CAT - MBA Quant Points to remember Part -2
- Roots of x2 + x + 1=0 are 1, w, w2 where 1 + w + w2=0 and w3=1
- |a| + |b| = |a + b| if a*b>=0
else, |a| + |b| >= |a + b|
- The equation ax2+bx+c=0 will have max. value when a<0 and min. value when a>0. The max. or min. value is given by (4ac-b2)/4a and will occur at x = -b/2a
- If for two numbers x + y=k (a constant), then their PRODUCT is MAXIMUM if x=y (=k/2). The maximum product is then (k2)/4.
- If for two numbers x*y=k (a constant), then their SUM is MINIMUM if
x=y (=root(k)). The minimum sum is then 2*root (k).
- Product of any two numbers = Product of their HCF and LCM. Hence product of two numbers = LCM of the numbers if they are prime to each other.
- For any 2 numbers a, b where a>b
-- a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic means respectively)
-- (GM)^2 = AM * HM
- For three positive numbers a, b, c
(a + b + c) * (1/a + 1/b + 1/c)>=9