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

## 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 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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## Quantitative Aptitude (Quant)

116 videos|131 docs|131 tests

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