Which are the most important Quantitative Aptitude topics?

x⁴ + x² + 1 = 0

x⁴ + 2x² + 1 – x² = 0

  $\Rightarrow \left(x^2+1+x\right)\left(x^2-x+1\right)=0$

  $x=\pm \omega ,?{\omega }^2$

Now, = ${\alpha }^{1011}+{\alpha }^{2022}-{\alpha }^{3033}$  

= ${\omega }^{1011}+{\omega }^{2022}-{\omega }^{3033}$  

= 1 + 1 – 1 = 1

Let the capacity of container be 70L (LCM of 5,7 & 10)

Now,

I container, milk = 28L

    Water = 42L

II container, milk = 20L

    Water = 50L

III container, milk = 21L

    Water = 49L

In large container, milk = (28 + 20 + 21)

= 69L

Water = 42 + 50 + 49

= 141L

Milk :

Distance is same. So, speed will be inversely propornonel to time.

Ratio of time taken by car and motorcycle = 28 : 20

= 7 : 5

So, ratio of speed of car and motorcycle = 5 : 7

5/7 = 32/M

M = (32*7)/5 = 44.8 km/hr

Work done by 10 men = work done by 16 women

Work done by 15 men = work done by (16*3/2) women

=24 women

So, 40 women and 15 men = 40 women and 24 women

= 64 women

Therefore we can say

16 women will take 40 days

Hence, 64 women will take 40/4 =10 days

P/Q *Q/R * R/S = 3/8 * 5/4 * 16/15

P/S =1/2