formulae of Number system - Free Example, for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Inequalities - Important Formulae of Number system - Free.

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If a > b and c > 0,
⇒ a + c > b + c
⇒ a - c > b - c
⇒ ac > bc
⇒ a/c > b/c
If a, b ≥ 0, then an > bn and 1/an < 1/bn, where n is positive.
a < b and x > 0, then Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
a > b and x > 0, then Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT

Modular Inequalities
|x- y| = |y - x|
|x. y| = |x|  . |y|
|x+ y| < |x| + |y|
|x+ y| > |x| - |y|

Quadratic Inequalities
(x – a) (x – b) > 0 {a < b}
⇒ (x < a) U (x > b)
(x – a) (x – b) < 0 {a > b}
⇒ a < x < b
For any set of positive numbers: AM≥GM≥HM
⇒ (a1+a2+ ….+an)/n ≥(a1.a2. …..an)1/n
If a and b are positive quantities, then
Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
If a,b,c,d are positive quantities, then
Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
⇒ a4 + b4 + c4 + d4 ≥ 4abcd
If a,b,c …. k are n positive quantities and m is a natural number, then
Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT

EduRev's Tip:

  • Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
    Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
  • For any positive integer n, 2 ≤ Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
  • ambncp……..will be greatest when Inequalities - Important Formulae of Number system - Free Notes | Study Quantitative Aptitude (Quant) - CAT
  • If a > b and both are natural numbers, then
    ⇒ ab < ba {Except 32 > 23 & 42 = 24}
  • (n!)2 ≥ nn
  •  If the sum of two or more positive quantities is constant, their product is greatest when they are equal and if their product is constant then their sum is the least when the numbers are equal.
    ⇒ If x + y = k, then xy is greatest when x = y
    ⇒ If xy = k, then x + y is least when x = y
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