Quantitative Aptitude - Arithmetic Ability Questions

Here given series follows a pattern that

0.25, 8, 128, 1024, ?

0.25 x 32 = 8

8 x 16 = 128

128 x 8 = 1024

1024 x 4 = 4096

The given number series 410, 409, 413, 404, ? , follows a pattern that 

410

$$\begin{gathered} 410 - 13 = 409 \\ 409 + 22 = 413 \\ 413 - 33 = 404 \\ 404 + 42 = 420 \end{gathered}$$

Hence, the next number in the given series is 420.

When at least 2 women are included.

The committee may consist of 3 women, 2 men : It can be done in  4C3*6C2  ways

or, 4 women, 1 man : It can be done in  4C4*6C1ways

or, 2 women, 3 men : It can be done in 4C2*6C3 ways.

Total number of ways of forming the committees

= 4C2*6C3+4C3*6C2+4C4*6C1

= 6 x 20 + 4 x 15 + 1x 6

= 120 + 60 + 6 =186

Ratio of times taken by A and B = 1 : 2.

The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/60

(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

In this type of problems the formulae is 5x-30×1211
x is replaced by the first interval of given time Here i.e 8
5*8-30*1211
= 12011min

Therefore the hands will be in the same straight line but not
together at 12011 min.past 8.

Let the quantity of alcohol and water be 4x litres and 3x litres respectively

4x/(3x+5) = 4/5 

20x = 4(3x+5)

8x = 20

x = 2.5

Quantity of alcohol = (4 x 2.5) litres = 10 litres.