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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
a > b and x > 0, then

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

(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

If a,b,c,d are positive quantities, then

⇒ a4 + b4 + c4 + d4 ≥ 4abcd
If a,b,c …. k are n positive quantities and m is a natural number, then

EduRev's Tip:

• For any positive integer n, 2 ≤
• ambncp……..will be greatest when
• 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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