Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev

Quantitative Aptitude (Quant)

CAT : Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev

The document Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev is a part of the CAT Course Quantitative Aptitude (Quant).
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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 CAT Notes | EduRev
a > b and x > 0, then Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev

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 CAT Notes | EduRev
If a,b,c,d are positive quantities, then
Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev
⇒ 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 CAT Notes | EduRev

EduRev's Tip:

  • Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev
    Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev
  • For any positive integer n, 2 ≤ Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev
  • ambncp……..will be greatest when Inequalities - Important Formulae of Number system - Free CAT Notes | EduRev
  • 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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